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Algorithms
Volume 10
Issue 3
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Algorithms, Volume 10, Issue 3 (September 2017) – 37 articles

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619 KiB  
Article
Type-1 Fuzzy Sets and Intuitionistic Fuzzy Sets
by Krassimir T. Atanassov
Algorithms 2017, 10(3), 106; https://doi.org/10.3390/a10030106 - 13 Sep 2017
Cited by 36 | Viewed by 7987
Abstract
A comparison between type-1 fuzzy sets (T1FSs) and intuitionistic fuzzy sets (IFSs) is made. The operators defined over IFSs that do not have analogues in T1FSs are shown, and such analogues are introduced whenever possible. Full article
(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)
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Figure 1

Figure 1
<p>First geometrical interpretation—first form.</p> Full article ">Figure 2
<p>First geometrical interpretation—second form.</p> Full article ">Figure 3
<p>V. Atanassova’s geometrical interpretation.</p> Full article ">Figure 4
<p>Second geometrical interpretation.</p> Full article ">Figure 5
<p>Third geometrical interpretation.</p> Full article ">Figure 6
<p>Fourth geometrical interpretation, where <math display="inline"> <semantics> <mrow> <mi>α</mi> <mo>=</mo> <mi>π</mi> <msub> <mi>μ</mi> <mi>A</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <mi>β</mi> <mo>=</mo> <mi>π</mi> <msub> <mi>ν</mi> <mi>A</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> and here <math display="inline"> <semantics> <mrow> <mi>π</mi> <mo>=</mo> <mn>3</mn> <mo>.</mo> <mn>14</mn> <mo>⋯</mo> </mrow> </semantics> </math>.</p> Full article ">Figure 7
<p>S. Danchev’s geometrical interpretation.</p> Full article ">Figure 8
<p>Szmidt and Kacprzyk’s geometrical interpretation.</p> Full article ">Figure 9
<p>Fifth geometrical interpretation.</p> Full article ">Figure 10
<p>Central point in the fifth geometrical interpretation.</p> Full article ">Figure 11
<p>Geometrical interpretation of a T1FS element.</p> Full article ">
6074 KiB  
Article
Performance Analysis of Four Decomposition-Ensemble Models for One-Day-Ahead Agricultural Commodity Futures Price Forecasting
by Deyun Wang, Chenqiang Yue, Shuai Wei and Jun Lv
Algorithms 2017, 10(3), 108; https://doi.org/10.3390/a10030108 - 12 Sep 2017
Cited by 35 | Viewed by 7559
Abstract
Agricultural commodity futures prices play a significant role in the change tendency of these spot prices and the supply–demand relationship of global agricultural product markets. Due to the nonlinear and nonstationary nature of this kind of time series data, it is inevitable for [...] Read more.
Agricultural commodity futures prices play a significant role in the change tendency of these spot prices and the supply–demand relationship of global agricultural product markets. Due to the nonlinear and nonstationary nature of this kind of time series data, it is inevitable for price forecasting research to take this nature into consideration. Therefore, we aim to enrich the existing research literature and offer a new way of thinking about forecasting agricultural commodity futures prices, so that four hybrid models are proposed based on the back propagation neural network (BPNN) optimized by the particle swarm optimization (PSO) algorithm and four decomposition methods: empirical mode decomposition (EMD), wavelet packet transform (WPT), intrinsic time-scale decomposition (ITD) and variational mode decomposition (VMD). In order to verify the applicability and validity of these hybrid models, we select three futures prices of wheat, corn and soybean to conduct the experiment. The experimental results show that (1) all the hybrid models combined with decomposition technique have a better performance than the single PSO–BPNN model; (2) VMD contributes the most in improving the forecasting ability of the PSO–BPNN model, while WPT ranks second; (3) ITD performs better than EMD in both cases of corn and soybean; and (4) the proposed models perform well in the forecasting of agricultural commodity futures prices. Full article
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<p>Comparison between three-level wavelet transform (WT) and three-level wavelet packet transform (WPT).</p> Full article ">Figure 2
<p>Basic structure of a standard three-layer back propagation neural network (BPNN).</p> Full article ">Figure 3
<p>Basic structure of the proposed hybrid model.</p> Full article ">Figure 4
<p>Futures prices series of corn, soybean and wheat.</p> Full article ">Figure 5
<p>The process of the four decomposition methods.</p> Full article ">Figure 6
<p>Training and forecasting results of the PSO–BPNN model (Wheat).</p> Full article ">Figure 7
<p>Decomposition results of the empirical mode decomposition (EMD) method (wheat).</p> Full article ">Figure 8
<p>Decomposition results of the WPT method (wheat).</p> Full article ">Figure 9
<p>Decomposition results of the intrinsic time-scale decomposition (ITD) method (wheat).</p> Full article ">Figure 10
<p>Decomposition results of the variational mode decomposition (VMD) method (wheat).</p> Full article ">Figure 11
<p>One-day-ahead forecasting results of different models of wheat.</p> Full article ">Figure 12
<p>Error graphics of different models of wheat.</p> Full article ">Figure 13
<p>Decomposition results of the EMD method (corn).</p> Full article ">Figure 14
<p>Decomposition results of the WPT method (corn).</p> Full article ">Figure 15
<p>Decomposition results of the ITD method (corn).</p> Full article ">Figure 16
<p>Decomposition results of the VMD method (corn).</p> Full article ">Figure 17
<p>One-day-ahead forecasting results of different models of corn.</p> Full article ">Figure 18
<p>Error graphics of different models of corn.</p> Full article ">Figure 19
<p>Decomposition results of the EMD method (soybean).</p> Full article ">Figure 20
<p>Decomposition results of the WPT method (soybean).</p> Full article ">Figure 21
<p>Decomposition results of the ITD method (soybean).</p> Full article ">Figure 22
<p>Decomposition results of the VMD method (soybean).</p> Full article ">Figure 23
<p>One-day-ahead forecasting results of different models of soybean.</p> Full article ">Figure 24
<p>Error graphics of different models of soybean.</p> Full article ">
1517 KiB  
Article
A Monarch Butterfly Optimization for the Dynamic Vehicle Routing Problem
by Shifeng Chen, Rong Chen and Jian Gao
Algorithms 2017, 10(3), 107; https://doi.org/10.3390/a10030107 - 12 Sep 2017
Cited by 42 | Viewed by 8395
Abstract
The dynamic vehicle routing problem (DVRP) is a variant of the Vehicle Routing Problem (VRP) in which customers appear dynamically. The objective is to determine a set of routes that minimizes the total travel distance. In this paper, we propose a monarch butterfly [...] Read more.
The dynamic vehicle routing problem (DVRP) is a variant of the Vehicle Routing Problem (VRP) in which customers appear dynamically. The objective is to determine a set of routes that minimizes the total travel distance. In this paper, we propose a monarch butterfly optimization (MBO) algorithm to solve DVRPs, utilizing a greedy strategy. Both migration operation and the butterfly adjusting operator only accept the offspring of butterfly individuals that have better fitness than their parents. To improve performance, a later perturbation procedure is implemented, to maintain a balance between global diversification and local intensification. The computational results indicate that the proposed technique outperforms the existing approaches in the literature for average performance by at least 9.38%. In addition, 12 new best solutions were found. This shows that this proposed technique consistently produces high-quality solutions and outperforms other published heuristics for the DVRP. Full article
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<p>An illustration of a typical dynamic vehicle routing problem.</p> Full article ">Figure 2
<p>Butterfly representation and solution decoding.</p> Full article ">Figure 3
<p>Illustration of operators in the later perturbation.</p> Full article ">Figure 4
<p>Deviation from the known optimal solution.</p> Full article ">Figure 5
<p>dispersion diagrams.</p> Full article ">
516 KiB  
Article
Comparison of Internal Clustering Validation Indices for Prototype-Based Clustering
by Joonas Hämäläinen, Susanne Jauhiainen and Tommi Kärkkäinen
Algorithms 2017, 10(3), 105; https://doi.org/10.3390/a10030105 - 6 Sep 2017
Cited by 82 | Viewed by 9826
Abstract
Clustering is an unsupervised machine learning and pattern recognition method. In general, in addition to revealing hidden groups of similar observations and clusters, their number needs to be determined. Internal clustering validation indices estimate this number without any external information. The purpose of [...] Read more.
Clustering is an unsupervised machine learning and pattern recognition method. In general, in addition to revealing hidden groups of similar observations and clusters, their number needs to be determined. Internal clustering validation indices estimate this number without any external information. The purpose of this article is to evaluate, empirically, characteristics of a representative set of internal clustering validation indices with many datasets. The prototype-based clustering framework includes multiple, classical and robust, statistical estimates of cluster location so that the overall setting of the paper is novel. General observations on the quality of validation indices and on the behavior of different variants of clustering algorithms will be given. Full article
(This article belongs to the Special Issue Clustering Algorithms 2017)
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<p>Scatter plots of <span class="html-italic">Sim5</span> datasets.</p> Full article ">Figure 2
<p>Median of the number of iterations needed for convergence with varying <span class="html-italic">K</span>.</p> Full article ">Figure 2 Cont.
<p>Median of the number of iterations needed for convergence with varying <span class="html-italic">K</span>.</p> Full article ">
1087 KiB  
Article
Contract-Based Incentive Mechanism for Mobile Crowdsourcing Networks
by Nan Zhao, Menglin Fan, Chao Tian and Pengfei Fan
Algorithms 2017, 10(3), 104; https://doi.org/10.3390/a10030104 - 4 Sep 2017
Cited by 6 | Viewed by 5627
Abstract
Mobile crowdsourcing networks (MCNs) are a promising method of data collecting and processing by leveraging the mobile devices’ sensing and computing capabilities. However, because of the selfish characteristics of the service provider (SP) and mobile users (MUs), crowdsourcing participants only aim to maximize [...] Read more.
Mobile crowdsourcing networks (MCNs) are a promising method of data collecting and processing by leveraging the mobile devices’ sensing and computing capabilities. However, because of the selfish characteristics of the service provider (SP) and mobile users (MUs), crowdsourcing participants only aim to maximize their own benefits. This paper investigates the incentive mechanism between the above two parties to create mutual benefits. By modeling MCNs as a labor market, a contract-based crowdsourcing model with moral hazard is proposed under the asymmetric information scenario. In order to incentivize the potential MUs to participate in crowdsourcing tasks, the optimization problem is formulated to maximize the SP’s utility by jointly examining the crowdsourcing participants’ risk preferences. The impact of crowdsourcing participants’ attitudes of risks on the incentive mechanism has been studied analytically and experimentally. Numerical simulation results demonstrate the effectiveness of the proposed contract design scheme for the crowdsourcing incentive. Full article
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<p>Mobile crowdsourcing network (MCN).</p> Full article ">Figure 2
<p>Contract-based incentive mechanism for mobile crowdsourcing.</p> Full article ">Figure 3
<p>Mobile users’ (MUs’) optimal contract design with various <math display="inline"> <semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics> </math> for fixed <math display="inline"> <semantics> <mrow> <msub> <mi>η</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>3</mn> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi>η</mi> <mi>S</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>3</mn> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi>c</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>4</mn> </mrow> </semantics> </math>, and <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi>U</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>2</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 4
<p>Mobile users’ (MUs’) optimal utility with different types of effort-incentive design.</p> Full article ">Figure 5
<p>Mobile users’ (MUs’) optimal contract design with the crowdsourcing cost coefficient <math display="inline"> <semantics> <msub> <mi>c</mi> <mi>i</mi> </msub> </semantics> </math> for fixed <math display="inline"> <semantics> <mrow> <msub> <mi>η</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>3</mn> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi>η</mi> <mi>S</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>3</mn> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>2</mn> </mrow> </semantics> </math>, and <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi>U</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 6
<p>Mobile users’ (MUs’) optimal bonus coefficient <math display="inline"> <semantics> <msup> <mi>β</mi> <mo>*</mo> </msup> </semantics> </math> for fixed <math display="inline"> <semantics> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi>U</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 7
<p>Service provider’s (SP’s) optimal expected utility for fixed <math display="inline"> <semantics> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi>U</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 8
<p>Comparison between the service provider’s (SP’s) optimal expected utility with the various incentive mechanisms for fixed <math display="inline"> <semantics> <mrow> <msub> <mi>η</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>3</mn> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi>c</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>1</mn> </mrow> </semantics> </math>, and <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi>U</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math>.</p> Full article ">
5998 KiB  
Article
An Enhanced Dynamic Spectrum Allocation Algorithm Based on Cournot Game in Maritime Cognitive Radio Communication System
by Jingbo Zhang, Henan Yu and Shufang Zhang
Algorithms 2017, 10(3), 103; https://doi.org/10.3390/a10030103 - 3 Sep 2017
Cited by 2 | Viewed by 6011
Abstract
The recent development of maritime transport has resulted in the demand for a wider communication bandwidth being more intense. Cognitive radios can dynamically manage resources in a spectrum. Thus, building a new type of maritime cognitive radio communication system (MCRCS) is an effective [...] Read more.
The recent development of maritime transport has resulted in the demand for a wider communication bandwidth being more intense. Cognitive radios can dynamically manage resources in a spectrum. Thus, building a new type of maritime cognitive radio communication system (MCRCS) is an effective solution. In this paper, the enhanced dynamic spectrum allocation algorithm (EDSAA) is proposed, which is based on the Cournot game model. In EDSAA, the decision-making center (DC) sets the weights according to the detection capability of the secondary user (SU), before adding these weighting coefficients in the price function. Furthermore, the willingness of the SU will reduce after meeting their basic communication needs when it continues to increase the leasable spectrum by adding the elastic model in the SU’s revenue function. On this basis, the profit function is established. The simulation results show that the EDSAA has Nash equilibrium and conforms to the actual situation. It shows that the results of spectrum allocation are fair, efficient and reasonable. Full article
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<p>System Components.</p> Full article ">Figure 2
<p>Enhanced dynamic spectrum allocation algorithm (EDSAA) model.</p> Full article ">Figure 3
<p>Best spectrum allocation curve and Nash equilibrium point under the static game.</p> Full article ">Figure 4
<p>The influence of learning factors on game stability.</p> Full article ">Figure 5
<p>Iteration curve of the dynamic game of secondary user (SU).</p> Full article ">Figure 6
<p><math display="inline"> <semantics> <mrow> <mi>S</mi> <msub> <mi>U</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mi>S</mi> <msub> <mi>U</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> price function with different detection capabilities and different evaluation criteria.</p> Full article ">
840 KiB  
Article
Local Community Detection in Dynamic Graphs Using Personalized Centrality
by Eisha Nathan, Anita Zakrzewska, Jason Riedy and David A. Bader
Algorithms 2017, 10(3), 102; https://doi.org/10.3390/a10030102 - 29 Aug 2017
Cited by 9 | Viewed by 7859
Abstract
Analyzing massive graphs poses challenges due to the vast amount of data available. Extracting smaller relevant subgraphs allows for further visualization and analysis that would otherwise be too computationally intensive. Furthermore, many real data sets are constantly changing, and require algorithms to update [...] Read more.
Analyzing massive graphs poses challenges due to the vast amount of data available. Extracting smaller relevant subgraphs allows for further visualization and analysis that would otherwise be too computationally intensive. Furthermore, many real data sets are constantly changing, and require algorithms to update as the graph evolves. This work addresses the topic of local community detection, or seed set expansion, using personalized centrality measures, specifically PageRank and Katz centrality. We present a method to efficiently update local communities in dynamic graphs. By updating the personalized ranking vectors, we can incrementally update the corresponding local community. Applying our methods to real-world graphs, we are able to obtain speedups of up to 60× compared to static recomputation while maintaining an average recall of 0.94 of the highly ranked vertices returned. Next, we investigate how approximations of a centrality vector affect the resulting local community. Specifically, our method guarantees that the vertices returned in the community are the highly ranked vertices from a personalized centrality metric. Full article
(This article belongs to the Special Issue Algorithms for Community Detection in Complex Networks)
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<p>The speedup of the personalized Katz centrality method compared to greedy expansion is shown for SBM graphs with different parameters. (<b>a</b>) The number of vertices <span class="html-italic">n</span> in the graph varies, with <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics> </math>. (<b>b</b>) The number of communities <span class="html-italic">k</span> in the graph varies, with <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>47104</mn> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics> </math>. (<b>c</b>) The average vertex degree <span class="html-italic">d</span> varies, with <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>1000</mn> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 1 Cont.
<p>The speedup of the personalized Katz centrality method compared to greedy expansion is shown for SBM graphs with different parameters. (<b>a</b>) The number of vertices <span class="html-italic">n</span> in the graph varies, with <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics> </math>. (<b>b</b>) The number of communities <span class="html-italic">k</span> in the graph varies, with <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>47104</mn> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics> </math>. (<b>c</b>) The average vertex degree <span class="html-italic">d</span> varies, with <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>1000</mn> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 2
<p>Synthetic dynamic graph showing merging and splitting of communities. (<b>a</b>) <math display="inline"> <semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math>, (<b>b</b>) <math display="inline"> <semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics> </math>, (<b>c</b>) <math display="inline"> <semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics> </math>, (<b>d</b>) <math display="inline"> <semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 3
<p>Performance and quality behavior of dynamic algorithm compared to static recomputation over time. (<b>a</b>) speedup in iterations over time for <span class="html-italic">b</span> = 10, (<b>b</b>) ratio of conductance scores over time for <span class="html-italic">b</span> = 100.</p> Full article ">Figure 4
<p>Katz precision vs. iteration count. (<b>a</b>) <span class="html-italic">R</span> = 100, (<b>b</b>) <span class="html-italic">R</span> = 1000.</p> Full article ">Figure 5
<p>Speedup in iterations.</p> Full article ">
4449 KiB  
Article
Comparative Study of Type-2 Fuzzy Particle Swarm, Bee Colony and Bat Algorithms in Optimization of Fuzzy Controllers
by Frumen Olivas, Leticia Amador-Angulo, Jonathan Perez, Camilo Caraveo, Fevrier Valdez and Oscar Castillo
Algorithms 2017, 10(3), 101; https://doi.org/10.3390/a10030101 - 28 Aug 2017
Cited by 60 | Viewed by 7102
Abstract
In this paper, a comparison among Particle swarm optimization (PSO), Bee Colony Optimization (BCO) and the Bat Algorithm (BA) is presented. In addition, a modification to the main parameters of each algorithm through an interval type-2 fuzzy logic system is presented. The main [...] Read more.
In this paper, a comparison among Particle swarm optimization (PSO), Bee Colony Optimization (BCO) and the Bat Algorithm (BA) is presented. In addition, a modification to the main parameters of each algorithm through an interval type-2 fuzzy logic system is presented. The main aim of using interval type-2 fuzzy systems is providing dynamic parameter adaptation to the algorithms. These algorithms (original and modified versions) are compared with the design of fuzzy systems used for controlling the trajectory of an autonomous mobile robot. Simulation results reveal that PSO algorithm outperforms the results of the BCO and BA algorithms. Full article
(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)
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<p>Type-1 fuzzy system for dynamic parameter adaptation in BCO (Bee Colony Optimization).</p> Full article ">Figure 2
<p>Interval type-2 fuzzy system for dynamic parameter adaptation in BCO.</p> Full article ">Figure 3
<p>Type-1 fuzzy system for dynamic parameter adaptation in PSO (Particle Swarm Optimization).</p> Full article ">Figure 4
<p>Interval type-2 fuzzy system for dynamic parameter adaptation in PSO.</p> Full article ">Figure 5
<p>Type-1 Fuzzy System.</p> Full article ">Figure 6
<p>Interval Type-2 Fuzzy System.</p> Full article ">Figure 7
<p>Scheme of the autonomous mobile robot.</p> Full article ">Figure 8
<p>Complex plant for an autonomous mobile robot.</p> Full article ">Figure 9
<p>Fuzzy system for control.</p> Full article ">Figure 10
<p>Reference trajectory for the autonomous mobile robot.</p> Full article ">Figure 11
<p>Complex plant for an autonomous mobile robot with noise.</p> Full article ">Figure 12
<p>Reference trajectory with noise for the autonomous mobile robot.</p> Full article ">Figure 13
<p>Optimization problem (points of the membership functions).</p> Full article ">Figure 14
<p>Best simulation of BA algorithm.</p> Full article ">Figure 15
<p>Best simulation of BCO algorithm.</p> Full article ">Figure 16
<p>Best simulation of the PSO algorithm.</p> Full article ">
4758 KiB  
Article
Hybrid Learning for General Type-2 TSK Fuzzy Logic Systems
by Mauricio A. Sanchez, Juan R. Castro, Violeta Ocegueda-Miramontes and Leticia Cervantes
Algorithms 2017, 10(3), 99; https://doi.org/10.3390/a10030099 - 25 Aug 2017
Cited by 18 | Viewed by 5982
Abstract
This work is focused on creating fuzzy granular classification models based on general type-2 fuzzy logic systems when consequents are represented by interval type-2 TSK linear functions. Due to the complexity of general type-2 TSK fuzzy logic systems, a hybrid learning approach is [...] Read more.
This work is focused on creating fuzzy granular classification models based on general type-2 fuzzy logic systems when consequents are represented by interval type-2 TSK linear functions. Due to the complexity of general type-2 TSK fuzzy logic systems, a hybrid learning approach is proposed, where the principle of justifiable granularity is heuristically used to define an amount of uncertainty in the system, which in turn is used to define the parameters in the interval type-2 TSK linear functions via a dual LSE algorithm. Multiple classification benchmark datasets were tested in order to assess the quality of the formed granular models; its performance is also compared against other common classification algorithms. Shown results conclude that classification performance in general is better than results obtained by other techniques, and in general, all achieved results, when averaged, have a better performance rate than compared techniques, demonstrating the stability of the proposed hybrid learning technique. Full article
(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)
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<p>Generic general type-2 fuzzy set (GT2 FS) as shown from the primary function’s perspective.</p> Full article ">Figure 2
<p>Generic GT2 FS as shown from an isometric view.</p> Full article ">Figure 3
<p>Support of the primary membership function of the used GT2 FS.</p> Full article ">Figure 4
<p>Visual representation of both contradicting objectives in data coverage, where (<b>a</b>) complete experimental data coverage is obtained; and (<b>b</b>) a limited coverage of experimental data is obtained.</p> Full article ">Figure 5
<p>Intervals <span class="html-italic">a</span> and <span class="html-italic">b</span> are optimized from available experimental data for the formation of said information granule, where both lengths start at the median of the information granule’s experimental data.</p> Full article ">Figure 6
<p>General schematic of the sequence taken by the proposed hybrid algorithm, such that antecedents are calculated first, and consequents afterwards.</p> Full article ">Figure 7
<p>Input partition of the GT2 TSK fuzzy logic system (FLS) for the first input of the iris dataset, where (<b>a</b>) shows a top view of the GT2 membership functions; and (<b>b</b>) shows an orthogonal view of the same GT2 membership functions.</p> Full article ">Figure 8
<p>Input partition of the GT2 TSK FLS for the second input of the iris dataset, where (<b>a</b>) shows a top view of the GT2 membership functions; and (<b>b</b>) shows an orthogonal view of the same GT2 membership functions.</p> Full article ">Figure 9
<p>Input partition of the GT2 TSK FLS for the third input of the iris dataset, where (<b>a</b>) shows a top view of the GT2 membership functions; and (<b>b</b>) shows an orthogonal view of the same GT2 membership functions.</p> Full article ">Figure 10
<p>Input partition of the GT2 TSK FLS for the fourth input of the iris dataset, where (<b>a</b>) shows a top view of the GT2 membership functions; and (<b>b</b>) shows an orthogonal view of the same GT2 membership functions.</p> Full article ">
463 KiB  
Article
Biogeography-Based Optimization of the Portfolio Optimization Problem with Second Order Stochastic Dominance Constraints
by Tao Ye, Ziqiang Yang and Siling Feng
Algorithms 2017, 10(3), 100; https://doi.org/10.3390/a10030100 - 25 Aug 2017
Cited by 9 | Viewed by 5352
Abstract
The portfolio optimization problem is the central problem of modern economics and decision theory; there is the Mean-Variance Model and Stochastic Dominance Model for solving this problem. In this paper, based on the second order stochastic dominance constraints, we propose the improved biogeography-based [...] Read more.
The portfolio optimization problem is the central problem of modern economics and decision theory; there is the Mean-Variance Model and Stochastic Dominance Model for solving this problem. In this paper, based on the second order stochastic dominance constraints, we propose the improved biogeography-based optimization algorithm to optimize the portfolio, which we called ε BBO. In order to test the computing power of ε BBO, we carry out two numerical experiments in several kinds of constraints. In experiment 1, comparing the Stochastic Approximation (SA) method with the Level Function (LF) algorithm and Genetic Algorithm (GA), we get a similar optimal solution by ε BBO in [ 0 , 0 . 6 ] and [ 0 , 1 ] constraints with the return of 1.174% and 1.178%. In [ - 1 , 2 ] constraint, we get the optimal return of 1.3043% by ε BBO, while the return of SA and LF is 1.23% and 1.26%. In experiment 2, we get the optimal return of 0.1325% and 0.3197% by ε BBO in [ 0 , 0 . 1 ] and [ - 0 . 05 , 0 . 15 ] constraints. As a comparison, the return of FTSE100 Index portfolio is 0.0937%. The results prove that ε BBO algorithm has great potential in the field of financial decision-making, it also shows that ε BBO algorithm has a better performance in optimization problem. Full article
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<p>The procedure chat of the <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math>BBO algorithm.</p> Full article ">Figure 2
<p>The performance of the <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math>BBO and the optimal portfolio in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>0.6</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD28-algorithms-10-00100" class="html-disp-formula">28</a>).</p> Full article ">Figure 3
<p>The performance of the <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math>BBO and the optimal portfolio in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD28-algorithms-10-00100" class="html-disp-formula">28</a>).</p> Full article ">Figure 4
<p>The performance of the <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math>BBO and the optimal portfolio in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD28-algorithms-10-00100" class="html-disp-formula">28</a>).</p> Full article ">Figure 5
<p>The performance of the <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math>BBO and the optimal portfolio in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>0.6</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD29-algorithms-10-00100" class="html-disp-formula">29</a>).</p> Full article ">Figure 6
<p>The performance of the <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math>BBO and the optimal portfolio in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD29-algorithms-10-00100" class="html-disp-formula">29</a>).</p> Full article ">Figure 7
<p>The performance of the <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math>BBO and the optimal portfolio in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD29-algorithms-10-00100" class="html-disp-formula">29</a>).</p> Full article ">Figure 8
<p>The specific asset structure of optimal portfolio in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>0.1</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD30-algorithms-10-00100" class="html-disp-formula">30</a>) for 101 assets.</p> Full article ">Figure 9
<p>The specific asset structure of optimal portfolio in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mo>−</mo> <mn>0.05</mn> <mo>,</mo> <mn>0.15</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD30-algorithms-10-00100" class="html-disp-formula">30</a>) for 101 assets.</p> Full article ">Figure 10
<p>The return of optimal portfolio in different iterations in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>0.1</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD30-algorithms-10-00100" class="html-disp-formula">30</a>).</p> Full article ">Figure 11
<p>The return of optimal portfolio by <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math>BBO in each period with benchmark portfolio and the FTSE100 Index portfolio in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>0.1</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD30-algorithms-10-00100" class="html-disp-formula">30</a>).</p> Full article ">Figure 12
<p>The return of optimal portfolio in different iterations in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mo>−</mo> <mn>0.05</mn> <mo>,</mo> <mn>0.15</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD30-algorithms-10-00100" class="html-disp-formula">30</a>).</p> Full article ">Figure 13
<p>The return of optimal portfolio by <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math>BBO in each period with benchmark portfolio and the FTSE100 Index portfolio in <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>∈</mo> <mo>[</mo> <mo>−</mo> <mn>0.05</mn> <mo>,</mo> <mn>0.15</mn> <mo>]</mo> </mrow> </semantics> </math> of model (<a href="#FD30-algorithms-10-00100" class="html-disp-formula">30</a>).</p> Full article ">
1767 KiB  
Article
Adaptive Virtual RSU Scheduling for Scalable Coverage under Bidirectional Vehicle Traffic Flow
by Fei Chen, Xiaohong Bi, Ruimin Lyu, Zhongwei Hua, Yuan Liu and Xiaoting Zhang
Algorithms 2017, 10(3), 98; https://doi.org/10.3390/a10030098 - 24 Aug 2017
Viewed by 5766
Abstract
Over the past decades, vehicular ad hoc networks (VANETs) have been a core networking technology to provide drivers and passengers with safety and convenience. As a new emerging technology, the vehicular cloud computing (VCC) can provide cloud services for various data-intensive applications in [...] Read more.
Over the past decades, vehicular ad hoc networks (VANETs) have been a core networking technology to provide drivers and passengers with safety and convenience. As a new emerging technology, the vehicular cloud computing (VCC) can provide cloud services for various data-intensive applications in VANETs, such as multimedia streaming. However, the vehicle mobility and intermittent connectivity present challenges to the large-scale data dissemination with underlying computing and networking architecture. In this paper, we will explore the service scheduling of virtual RSUs for diverse request demands in the dynamic traffic flow in vehicular cloud environment. Specifically, we formulate the RSU allocation problem as maximum service capacity with multiple-source and multiple-destination, and propose a bidirectional RSU allocation strategy. In addition, we formulate the content replication in distributed RSUs as the minimum replication set coverage problem in a two-layer mapping model, and analyze the solutions in different scenarios. Numerical results further prove the superiority of our proposed solution, as well as the scalability to various traffic condition variations. Full article
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<p>A road segment with a bidirectional road.</p> Full article ">Figure 2
<p>RSU scheduling strategy design.</p> Full article ">Figure 3
<p>RSU allocation in a constructed graph.</p> Full article ">Figure 4
<p>Ladder graph for bidirectional traffic flow.</p> Full article ">Figure 5
<p>Two layer mapping model.</p> Full article ">Figure 6
<p>Adaptive greedy replication.</p> Full article ">Figure 7
<p>Distributed online replication.</p> Full article ">Figure 8
<p>Skewness with different parameter <span class="html-italic">s</span>.</p> Full article ">Figure 9
<p>Connectivity under different allocation strategies. (<b>a</b>) number of RSUs <math display="inline"> <semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics> </math>; (<b>b</b>) number of RSUs <math display="inline"> <semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics> </math>; (<b>c</b>) number of RSUs <math display="inline"> <semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>40</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 10
<p>Connectivity with vehicle density variation.</p> Full article ">Figure 11
<p>Performance comparison with different skewness.</p> Full article ">Figure 12
<p>Cumulative distribution functions with different RSUs.</p> Full article ">
906 KiB  
Article
A Simplified Matrix Formulation for Sensitivity Analysis of Hidden Markov Models
by Seifemichael B. Amsalu,  Abdollah Homaifar and Albert C. Esterline
Algorithms 2017, 10(3), 97; https://doi.org/10.3390/a10030097 - 22 Aug 2017
Cited by 3 | Viewed by 7268
Abstract
In this paper, a new algorithm for sensitivity analysis of discrete hidden Markov models (HMMs) is proposed. Sensitivity analysis is a general technique for investigating the robustness of the output of a system model. Sensitivity analysis of probabilistic networks has recently been studied [...] Read more.
In this paper, a new algorithm for sensitivity analysis of discrete hidden Markov models (HMMs) is proposed. Sensitivity analysis is a general technique for investigating the robustness of the output of a system model. Sensitivity analysis of probabilistic networks has recently been studied extensively. This has resulted in the development of mathematical relations between a parameter and an output probability of interest and also methods for establishing the effects of parameter variations on decisions. Sensitivity analysis in HMMs has usually been performed by taking small perturbations in parameter values and re-computing the output probability of interest. As recent studies show, the sensitivity analysis of an HMM can be performed using a functional relationship that describes how an output probability varies as the network’s parameters of interest change. To derive this sensitivity function, existing Bayesian network algorithms have been employed for HMMs. These algorithms are computationally inefficient as the length of the observation sequence and the number of parameters increases. In this study, a simplified efficient matrix-based algorithm for computing the coefficients of the sensitivity function for all hidden states and all time steps is proposed and an example is presented. Full article
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<p>(<b>a</b>) An example of an HMM representation. (<b>b</b>) Its dynamic Bayesian network representation, unrolled for <span class="html-italic">T</span> time slices.</p> Full article ">Figure 2
<p>Sensitivity functions: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mi>p</mi> <mrow> <mo stretchy="false">(</mo> <msup> <mi>X</mi> <mn>2</mn> </msup> <mo>|</mo> <msubsup> <mrow> <mi mathvariant="bold">y</mi> </mrow> <mi mathvariant="bold">e</mi> <mrow> <mn>1</mn> <mo>:</mo> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>θ</mi> <mi>a</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics> </math> for both states of <math display="inline"> <semantics> <msup> <mi>X</mi> <mn>2</mn> </msup> </semantics> </math>. (<b>b</b>) <math display="inline"> <semantics> <mrow> <mi>p</mi> <mrow> <mo stretchy="false">(</mo> <msup> <mi>X</mi> <mn>3</mn> </msup> <mo>|</mo> <msubsup> <mrow> <mi mathvariant="bold">y</mi> </mrow> <mi mathvariant="bold">e</mi> <mrow> <mn>1</mn> <mo>:</mo> <mn>3</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>θ</mi> <mi>a</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics> </math> for both states of <math display="inline"> <semantics> <msup> <mi>X</mi> <mn>3</mn> </msup> </semantics> </math>.</p> Full article ">Figure 3
<p>Time in seconds to compute the sensitivity coefficients for an observation sequence length from 1 to 1000 with a step size of 10.</p> Full article ">
784 KiB  
Article
Double-Threshold Cooperative Spectrum Sensing Algorithm Based on Sevcik Fractal Dimension
by Xueying Diao, Qianhui Dong, Zijian Yang and Yibing Li
Algorithms 2017, 10(3), 96; https://doi.org/10.3390/a10030096 - 21 Aug 2017
Cited by 7 | Viewed by 4992
Abstract
Spectrum sensing is of great importance in the cognitive radio (CR) networks. Compared with individual spectrum sensing, cooperative spectrum sensing (CSS) has been shown to greatly improve the accuracy of the detection. However, the existing CSS algorithms are sensitive to noise uncertainty and [...] Read more.
Spectrum sensing is of great importance in the cognitive radio (CR) networks. Compared with individual spectrum sensing, cooperative spectrum sensing (CSS) has been shown to greatly improve the accuracy of the detection. However, the existing CSS algorithms are sensitive to noise uncertainty and are inaccurate in low signal-to-noise ratio (SNR) detection. To address this, we propose a double-threshold CSS algorithm based on Sevcik fractal dimension (SFD) in this paper. The main idea of the presented scheme is to sense the presence of primary users in the local spectrum sensing by analyzing different characteristics of the SFD between signals and noise. Considering the stochastic fluctuation characteristic of the noise SFD in a certain range, we adopt the double-threshold method in the multi-cognitive user CSS so as to improve the detection accuracy, where thresholds are set according to the maximum and minimum values of the noise SFD. After obtaining the detection results, the cognitive user sends local detection results to the fusion center for reliability fusion. Simulation results demonstrate that the proposed method is insensitive to noise uncertainty. Simulations also show that the algorithm presented in this paper can achieve high detection performance at the low SNR region. Full article
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<p>Sevcik fractal dimension of different kinds of signals. ASK: amplitude shift keying; FSK: frequency shift keying; QPSK: quadrature phase shift keying; WGN: white Gaussian noise.</p> Full article ">Figure 2
<p>The relationship between noise power and the noise Sevcik fractal dimension.</p> Full article ">Figure 3
<p>The block diagram of spectrum sensing system based on Sevcik fractal dimension (SFD) in the frequency domain. DFT: discrete Fourier transform.</p> Full article ">Figure 4
<p>Double-threshold decision.</p> Full article ">Figure 5
<p>Detection probability comparison of the proposed method with the other three methods. SNR: signal-to-noise ratio.</p> Full article ">Figure 6
<p>Detection probability comparison of different numbers of secondary users (SUs).</p> Full article ">Figure 7
<p>Detection performance comparison of the proposed algorithm with the single threshold detection.</p> Full article ">Figure 8
<p>The influence of noise uncertainty on detection probability.</p> Full article ">
247 KiB  
Article
A Parallel Two-Stage Iteration Method for Solving Continuous Sylvester Equations
by Manyu Xiao, Quanyi Lv, Zhuo Xing and Yingchun Zhang
Algorithms 2017, 10(3), 95; https://doi.org/10.3390/a10030095 - 21 Aug 2017
Cited by 1 | Viewed by 4231
Abstract
In this paper we propose a parallel two-stage iteration algorithm for solving large-scale continuous Sylvester equations. By splitting the coefficient matrices, the original linear system is transformed into a symmetric linear system which is then solved by using the SYMMLQ algorithm. In order [...] Read more.
In this paper we propose a parallel two-stage iteration algorithm for solving large-scale continuous Sylvester equations. By splitting the coefficient matrices, the original linear system is transformed into a symmetric linear system which is then solved by using the SYMMLQ algorithm. In order to improve the relative parallel efficiency, an adjusting strategy is explored during the iteration calculation of the SYMMLQ algorithm to decrease the degree of the reduce-operator from two to one communications at each step. Moreover, the convergence of the iteration scheme is discussed, and finally numerical results are reported showing that the proposed method is an efficient and robust algorithm for this class of continuous Sylvester equations on a parallel machine. Full article
3034 KiB  
Article
NBTI and Power Reduction Using an Input Vector Control and Supply Voltage Assignment Method
by Peng Sun, Zhiming Yang, Yang Yu, Junbao Li and Xiyuan Peng
Algorithms 2017, 10(3), 94; https://doi.org/10.3390/a10030094 - 19 Aug 2017
Cited by 6 | Viewed by 5861
Abstract
As technology scales, negative bias temperature instability (NBTI) becomes one of the primary failure mechanisms for Very Large Scale Integration (VLSI) circuits. Meanwhile, the leakage power increases dramatically as the supply/threshold voltage continues to scale down. These two issues pose severe reliability problems [...] Read more.
As technology scales, negative bias temperature instability (NBTI) becomes one of the primary failure mechanisms for Very Large Scale Integration (VLSI) circuits. Meanwhile, the leakage power increases dramatically as the supply/threshold voltage continues to scale down. These two issues pose severe reliability problems for complementary metal oxide semiconductor (CMOS) devices. Because both the NBTI and leakage are dependent on the input vector of the circuit, we present an input vector control (IVC) method based on a linear programming algorithm, which can co-optimize circuit aging and power dissipation simultaneously. In addition, our proposed IVC method is combined with the supply voltage assignment technique to further reduce delay degradation and leakage power. Experimental results on various circuits show the effectiveness of the proposed combination method. Full article
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<p>The flow of the proposed input vector control (IVC) and supply voltage assignment (SVA) combination method. NBTI, negative bias temperature instability.</p> Full article ">Figure 2
<p>The input vector combination and corresponding delay increase for an NAND gate.</p> Full article ">Figure 3
<p>The basic principle of supply voltage assignment.</p> Full article ">Figure 4
<p>Leakage power change of an NAND gate under different supply voltage.</p> Full article ">Figure 5
<p>Threshold voltage change for a positive-channel Metal Oxide Semiconductor (pMOS) transistor with different <span class="html-italic">V<sub>gs</sub></span>.</p> Full article ">Figure 6
<p>Degradation and leakage minimization result by different ILP formulations. (<b>a</b>) c880 circuit; (<b>b</b>) c3540 circuit.</p> Full article ">Figure 7
<p>Leakage power dissipation of SVA with different input vectors for c432 and c7552 circuits. c432 circuit; (<b>b</b>) c7552 circuit.</p> Full article ">Figure 8
<p>Leakage and dynamic power of SVA for the c880 and c3540 circuits when using the input vector obtained by the co-optimization method in Ref. [<a href="#B27-algorithms-10-00094" class="html-bibr">27</a>] under different power constrain settings. (<b>a</b>) c880 circuit; (<b>b</b>) c3540 circuit.</p> Full article ">Figure 9
<p>Leakage and dynamic power of SVA for c880 and c3540 circuits when using the input vector obtained by MC simulation and our proposed IVC #3 method. (<b>a</b>) c880 circuit; (<b>b</b>) c3540 circuit.</p> Full article ">
6529 KiB  
Article
Post-Processing Partitions to Identify Domains of Modularity Optimization
by William H. Weir, Scott Emmons, Ryan Gibson, Dane Taylor and Peter J. Mucha
Algorithms 2017, 10(3), 93; https://doi.org/10.3390/a10030093 - 19 Aug 2017
Cited by 35 | Viewed by 8741
Abstract
We introduce the Convex Hull of Admissible Modularity Partitions (CHAMP) algorithm to prune and prioritize different network community structures identified across multiple runs of possibly various computational heuristics. Given a set of partitions, CHAMP identifies the domain of modularity optimization for each partition—i.e., [...] Read more.
We introduce the Convex Hull of Admissible Modularity Partitions (CHAMP) algorithm to prune and prioritize different network community structures identified across multiple runs of possibly various computational heuristics. Given a set of partitions, CHAMP identifies the domain of modularity optimization for each partition—i.e., the parameter-space domain where it has the largest modularity relative to the input set—discarding partitions with empty domains to obtain the subset of partitions that are “admissible” candidate community structures that remain potentially optimal over indicated parameter domains. Importantly, CHAMP can be used for multi-dimensional parameter spaces, such as those for multilayer networks where one includes a resolution parameter and interlayer coupling. Using the results from CHAMP, a user can more appropriately select robust community structures by observing the sizes of domains of optimization and the pairwise comparisons between partitions in the admissible subset. We demonstrate the utility of CHAMP with several example networks. In these examples, CHAMP focuses attention onto pruned subsets of admissible partitions that are 20-to-1785 times smaller than the sets of unique partitions obtained by community detection heuristics that were input into CHAMP. Full article
(This article belongs to the Special Issue Algorithms for Community Detection in Complex Networks)
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<p>(<b>A</b>) Modularity <math display="inline"> <semantics> <mrow> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> given by Equation (<a href="#FD1-algorithms-10-00093" class="html-disp-formula">1</a>) versus resolution parameter <math display="inline"> <semantics> <mi>γ</mi> </semantics> </math> for <math display="inline"> <semantics> <mrow> <mn>50</mn> <mo>,</mo> <mn>000</mn> </mrow> </semantics> </math> runs (<math display="inline"> <semantics> <mrow> <mn>10</mn> <mo>%</mo> </mrow> </semantics> </math> of results displayed here) of the Louvain algorithm [<a href="#B42-algorithms-10-00093" class="html-bibr">42</a>,<a href="#B47-algorithms-10-00093" class="html-bibr">47</a>] at different <math display="inline"> <semantics> <mi>γ</mi> </semantics> </math> on the unweighted NCAA Division I-A (2000) college football network [<a href="#B37-algorithms-10-00093" class="html-bibr">37</a>,<a href="#B38-algorithms-10-00093" class="html-bibr">38</a>]. Grey triangles indicate the number of communities that include <math display="inline"> <semantics> <mrow> <mo>≥</mo> <mn>5</mn> </mrow> </semantics> </math> nodes in each run, while the green step function shows the number in the optimal partition in each domain; (<b>B</b>) Graphical depiction of CHAMP algorithm (see <a href="#sec2-algorithms-10-00093" class="html-sec">Section 2</a>). Each line indicates <math display="inline"> <semantics> <mrow> <msub> <mi>Q</mi> <mi>σ</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics> </math> given by Equation (<a href="#FD2-algorithms-10-00093" class="html-disp-formula">2</a>) for a particular partition <math display="inline"> <semantics> <mi>σ</mi> </semantics> </math>. Both panels show the convex hull of these lines as the dashed green piecewise-linear curve, with the transition values represented by downward triangles.</p> Full article ">Figure 2
<p>(<b>A</b>) ForceAtlas2 [<a href="#B52-algorithms-10-00093" class="html-bibr">52</a>] layout, created with [<a href="#B53-algorithms-10-00093" class="html-bibr">53</a>], of the unweighted NCAA Division I-A (2000) college football network. Nodes are colored according to the dominant 12-community partition with the widest <math display="inline"> <semantics> <mi>γ</mi> </semantics> </math>-domain <math display="inline"> <semantics> <mrow> <mi>γ</mi> <mo>∈</mo> <mo>[</mo> <mn>1.45</mn> <mo>,</mo> <mn>3.89</mn> <mo>]</mo> </mrow> </semantics> </math>, with node shapes and border indicating their conference labels; (<b>B</b>) Pairwise adjusted mutual information (N = AMI) between all partitions in the admissible subset identified by CHAMP, arranged by their corresponding <math display="inline"> <semantics> <mi>γ</mi> </semantics> </math>-domains of optimality. Dashed lines indicate the transition values of <math display="inline"> <semantics> <mi>γ</mi> </semantics> </math> identified by CHAMP.</p> Full article ">Figure 3
<p>(<b>A</b>) Modularity <math display="inline"> <semantics> <mrow> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> given by Equation (<a href="#FD1-algorithms-10-00093" class="html-disp-formula">1</a>) v. resolution parameter <math display="inline"> <semantics> <mi>γ</mi> </semantics> </math> for <math display="inline"> <semantics> <mrow> <mn>20</mn> <mo>,</mo> <mn>000</mn> </mrow> </semantics> </math> runs (<math display="inline"> <semantics> <mrow> <mn>25</mn> <mo>%</mo> </mrow> </semantics> </math> of results shown) of Louvain [<a href="#B42-algorithms-10-00093" class="html-bibr">42</a>,<a href="#B47-algorithms-10-00093" class="html-bibr">47</a>] on the Human Protein Reactome network [<a href="#B54-algorithms-10-00093" class="html-bibr">54</a>]. Small, grey triangles indicate the number of communities that include <math display="inline"> <semantics> <mrow> <mo>≥</mo> <mn>5</mn> </mrow> </semantics> </math> nodes in each run, while the dark green step function shows the number in the optimal partition in each domain. The dashed green curve is the piecewise-linear modularity function for the optimal partitions, with the transition values marked by blue triangles; (<b>B</b>) Pairwise AMI between all partitions in the admissible subset identified by CHAMP, arranged by their corresponding <math display="inline"> <semantics> <mi>γ</mi> </semantics> </math>-domains of optimality.</p> Full article ">Figure 4
<p>ForceAtlas2 layout [<a href="#B52-algorithms-10-00093" class="html-bibr">52</a>], created with [<a href="#B53-algorithms-10-00093" class="html-bibr">53</a>], of the Human Reactome Network (edges downsampled to 50,000), colored according to the partitions with the two widest <math display="inline"> <semantics> <mi>γ</mi> </semantics> </math>-domains of optimization identified by CHAMP from <math display="inline"> <semantics> <mrow> <mn>20</mn> <mo>,</mo> <mn>000</mn> </mrow> </semantics> </math> runs of Louvain.</p> Full article ">Figure 5
<p>(<b>A</b>) Modularity <math display="inline"> <semantics> <mrow> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> v. <math display="inline"> <semantics> <mi>γ</mi> </semantics> </math> for <math display="inline"> <semantics> <mrow> <mn>100</mn> <mo>,</mo> <mn>000</mn> </mrow> </semantics> </math> runs (<math display="inline"> <semantics> <mrow> <mn>5</mn> <mo>%</mo> </mrow> </semantics> </math> of results shown) of Louvain [<a href="#B42-algorithms-10-00093" class="html-bibr">42</a>,<a href="#B47-algorithms-10-00093" class="html-bibr">47</a>] on the Caltech Facebook network [<a href="#B31-algorithms-10-00093" class="html-bibr">31</a>]. Orange triangles indicate the number of communities that include <math display="inline"> <semantics> <mrow> <mo>≥</mo> <mn>5</mn> </mrow> </semantics> </math> nodes in each run, while the red step function shows the number in the optimal partition in each domain. The dashed green curve is the piecewise-linear modularity function for the optimal partitions, with the transition values marked by blue triangles. The condensed layout of communities (created with [<a href="#B53-algorithms-10-00093" class="html-bibr">53</a>]) here visualizes the optimal partition found for <math display="inline"> <semantics> <mrow> <mi>γ</mi> <mo>∈</mo> <mo>[</mo> <mn>0.908</mn> <mo>,</mo> <mn>1.09</mn> <mo>]</mo> </mrow> </semantics> </math>, with each pie-chart corresponding to a community, fractionally colored according to the House membership of the nodes in the community. The AMI between this partition and House labels (including the missing label) is 0.513; (<b>B</b>) Pairwise AMI between all partitions in the admissible subset identified by CHAMP, arranged by their corresponding <math display="inline"> <semantics> <mi>γ</mi> </semantics> </math>-domains of optimality.</p> Full article ">Figure 6
<p>(<b>A</b>) Domains of optimization for the pruned set of partitions, colored by the number of communities within each partition. The set of partitions was generated from <math display="inline"> <semantics> <mrow> <mn>240</mn> <mo>,</mo> <mn>000</mn> </mrow> </semantics> </math> runs of GenLouvain [<a href="#B41-algorithms-10-00093" class="html-bibr">41</a>] on a <math display="inline"> <semantics> <mrow> <mn>600</mn> <mo>×</mo> <mn>400</mn> </mrow> </semantics> </math> uniform grid over <math display="inline"> <semantics> <mrow> <mo>[</mo> <mn>0.3</mn> <mo>,</mo> <mn>2</mn> <mo>]</mo> <mo>×</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo>]</mo> </mrow> </semantics> </math> in <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mi>γ</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math>. The largest partitions are labeled “<math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>.</mo> <mi>Y</mi> </mrow> </semantics> </math>” with <span class="html-italic">X</span> the number of communities with ≥ 5 nodes and <span class="html-italic">Y</span> the rank of the domain area (that is, in terms of size) for that given number of communities (e.g., “5.2” is the second-largest domain corresponding to 5-community partitions). The partitions of each labeled domain are visualized in <a href="#app1-algorithms-10-00093" class="html-app">Appendix A</a>; (<b>B</b>) Weighted-average AMI of each partition with its neighboring domains’ partitions, weighted by the length of the borders between neighboring domains.</p> Full article ">Figure 7
<p>Time-varying community structure for the U.S. Senate from 1789 to 2008 according to the (<b>A</b>,<b>B</b>) 5-community and (<b>C</b>,<b>D</b>) 8-community partitions with widest domains of optimality (see labels <math display="inline"> <semantics> <mrow> <mn>5.1</mn> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mn>8.1</mn> </mrow> </semantics> </math> in <a href="#algorithms-10-00093-f006" class="html-fig">Figure 6</a>A); (<b>A</b>,<b>C</b>) The vertical axis indicates individual Senators, sorted by community label and time. The AMI reported here is the average over layers (Congresses) of the AMIs in each layer between the identified communities in that layer and political party labels. (This layer-averaged AMI is shown for all partitions in the convex hull over the originally searched parameter range in <a href="#algorithms-10-00093-f008" class="html-fig">Figure 8</a>.) (<b>B</b>,<b>D</b>) The vertical axis indicates the state of a Senator, sorted according to geographic region, and the horizontal axis represents time (two-year Congresses).</p> Full article ">Figure 8
<p>The domains of optimality for the time-varying U.S. Senate roll-call similarity network (as in <a href="#algorithms-10-00093-f006" class="html-fig">Figure 6</a>), colored by the layer-averaged AMI between the political-party affiliations of Senators and the community labels <math display="inline"> <semantics> <mrow> <mo>{</mo> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>σ</mi> </mrow> </msub> <mo>}</mo> </mrow> </semantics> </math> for that layer.</p> Full article ">Figure 9
<p>Visualizations of partitions labeled in white in <a href="#algorithms-10-00093-f006" class="html-fig">Figure 6</a>A, with Senators grouped according to their state. The listed AMI is the average over layers of the AMI in each layer (Congress) between the communities and political party affiliations for that Congress. Partitions are labeled “<math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>.</mo> <mi>Y</mi> </mrow> </semantics> </math>” with <span class="html-italic">X</span> the number of communities with ≥ 5 nodes and <span class="html-italic">Y</span> the rank of the domain area for that number of communities.</p> Full article ">Figure 10
<p>Visualizations of partitions labeled in white in <a href="#algorithms-10-00093-f006" class="html-fig">Figure 6</a>A, with Senators sorted by their most frequent community label (with the labels sorted by last appearance in time), and within communities by first appearance. The listed AMI is the average over layers of the AMI in each layer (Congress) between the communities and political party affiliations in that Congress.</p> Full article ">
326 KiB  
Letter
Automatic Modulation Recognition Using Compressive Cyclic Features
by Lijin Xie and Qun Wan
Algorithms 2017, 10(3), 92; https://doi.org/10.3390/a10030092 - 18 Aug 2017
Cited by 1 | Viewed by 4081
Abstract
Higher-order cyclic cumulants (CCs) have been widely adopted for automatic modulation recognition (AMR) in cognitive radio. However, the CC-based AMR suffers greatly from the requirement of high-rate sampling. To overcome this limit, we resort to the theory of compressive sensing (CS). By exploiting [...] Read more.
Higher-order cyclic cumulants (CCs) have been widely adopted for automatic modulation recognition (AMR) in cognitive radio. However, the CC-based AMR suffers greatly from the requirement of high-rate sampling. To overcome this limit, we resort to the theory of compressive sensing (CS). By exploiting the sparsity of CCs, recognition features can be extracted from a small amount of compressive measurements via a rough CS reconstruction algorithm. Accordingly, a CS-based AMR scheme is formulated. Simulation results demonstrate the availability and robustness of the proposed approach. Full article
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<p>Performance versus signal-to-noise ratio (SNR) for <math display="inline"> <semantics> <msub> <mo>Ω</mo> <mn>1</mn> </msub> </semantics> </math>.</p> Full article ">Figure 2
<p>Performance versus SNR for <math display="inline"> <semantics> <msub> <mo>Ω</mo> <mn>2</mn> </msub> </semantics> </math>.</p> Full article ">Figure 3
<p>Performance versus SNR for <math display="inline"> <semantics> <msub> <mo>Ω</mo> <mn>1</mn> </msub> </semantics> </math>. AMR: automatic modulation recognition.</p> Full article ">Figure 4
<p>Performance versus SNR for <math display="inline"> <semantics> <msub> <mo>Ω</mo> <mn>2</mn> </msub> </semantics> </math>.</p> Full article ">
889 KiB  
Article
Transformation-Based Fuzzy Rule Interpolation Using Interval Type-2 Fuzzy Sets
by Chengyuan Chen and Qiang Shen
Algorithms 2017, 10(3), 91; https://doi.org/10.3390/a10030091 - 15 Aug 2017
Cited by 8 | Viewed by 5613
Abstract
In support of reasoning with sparse rule bases, fuzzy rule interpolation (FRI) offers a helpful inference mechanism for deriving an approximate conclusion when a given observation has no overlap with any rule in the existing rule base. One of the recent and popular [...] Read more.
In support of reasoning with sparse rule bases, fuzzy rule interpolation (FRI) offers a helpful inference mechanism for deriving an approximate conclusion when a given observation has no overlap with any rule in the existing rule base. One of the recent and popular FRI approaches is the scale and move transformation-based rule interpolation, known as T-FRI in the literature. It supports both interpolation and extrapolation with multiple multi-antecedent rules. However, the difficult problem of defining the precise-valued membership functions required in the representation of fuzzy rules, or of the observations, restricts its applications. Fortunately, this problem can be alleviated through the use of type-2 fuzzy sets, owing to the fact that the membership functions of such fuzzy sets are themselves fuzzy, providing a more flexible means of modelling. This paper therefore, extends the existing T-FRI approach using interval type-2 fuzzy sets, which covers the original T-FRI as its specific instance. The effectiveness of this extension is demonstrated by experimental investigations and, also, by a practical application in comparison to the state-of-the-art alternative approach developed using rough-fuzzy sets. Full article
(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)
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<p>Different membership functions for some eye contact perceived by different people [<a href="#B23-algorithms-10-00091" class="html-bibr">23</a>].</p> Full article ">Figure 2
<p>A type-2 fuzzy set corresponding to the situation depicted by <a href="#algorithms-10-00091-f001" class="html-fig">Figure 1</a>.</p> Full article ">Figure 3
<p>Lower membership function <math display="inline"> <semantics> <msup> <mover accent="true"> <mi>A</mi> <mo stretchy="false">˜</mo> </mover> <mi>L</mi> </msup> </semantics> </math> and upper membership function <math display="inline"> <semantics> <msup> <mover accent="true"> <mi>A</mi> <mo stretchy="false">˜</mo> </mover> <mi>U</mi> </msup> </semantics> </math> of a triangular interval type-2 fuzzy set <math display="inline"> <semantics> <mover accent="true"> <mi>A</mi> <mo stretchy="false">˜</mo> </mover> </semantics> </math>.</p> Full article ">Figure 4
<p>Two single-antecedent rules interpolation with identical normal points.</p> Full article ">Figure 5
<p>Two multi-antecedent rules interpolation with singleton-valued conditions.</p> Full article ">Figure 6
<p>Interpolation and extrapolation involving multiple multi-antecedent rules for Case 3.</p> Full article ">Figure 7
<p>Interpolation for type-1 fuzzy sets case.</p> Full article ">Figure 8
<p>Causal diagram of the simplified application problem [<a href="#B23-algorithms-10-00091" class="html-bibr">23</a>].</p> Full article ">Figure 9
<p>Interpolated results from conventional FRI [<a href="#B23-algorithms-10-00091" class="html-bibr">23</a>].</p> Full article ">Figure 9 Cont.
<p>Interpolated results from conventional FRI [<a href="#B23-algorithms-10-00091" class="html-bibr">23</a>].</p> Full article ">Figure 10
<p>Interpolated results from interval type-2 interpolation [<a href="#B23-algorithms-10-00091" class="html-bibr">23</a>].</p> Full article ">Figure 10 Cont.
<p>Interpolated results from interval type-2 interpolation [<a href="#B23-algorithms-10-00091" class="html-bibr">23</a>].</p> Full article ">Figure 11
<p>Interpolated results from rough-fuzzy interpolation (taken from [<a href="#B23-algorithms-10-00091" class="html-bibr">23</a>]).</p> Full article ">
464 KiB  
Article
Local Community Detection Based on Small Cliques
by Michael Hamann, Eike Röhrs and Dorothea Wagner
Algorithms 2017, 10(3), 90; https://doi.org/10.3390/a10030090 - 11 Aug 2017
Cited by 12 | Viewed by 5997
Abstract
Community detection aims to find dense subgraphs in a network. We consider the problem of finding a community locally around a seed node both in unweighted and weighted networks. This is a faster alternative to algorithms that detect communities that cover the whole [...] Read more.
Community detection aims to find dense subgraphs in a network. We consider the problem of finding a community locally around a seed node both in unweighted and weighted networks. This is a faster alternative to algorithms that detect communities that cover the whole network when actually only a single community is required. Further, many overlapping community detection algorithms use local community detection algorithms as basic building block. We provide a broad comparison of different existing strategies of expanding a seed node greedily into a community. For this, we conduct an extensive experimental evaluation both on synthetic benchmark graphs as well as real world networks. We show that results both on synthetic as well as real-world networks can be significantly improved by starting from the largest clique in the neighborhood of the seed node. Further, our experiments indicate that algorithms using scores based on triangles outperform other algorithms in most cases. We provide theoretical descriptions as well as open source implementations of all algorithms used. Full article
(This article belongs to the Special Issue Algorithms for Community Detection in Complex Networks)
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<p>Avg. <math display="inline"> <semantics> <msub> <mi>F</mi> <mn>1</mn> </msub> </semantics> </math>-scores on the LFR benchmark with the parameter set Unweighted, which we specify in <a href="#algorithms-10-00090-t001" class="html-table">Table 1</a>. The left column shows results when starting with a single seed node, the right column shows results for starting with the maximum clique as well as Infomap for comparison.</p> Full article ">Figure 2
<p>Different measures for the 5000 node unweighted graph with disjoint big communities.</p> Full article ">Figure 3
<p>Results for overlapping communities with LFR graphs with parameter set “Overlapping” as specified in <a href="#algorithms-10-00090-t001" class="html-table">Table 1</a>.</p> Full article ">Figure 4
<p>Avg. <math display="inline"> <semantics> <msub> <mi>F</mi> <mn>1</mn> </msub> </semantics> </math>-scores on the LFR benchmark with the parameter set Weighted, as specified in <a href="#algorithms-10-00090-t001" class="html-table">Table 1</a>.</p> Full article ">Figure 5
<p>Average <math display="inline"> <semantics> <msub> <mi>F</mi> <mn>1</mn> </msub> </semantics> </math>-scores of the algorithms on all 100 Facebook graphs. The scores are calculated by treating the dormitory attribute as communities. The graphs are sorted by the <math display="inline"> <semantics> <msub> <mi>F</mi> <mn>1</mn> </msub> </semantics> </math>-score of CCE.</p> Full article ">Figure 6
<p>Summary of F1-Score - seed values of all types of networks considered. The results for the Facebook networks are averages over the 10 networks where “Cl+LTE” had the best scores. LocalT does not support edge weights and is therefore omitted for weighted graphs.</p> Full article ">
282 KiB  
Article
On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich’s Technique
by José Antonio Ezquerro and Miguel Ángel Hernández-Verón
Algorithms 2017, 10(3), 89; https://doi.org/10.3390/a10030089 - 2 Aug 2017
Cited by 5 | Viewed by 4389
Abstract
The well-known Kantorovich technique based on majorizing sequences is used to analyse the convergence of Newton’s method when it is used to solve nonlinear Fredholm integral equations. In addition, we obtain information about the domains of existence and uniqueness of a solution for [...] Read more.
The well-known Kantorovich technique based on majorizing sequences is used to analyse the convergence of Newton’s method when it is used to solve nonlinear Fredholm integral equations. In addition, we obtain information about the domains of existence and uniqueness of a solution for these equations. Finally, we illustrate the above with two particular Fredholm integral equations. Full article
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems 2017)
4338 KiB  
Article
On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems
by Francesco Mezzadri and Emanuele Galligani
Algorithms 2017, 10(3), 88; https://doi.org/10.3390/a10030088 - 2 Aug 2017
Cited by 1 | Viewed by 4938
Abstract
In this paper, we extend the analysis of the Lagged Diffusivity Method for nonlinear, non-steady reaction-convection-diffusion equations. In particular, we describe how the method can be used to solve the systems arising from different discretization schemes, recalling some results on the convergence of [...] Read more.
In this paper, we extend the analysis of the Lagged Diffusivity Method for nonlinear, non-steady reaction-convection-diffusion equations. In particular, we describe how the method can be used to solve the systems arising from different discretization schemes, recalling some results on the convergence of the method itself. Moreover, we also analyze the behavior of the method in case of problems presenting boundary layers or blow-up solutions. Full article
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems 2017)
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<p>Summary of the nonlinear terms present at each time level and at each lagging iteration for different time discretizations. (<b>a</b>) <math display="inline"> <semantics> <mrow> <mi>θ</mi> <mo>−</mo> </mrow> </semantics> </math>method; (<b>b</b>) IMEX scheme with explicit treatment of <math display="inline"> <semantics> <mrow> <mi mathvariant="bold-italic">G</mi> <mo>(</mo> <mi mathvariant="bold-italic">u</mi> <mo>)</mo> </mrow> </semantics> </math>; (<b>c</b>) IMEX scheme with non-constant velocity term <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi mathvariant="bold-italic">v</mi> <mo stretchy="false">˜</mo> </mover> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">u</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> treated explicitly. Here <math display="inline"> <semantics> <mrow> <msub> <mi>A</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">u</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> represents the part of <span class="html-italic">A</span> dependent on <math display="inline"> <semantics> <mrow> <mi>σ</mi> <mo>(</mo> <mi mathvariant="bold-italic">u</mi> <mo>)</mo> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi>A</mi> <mo stretchy="false">˜</mo> </mover> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">u</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> represents the part of <span class="html-italic">A</span> dependent on <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi mathvariant="bold-italic">v</mi> <mo stretchy="false">˜</mo> </mover> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">u</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math>.</p> Full article ">Figure 2
<p>Starting vectors and tolerances of the iterative methods.</p> Full article ">Figure 3
<p>Systems arising from the discretization of the initial PDE and from the used iterative methods.</p> Full article ">Figure 4
<p>Blow-up solutions and representation of where and how the blow-up occurs.</p> Full article ">Figure 5
<p>Evolution of the computed solution as <span class="html-italic">t</span> approaches <span class="html-italic">T</span> in the cases <math display="inline"> <semantics> <mrow> <msup> <mi>u</mi> <mo>*</mo> </msup> <mo>=</mo> <msubsup> <mi>u</mi> <mn>2</mn> <mo>*</mo> </msubsup> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msup> <mi>u</mi> <mo>*</mo> </msup> <mo>=</mo> <msubsup> <mi>u</mi> <mn>4</mn> <mo>*</mo> </msubsup> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <msup> <mi>u</mi> <mo>*</mo> </msup> <mo>=</mo> <msubsup> <mi>u</mi> <mn>5</mn> <mo>*</mo> </msubsup> </mrow> </semantics> </math>.</p> Full article ">Figure 6
<p>Last computed solution for the problems in <a href="#algorithms-10-00088-f004" class="html-fig">Figure 4</a> for <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics> </math>. (<b>a</b>) <math display="inline"> <semantics> <msub> <mi>u</mi> <mn>2</mn> </msub> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi>t</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.993</mn> </mrow> </semantics> </math>; (<b>b</b>) <math display="inline"> <semantics> <msub> <mi>u</mi> <mn>3</mn> </msub> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi>t</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.972</mn> </mrow> </semantics> </math>; (<b>c</b>) <math display="inline"> <semantics> <msub> <mi>u</mi> <mn>4</mn> </msub> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi>t</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.789</mn> </mrow> </semantics> </math>; (<b>d</b>) <math display="inline"> <semantics> <msub> <mi>u</mi> <mn>5</mn> </msub> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi>t</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.806</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 7
<p>Solution of the boundary layer test problem for <span class="html-italic">N</span> = 250; inner solver: BiCGstab(4).</p> Full article ">
334 KiB  
Article
Auxiliary Model Based Multi-Innovation Stochastic Gradient Identification Algorithm for Periodically Non-Uniformly Sampled-Data Hammerstein Systems
by Li Xie and Huizhong Yang
Algorithms 2017, 10(3), 84; https://doi.org/10.3390/a10030084 - 31 Jul 2017
Cited by 3 | Viewed by 5290
Abstract
Due to the lack of powerful model description methods, the identification of Hammerstein systems based on the non-uniform input-output dataset remains a challenging problem. This paper introduces a time-varying backward shift operator to describe periodically non-uniformly sampled-data Hammerstein systems, which can simplify the [...] Read more.
Due to the lack of powerful model description methods, the identification of Hammerstein systems based on the non-uniform input-output dataset remains a challenging problem. This paper introduces a time-varying backward shift operator to describe periodically non-uniformly sampled-data Hammerstein systems, which can simplify the structure of the lifted models using the traditional lifting technique. Furthermore, an auxiliary model-based multi-innovation stochastic gradient algorithm is presented to estimate the parameters involved in the linear and nonlinear blocks. The simulation results confirm that the proposed algorithm is effective and can achieve a high estimation performance. Full article
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<p>Periodically non-uniformly sampled-data Hammerstein system.</p> Full article ">Figure 2
<p>The flowchart of computing the parameter estimate.</p> Full article ">Figure 3
<p>The AM-MISG estimation errors <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math> versus <span class="html-italic">k</span> with <math display="inline"> <semantics> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math>, 5, 12.</p> Full article ">Figure 4
<p>The predicted outputs and the measured outputs. (<b>a</b>) For the noise variance <math display="inline"> <semantics> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mo>=</mo> <msup> <mn>0.10</mn> <mn>2</mn> </msup> </mrow> </semantics> </math>. (<b>b</b>) For the noise variance <math display="inline"> <semantics> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mo>=</mo> <msup> <mn>0.50</mn> <mn>2</mn> </msup> </mrow> </semantics> </math>.</p> Full article ">
44006 KiB  
Article
Evolutionary Optimization for Robust Epipolar-Geometry Estimation and Outlier Detection
by Mozhdeh Shahbazi, Gunho Sohn and Jérôme Théau
Algorithms 2017, 10(3), 87; https://doi.org/10.3390/a10030087 - 27 Jul 2017
Cited by 10 | Viewed by 8210
Abstract
In this paper, a robust technique based on a genetic algorithm is proposed for estimating two-view epipolar-geometry of uncalibrated perspective stereo images from putative correspondences containing a high percentage of outliers. The advantages of this technique are three-fold: (i) replacing random search with [...] Read more.
In this paper, a robust technique based on a genetic algorithm is proposed for estimating two-view epipolar-geometry of uncalibrated perspective stereo images from putative correspondences containing a high percentage of outliers. The advantages of this technique are three-fold: (i) replacing random search with evolutionary search applying new strategies of encoding and guided sampling; (ii) robust and fast estimation of the epipolar geometry via detecting a more-than-enough set of inliers without making any assumptions about the probability distribution of the residuals; (iii) determining the inlier-outlier threshold based on the uncertainty of the estimated model. The proposed method was evaluated both on synthetic data and real images. The results were compared with the most popular techniques from the state-of-the-art, including RANSAC (random sample consensus), MSAC, MLESAC, Cov-RANSAC, LO-RANSAC, StaRSAC, Multi-GS RANSAC and least median of squares (LMedS). Experimental results showed that the proposed approach performed better than other methods regarding the accuracy of inlier detection and epipolar-geometry estimation, as well as the computational efficiency for datasets majorly contaminated by outliers and noise. Full article
(This article belongs to the Special Issue Computational Intelligence and Nature-Inspired Algorithms for Real-World Data Analytics and Pattern Recognition)
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<p>Summary of outlier detection techniques in stereo sparse matching based on robust estimation of epipolar geometry.</p> Full article ">Figure 2
<p>Encoding scheme: (<b>a</b>) the overlapping rectangle, (<b>b</b>) an example list of some putative correspondences, which are identified by their indices, and their positions relative to the overlapping rectangle and (<b>c</b>) a part of the 2D lookup table constructed using Equation (<a href="#FD7-algorithms-10-00087" class="html-disp-formula">6</a>); the bold numbers show the indices of the original matches, and the regular numbers show the indices assigned to the other pixels.</p> Full article ">Figure 3
<p>Guided sampling: (<b>a</b>) a stereo pair and the putative correspondences; the bounding rectangle on the left image represents the overlapping rectangle; (<b>b</b>) dividing the overlapping rectangle into 12 sub-regions of equal area; (<b>c</b>) the minimal rectangle and the distribution of putative matches over the sub-regions; (<b>d</b>) density-based roulette-wheel for region selection.</p> Full article ">Figure 4
<p>Performance of sampling methods on the Table dataset as the ratio <math display="inline"> <semantics> <mi>λ</mi> </semantics> </math> increases: (<b>a</b>) percentage of outlier-free sample sets, (<b>b</b>) percentage of non-degenerate sample sets and (<b>c</b>) estimation accuracy.</p> Full article ">Figure 5
<p>Performance of sampling methods on the Church dataset as the outlier ratio increases: (<b>a</b>) percentage of outlier-free sample sets, (<b>b</b>) estimation accuracy.</p> Full article ">Figure 6
<p>Inlier probability of correspondences obtained using (<b>a</b>) our adaptive thresholding method: (<b>b</b>) median-based algorithm; (<b>c</b>) covariance-based algorithm.</p> Full article ">Figure 7
<p>Inlier thresholds determined by (<b>a</b>) our adaptive thresholding method; (<b>b</b>) the median-based algorithm and (<b>c</b>) the covariance-based algorithm.</p> Full article ">Figure 8
<p>Performance of different algorithms under various percentages of outliers for the Multiview dataset. In the graphs, the x-axis represents the percentage of synthetic outliers in the dataset.</p> Full article ">Figure 9
<p>Performance of the proposed algorithm with noisy images. The graph at the bottom of each surface-plot represents the average of respective performance criterion versus the amount of noise.</p> Full article ">Figure 10
<p>Performance of the proposed algorithm with varying GA population size. The graph at the bottom of each surface-plot represents the average of the respective performance criterion versus the population size.</p> Full article ">
908 KiB  
Article
An Improved MOEA/D with Optimal DE Schemes for Many-Objective Optimization Problems
by Wei Zheng, Yanyan Tan, Xiaonan Fang and Shengtao Li
Algorithms 2017, 10(3), 86; https://doi.org/10.3390/a10030086 - 26 Jul 2017
Cited by 8 | Viewed by 5997
Abstract
MOEA/D is a promising multi-objective evolutionary algorithm based on decomposition, and it has been used to solve many multi-objective optimization problems very well. However, there is a class of multi-objective problems, called many-objective optimization problems, but the original MOEA/D cannot solve them well. [...] Read more.
MOEA/D is a promising multi-objective evolutionary algorithm based on decomposition, and it has been used to solve many multi-objective optimization problems very well. However, there is a class of multi-objective problems, called many-objective optimization problems, but the original MOEA/D cannot solve them well. In this paper, an improved MOEA/D with optimal differential evolution (oDE) schemes is proposed, called MOEA/D-oDE, aiming to solve many-objective optimization problems. Compared with MOEA/D, MOEA/D-oDE has two distinguishing points. On the one hand, MOEA/D-oDE adopts a newly-introduced decomposition approach to decompose the many-objective optimization problems, which combines the advantages of the weighted sum approach and the Tchebycheff approach. On the other hand, a kind of combination mechanism for DE operators is designed for finding the best child solution so as to do the a posteriori computing. In our experimental study, six continuous test instances with 4–6 objectives comparing NSGA-II (nondominated sorting genetic algorithm II) and MOEA/D as accompanying experiments are applied. Additionally, the final results indicate that MOEA/D-oDE outperforms NSGA-II and MOEA/D in almost all cases, particularly in those problems that have complicated Pareto shapes and higher dimensional objectives, where its advantages are more obvious. Full article
(This article belongs to the Special Issue Evolutionary Computation for Multiobjective Optimization)
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<p>Illustration of the improvement regions for the (<b>a</b>) weighted sum approach and the (<b>b</b>) weighted Tchebycheff approach.</p> Full article ">Figure 2
<p>Flowchart of generating differential evolution (DE) operators.</p> Full article ">Figure 3
<p>Evolution of the mean of IGD metric values for four-objective test problems.</p> Full article ">Figure 4
<p>Evolution of the mean of IGD metric values for five-objective test problems.</p> Full article ">Figure 5
<p>Evolution of the mean of IGD metric values for six-objective test problems.</p> Full article ">Figure 6
<p>Box plots of the IGD metric values based on 20 independent runs for four-objective test problems.</p> Full article ">Figure 7
<p>Box plots of the IGD metric values based on 20 independent runs for five-objective test problems.</p> Full article ">Figure 8
<p>Box plots of the IGD metric values based on 20 independent runs for six-objective test problems.</p> Full article ">
2842 KiB  
Article
A New Meta-Heuristics of Optimization with Dynamic Adaptation of Parameters Using Type-2 Fuzzy Logic for Trajectory Control of a Mobile Robot
by Camilo Caraveo, Fevrier Valdez and Oscar Castillo
Algorithms 2017, 10(3), 85; https://doi.org/10.3390/a10030085 - 26 Jul 2017
Cited by 39 | Viewed by 7340
Abstract
Fuzzy logic is a soft computing technique that has been very successful in recent years when it is used as a complement to improve meta-heuristic optimization. In this paper, we present a new variant of the bio-inspired optimization algorithm based on the self-defense [...] Read more.
Fuzzy logic is a soft computing technique that has been very successful in recent years when it is used as a complement to improve meta-heuristic optimization. In this paper, we present a new variant of the bio-inspired optimization algorithm based on the self-defense mechanisms of plants in the nature. The optimization algorithm proposed in this work is based on the predator-prey model originally presented by Lotka and Volterra, where two populations interact with each other and the objective is to maintain a balance. The system of predator-prey equations use four variables (α, β, λ, δ) and the values of these variables are very important since they are in charge of maintaining a balance between the pair of equations. In this work, we propose the use of Type-2 fuzzy logic for the dynamic adaptation of the variables of the system. This time a fuzzy controller is in charge of finding the optimal values for the model variables, the use of this technique will allow the algorithm to have a higher performance and accuracy in the exploration of the values. Full article
(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)
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<p>Graphic representation of self-defense techniques.</p> Full article ">Figure 2
<p>Flowchart with a fuzzy approach.</p> Full article ">Figure 3
<p>Reproduction method by pollination.</p> Full article ">Figure 4
<p>Input variable iteration.</p> Full article ">Figure 5
<p>Input variable diversity.</p> Full article ">Figure 6
<p>Output 1 Alpha.</p> Full article ">Figure 7
<p>Output 2 Beta.</p> Full article ">Figure 8
<p>Output 3 Delta.</p> Full article ">Figure 9
<p>Output 4 Lambda.</p> Full article ">Figure 10
<p>Representation of the mobile robot.</p> Full article ">Figure 11
<p>(<b>a</b>) Lineal velocity error (e<sub>v</sub>); (<b>b</b>) angular velocity error (e<sub>w</sub>); (<b>c</b>) left torque (T1); (<b>d</b>) right torque (T2).</p> Full article ">Figure 12
<p>Trajectory to be followed by robot.</p> Full article ">Figure 13
<p>Robot simulation.</p> Full article ">
4717 KiB  
Article
Fuzzy Fireworks Algorithm Based on a Sparks Dispersion Measure
by Juan Barraza, Patricia Melin, Fevrier Valdez and Claudia I. Gonzalez
Algorithms 2017, 10(3), 83; https://doi.org/10.3390/a10030083 - 21 Jul 2017
Cited by 21 | Viewed by 5763
Abstract
The main goal of this paper is to improve the performance of the Fireworks Algorithm (FWA). To improve the performance of the FWA we propose three modifications: the first modification is to change the stopping criteria, this is to say, previously, the number [...] Read more.
The main goal of this paper is to improve the performance of the Fireworks Algorithm (FWA). To improve the performance of the FWA we propose three modifications: the first modification is to change the stopping criteria, this is to say, previously, the number of function evaluations was utilized as a stopping criteria, and we decided to change this to specify a particular number of iterations; the second and third modifications consist on introducing a dispersion metric (dispersion percent), and both modifications were made with the goal of achieving dynamic adaptation of the two parameters in the algorithm. The parameters that were controlled are the explosion amplitude and the number of sparks, and it is worth mentioning that the control of these parameters is based on a fuzzy logic approach. To measure the impact of these modifications, we perform experiments with 14 benchmark functions and a comparative study shows the advantage of the proposed approach. We decided to call the proposed algorithms Iterative Fireworks Algorithm (IFWA) and two variants of the Dispersion Percent Iterative Fuzzy Fireworks Algorithm (DPIFWA-I and DPIFWA-II, respectively). Full article
(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)
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<p>Pseudo code of Fireworks Algorithm (FWA).</p> Full article ">Figure 2
<p>Flow chart of Dispersion Percent Iterative Fireworks Algorithm (DPIFFWA).</p> Full article ">Figure 3
<p>Current mean of the = fitness of the sparks.</p> Full article ">Figure 4
<p>Requirement for<math display="inline"> <semantics> <mrow> <mo> </mo> <mi>dispersion</mi> <mtext> </mtext> <mi>percent</mi> <mo> </mo> <mrow> <mo>(</mo> <mrow> <mi>D</mi> <mi>P</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math>.</p> Full article ">Figure 5
<p>Graphical representation of the Fuzzy System for DPIFFWA-I.</p> Full article ">Figure 6
<p>Input variable of DPFFWA-I (Iteration).</p> Full article ">Figure 7
<p>Input variable of DPFFWA-I (DispersionPercent).</p> Full article ">Figure 8
<p>Output variable of DPFFWA-I (AmplitudeExplosion).</p> Full article ">Figure 9
<p>Graphical representation of the Fuzzy System for DPIFFWA-II.</p> Full article ">Figure 10
<p>Output variable of DPFFWA-II (SPARKS).</p> Full article ">
4833 KiB  
Article
Optimization of Intelligent Controllers Using a Type-1 and Interval Type-2 Fuzzy Harmony Search Algorithm
by Cinthia Peraza, Fevrier Valdez and Patricia Melin
Algorithms 2017, 10(3), 82; https://doi.org/10.3390/a10030082 - 20 Jul 2017
Cited by 38 | Viewed by 5869
Abstract
This article focuses on the dynamic parameter adaptation in the harmony search algorithm using Type-1 and interval Type-2 fuzzy logic. In particular, this work focuses on the adaptation of the parameters of the original harmony search algorithm. At present there are several types [...] Read more.
This article focuses on the dynamic parameter adaptation in the harmony search algorithm using Type-1 and interval Type-2 fuzzy logic. In particular, this work focuses on the adaptation of the parameters of the original harmony search algorithm. At present there are several types of algorithms that can solve complex real-world problems with uncertainty management. In this case the proposed method is in charge of optimizing the membership functions of three benchmark control problems (water tank, shower, and mobile robot). The main goal is to find the best parameters for the membership functions in the controller to follow a desired trajectory. Noise experiments are performed to test the efficacy of the method. Full article
(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)
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<p>Flowchart of the FHS.</p> Full article ">Figure 2
<p>Scheme of the Type-1 fuzzy system method (FHS).</p> Full article ">Figure 3
<p>Input and output of the Type-1 fuzzy system.</p> Full article ">Figure 4
<p>Scheme of the interval Type-2 fuzzy system method (FHS2).</p> Full article ">Figure 5
<p>Input and output of the interval Type-2 fuzzy system.</p> Full article ">Figure 6
<p>Diagram of the water tank controller.</p> Full article ">Figure 7
<p>Structure of the water tank fuzzy system for control.</p> Full article ">Figure 8
<p>Diagram of the temperature controller.</p> Full article ">Figure 9
<p>Structure of the water tank fuzzy system for control.</p> Full article ">Figure 10
<p>Diagram of the robot mobile controller.</p> Full article ">Figure 11
<p>Structure of the mobile robot fuzzy system for control.</p> Full article ">Figure 12
<p>Simulation results of the water tank controller for the three methods. (<b>a</b>) The best result is shown using original harmony search algorithm (HS); (<b>b</b>) the best result is shown using the Type-1 fuzzy harmony search (FHS); (<b>c</b>) the best result is shown using the Type-2 fuzzy harmony search (FHS2). These methods were applied with noise to verify the stability of the methods. The blue line represents the desired trajectory and the pink line the obtained trajectory; the objective is for the obtained line to resemble the desired one.</p> Full article ">Figure 13
<p>Simulation results of the temperature controller for the three methods. (<b>a</b>) The best result is shown using original harmony search algorithm (HS); (<b>b</b>) the best result is shown using the Type-1 fuzzy harmony search (FHS); (<b>c</b>) the best result is shown using the Type-2 fuzzy harmony search (FHS2). These methods were applied with noise to verify the stability of the methods. The blue line represents the desired trajectory and the pink line the obtained trajectory; the objective is for the obtained line to resemble the desired one.</p> Full article ">Figure 14
<p>Simulation results of the robot mobile controller for the three methods. (<b>a</b>) The best result is shown using original harmony search algorithm (HS); (<b>b</b>) the best result is shown using the Type-1 fuzzy harmony search (FHS); (<b>c</b>) the best result is shown using the Type-2 fuzzy harmony search (FHS2). These methods were applied with noise to verify the stability of the methods. The green line is the desired trajectory and the blue line the obtained trajectory, and the objective is for the obtained line to resemble the desired one.</p> Full article ">Figure 14 Cont.
<p>Simulation results of the robot mobile controller for the three methods. (<b>a</b>) The best result is shown using original harmony search algorithm (HS); (<b>b</b>) the best result is shown using the Type-1 fuzzy harmony search (FHS); (<b>c</b>) the best result is shown using the Type-2 fuzzy harmony search (FHS2). These methods were applied with noise to verify the stability of the methods. The green line is the desired trajectory and the blue line the obtained trajectory, and the objective is for the obtained line to resemble the desired one.</p> Full article ">
385 KiB  
Article
Low-Resource Cross-Domain Product Review Sentiment Classification Based on a CNN with an Auxiliary Large-Scale Corpus
by Xiaocong Wei, Hongfei Lin, Yuhai Yu and Liang Yang
Algorithms 2017, 10(3), 81; https://doi.org/10.3390/a10030081 - 19 Jul 2017
Cited by 20 | Viewed by 5746
Abstract
The literature [-5]contains several reports evaluating the abilities of deep neural networks in text transfer learning. To our knowledge, however, there have been few efforts to fully realize the potential of deep neural networks in cross-domain product review sentiment classification. In this paper, [...] Read more.
The literature [-5]contains several reports evaluating the abilities of deep neural networks in text transfer learning. To our knowledge, however, there have been few efforts to fully realize the potential of deep neural networks in cross-domain product review sentiment classification. In this paper, we propose a two-layer convolutional neural network (CNN) for cross-domain product review sentiment classification (LM-CNN-LB). Transfer learning research into product review sentiment classification based on deep neural networks has been limited by the lack of a large-scale corpus; we sought to remedy this problem using a large-scale auxiliary cross-domain dataset collected from Amazon product reviews. Our proposed framework exhibits the dramatic transferability of deep neural networks for cross-domain product review sentiment classification and achieves state-of-the-art performance. The framework also outperforms complex engineered features used with a non-deep neural network method. The experiments demonstrate that introducing large-scale data from similar domains is an effective way to resolve the lack of training data. The LM-CNN-LB trained on the multi-source related domain dataset outperformed the one trained on a single similar domain. Full article
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<p>Architecture of LM-CNN-LB for cross-domain product review sentiment classification.</p> Full article ">Figure 2
<p>Comparison of different methods on the benchmark dataset for cross-domain sentiment classification.</p> Full article ">Figure 3
<p>Effect of corpus size and multi-source domain.</p> Full article ">Figure 4
<p>Comparison of word embedding pre-trained on Google News and the proposed corpus.</p> Full article ">Figure 5
<p>Comparison of different methods and corpus size on <math display="inline"> <semantics> <msub> <mi>D</mi> <mi>l</mi> </msub> </semantics> </math> for cross-domain sentiment classification.</p> Full article ">Figure 6
<p>Effect of <math display="inline"> <semantics> <msub> <mi>S</mi> <mrow> <mi>c</mi> <mi>n</mi> <mi>n</mi> </mrow> </msub> </semantics> </math> epoch number.</p> Full article ">Figure 7
<p>Effect of labeled target domain data ratio for training the <math display="inline"> <semantics> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mi>n</mi> <mi>n</mi> </mrow> </msub> </semantics> </math>.</p> Full article ">
23357 KiB  
Article
A Hybrid Algorithm for Optimal Wireless Sensor Network Deployment with the Minimum Number of Sensor Nodes
by Yasser El Khamlichi, Abderrahim Tahiri, Anouar Abtoy, Inmaculada Medina-Bulo and Francisco Palomo-Lozano
Algorithms 2017, 10(3), 80; https://doi.org/10.3390/a10030080 - 18 Jul 2017
Cited by 26 | Viewed by 10848
Abstract
Wireless sensor network (WSN) applications are rapidly growing and are widely used in various disciplines. Deployment is one of the key issues to be solved in WSNs, since the sensor nodes’ positioning affects highly the system performance. An optimal WSN deployment should maximize [...] Read more.
Wireless sensor network (WSN) applications are rapidly growing and are widely used in various disciplines. Deployment is one of the key issues to be solved in WSNs, since the sensor nodes’ positioning affects highly the system performance. An optimal WSN deployment should maximize the collection of the desired interest phenomena, guarantee the required coverage and connectivity, extend the network lifetime, and minimize the network cost in terms of energy consumption. Most of the research effort in this area aims to solve the deployment issue, without minimizing the network cost by reducing unnecessary working nodes in the network. In this paper, we propose a deployment approach based on the gradient method and the Simulated Annealing algorithm to solve the sensor deployment problem with the minimum number of sensor nodes. The proposed algorithm is able to heuristically optimize the number of sensors and their positions in order to achieve the desired application requirements. Full article
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<p>Typical wireless sensor network (WSN) architecture.</p> Full article ">Figure 2
<p>Perception model of sensor node.</p> Full article ">Figure 3
<p>The sensing area of sensor in terms of square.</p> Full article ">Figure 4
<p>Graph scenario of dividing an area into cover sets.</p> Full article ">Figure 5
<p>Description of the cluster in the supervised area.</p> Full article ">Figure 6
<p>Triangular deployment: (<b>a</b>) Iteration I where <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">d</mi> <mrow> <mi>min</mi> </mrow> </msub> </mrow> </semantics> </math> &lt; 2 × Rs; (<b>b</b>) Iteration I + k where <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">d</mi> <mrow> <mi>min</mi> <mtext> </mtext> </mrow> </msub> <mo> </mo> </mrow> </semantics> </math>&gt; 2 × Rs.</p> Full article ">Figure 7
<p>Triangular grid deployment.</p> Full article ">Figure 8
<p>Topology with selected sensor nodes.</p> Full article ">Figure 9
<p>Positions of the sensor nodes on the boundary: (<b>a</b>) before and (<b>b</b>) after applying the gradient method.</p> Full article ">Figure 10
<p>Topology with optimized sensor positions.</p> Full article ">Figure 11
<p>Topology ensuring maximum interest, full coverage, and connectivity.</p> Full article ">Figure 12
<p>Initial sensor deployment “Scenario 1”.</p> Full article ">Figure 13
<p>Optimal sensor deployment “Scenario 1”.</p> Full article ">Figure 14
<p>Illustration of WSN connection graph: (<b>a</b>) Before solving connectivity; (<b>b</b>) after solving connectivity.</p> Full article ">Figure 15
<p>Ratio Rips &amp; Ratio Rics “Scenario 1”.</p> Full article ">Figure 16
<p>Initial sensor deployment “Scenario 2”.</p> Full article ">Figure 17
<p>Optimal sensor deployment “Scenario 2”.</p> Full article ">Figure 18
<p>Illustration of WSN connection graph: (<b>a</b>) Before solving connectivity (<b>b</b>) after solving connectivity.</p> Full article ">Figure 19
<p>Ratio Rips &amp;Ratio Rics “Scenario 2”.</p> Full article ">Figure 20
<p>Optimal sensor deployment on area “UL-A”.</p> Full article ">Figure 21
<p>Illustration of the UL-A network connection graph.</p> Full article ">Figure 22
<p>Optimal sensor deployment on area “UL-B”.</p> Full article ">Figure 23
<p>Illustration of the UL-B network connection graph.</p> Full article ">
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Article
Design of an Optimized Fuzzy Classifier for the Diagnosis of Blood Pressure with a New Computational Method for Expert Rule Optimization
by Juan Carlos Guzman, Patricia Melin and German Prado-Arechiga
Algorithms 2017, 10(3), 79; https://doi.org/10.3390/a10030079 - 14 Jul 2017
Cited by 26 | Viewed by 6827
Abstract
A neuro fuzzy hybrid model (NFHM) is proposed as a new artificial intelligence method to classify blood pressure (BP). The NFHM uses techniques such as neural networks, fuzzy logic and evolutionary computation, and in the last case genetic algorithms (GAs) are used. The [...] Read more.
A neuro fuzzy hybrid model (NFHM) is proposed as a new artificial intelligence method to classify blood pressure (BP). The NFHM uses techniques such as neural networks, fuzzy logic and evolutionary computation, and in the last case genetic algorithms (GAs) are used. The main goal is to model the behavior of blood pressure based on monitoring data of 24 h per patient and based on this to obtain the trend, which is classified using a fuzzy system based on rules provided by an expert, and these rules are optimized by a genetic algorithm to obtain the best possible number of rules for the classifier with the lowest classification error. Simulation results are presented to show the advantage of the proposed model. Full article
(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)
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<p>General Neuro Fuzzy Hybrid Model.</p> Full article ">Figure 2
<p>Specific Neuro Fuzzy Hybrid Model.</p> Full article ">Figure 3
<p>Structure of the fuzzy logic classifier 1.</p> Full article ">Figure 4
<p>Systolic input for the fuzzy logic classifier 1.</p> Full article ">Figure 5
<p>Diastolic input for the fuzzy logic classifier 1.</p> Full article ">Figure 6
<p>BP_Levels is the output of the fuzzy logic classifier 1.</p> Full article ">Figure 7
<p>Structure of the fuzzy logic classifier 2.</p> Full article ">Figure 8
<p>Systolic input for the fuzzy logic classifier 2.</p> Full article ">Figure 9
<p>Diastolic input for the fuzzy logic classifier 2.</p> Full article ">Figure 10
<p>BP_Levels is the output of the fuzzy logic classifier 2.</p> Full article ">Figure 11
<p>Structure of the fuzzy logic classifier 3.</p> Full article ">Figure 12
<p>Systolic input for the fuzzy logic classifier 3.</p> Full article ">Figure 13
<p>Diastolic input for the fuzzy logic classifier 3.</p> Full article ">Figure 14
<p>BP_Levels is the output of the fuzzy logic classifier 3.</p> Full article ">Figure 15
<p>Structure of the chromosome.</p> Full article ">Figure 16
<p>Structure of the fuzzy logic classifier 4.</p> Full article ">Figure 17
<p>Systolic input for the fuzzy logic classifier 4.</p> Full article ">Figure 18
<p>Diastolic input for the fuzzy logic classifier 4.</p> Full article ">Figure 19
<p>BP_Levels is the output of the fuzzy logic classifier 4.</p> Full article ">Figure 20
<p>The input data for systolic.</p> Full article ">Figure 21
<p>The input data for diastolic.</p> Full article ">Figure 22
<p>The learning of the neural network with the systolic data provided.</p> Full article ">Figure 23
<p>The learning of the neural network with the diastolic data provided.</p> Full article ">Figure 24
<p>The trend of the systolic data.</p> Full article ">Figure 25
<p>The trend of the diastolic data.</p> Full article ">
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