Robust Face Recognition Based on a New Supervised Kernel Subspace Learning Method
<p>The interactions by attraction and repulsion for the points between different classes.</p> "> Figure 2
<p>A sample of pre-cropped face images in the Sheffield Face database [<a href="#B51-sensors-19-01643" class="html-bibr">51</a>].</p> "> Figure 3
<p>(<b>a</b>–<b>k</b>) The comparative recognition results changing the dimensionality of the transformation matrix for each given training number Tn on each data (Sheffield Face database).</p> "> Figure 3 Cont.
<p>(<b>a</b>–<b>k</b>) The comparative recognition results changing the dimensionality of the transformation matrix for each given training number Tn on each data (Sheffield Face database).</p> "> Figure 4
<p>(<b>a</b>) A subset of the original Yale database. (<b>b</b>) A subset of cropped images [<a href="#B53-sensors-19-01643" class="html-bibr">53</a>].</p> "> Figure 5
<p>(<b>a</b>–<b>e</b>). The comparative recognition results changing the dimensionality of the transformation matrix for each given training number Tn on each dataset (Yale Face database).</p> "> Figure 5 Cont.
<p>(<b>a</b>–<b>e</b>). The comparative recognition results changing the dimensionality of the transformation matrix for each given training number Tn on each dataset (Yale Face database).</p> "> Figure 6
<p>Example of six different subjects (each with 4 images) from the ORL database [<a href="#B56-sensors-19-01643" class="html-bibr">56</a>].</p> "> Figure 7
<p>(<b>a</b>–<b>f</b>) The comparative recognition results changing the dimensionality of the transforming matrix for each given training number Tn on each data (ORL database).</p> "> Figure 8
<p>A subset of some images of one subject from the Head Pose database [<a href="#B59-sensors-19-01643" class="html-bibr">59</a>].</p> "> Figure 9
<p>(<b>a</b>–<b>f</b>) Comparative recognition results changing the dimensionality of the transformation matrix for each given training number Tn in each dataset (Head Pose database).</p> "> Figure 10
<p>Example of captured images of one person in the Finger Vein database [<a href="#B61-sensors-19-01643" class="html-bibr">61</a>].</p> "> Figure 11
<p>(<b>a</b>–<b>g</b>). Comparative recognition results changing the dimensionality of the transformation matrix for each given training number <span class="html-italic">Tn</span> (Finger Vein database).</p> "> Figure 11 Cont.
<p>(<b>a</b>–<b>g</b>). Comparative recognition results changing the dimensionality of the transformation matrix for each given training number <span class="html-italic">Tn</span> (Finger Vein database).</p> "> Figure 12
<p>A cropped sample of the finger knuckle print (FKP) database [<a href="#B63-sensors-19-01643" class="html-bibr">63</a>].</p> "> Figure 13
<p>(<b>a</b>–<b>i</b>). Comparative recognition results changing the dimensionality of the transformation matrix for each given training number Tn (Finger Knuckle database).</p> "> Figure 13 Cont.
<p>(<b>a</b>–<b>i</b>). Comparative recognition results changing the dimensionality of the transformation matrix for each given training number Tn (Finger Knuckle database).</p> "> Figure 14
<p>(<b>a</b>–<b>f</b>). Maximum recognition rate of SKLDNE versus Wk for different number of training samples on Sheffield, Yale, ORL, Head Pose, Finger Vein and Finger Knuckle databases.</p> "> Figure 14 Cont.
<p>(<b>a</b>–<b>f</b>). Maximum recognition rate of SKLDNE versus Wk for different number of training samples on Sheffield, Yale, ORL, Head Pose, Finger Vein and Finger Knuckle databases.</p> ">
Abstract
:1. Introduction
- (1)
- SKLDNE has been successfully designed to retain local geometric relations of the within-class samples, which are very important for image recognition. Generally, the categorization strength of methods with a linear learning algorithm is restricted. They fail to deal with complicated problems. Many effective nonlinear data features may be lost during the classification progress using linear techniques such as LDNE, LDA, DNE, and LPP. Therefore, applying a nonlinear method can effectively improve the classification performance.
- (2)
- This technique is a supervised learning method, as the data scholar acts as a guide to instruct the main algorithm whose conclusion should be found. SKLDNE considers class label information of neighbors in which there is a direct connection with classification, in order to enhance final recognition performance.
- (3)
- It benefits from the advantages of “locality” in LPP in which, due to the prior class-label information, geometric relations are preserved.
- (4)
- Not only can it build a compact submanifold by minimizing the distance between the same points in the same class, but it also expands the gaps among submanifolds of distinct classes simultaneously, which is called “discrimination.”
- (5)
- SKLDNE can resolve the SSS problem that is mostly faced by other aforementioned techniques such as PCA, LDA, UDP, and LPP, and the “overlearning of locality” problem in the manifold learning.
- (6)
- Due to its kernel weighting, it is very efficient in reducing the negative influence of the outliers on the projection directions, which effectively handles the drawbacks of linear models and makes it more robust to outliers.
2. Outline of LPP, DNE, and LDNE
2.1. Locality Preserving Projection
2.2. Discriminant Neighborhood Embedding
- (1)
- The adjacent matrix of graph G which refers to the underlying supervised manifold structure is as follows:
- (2)
- The optimal transformation of matrix P can be defined as follows:
2.3. Locality-Based Discriminant Neighborhood Embedding
- (1)
- Intra-class absorption: the interaction between pairs of neighbors from the same class.
- (2)
- Inter-class expulsion: the interaction between pairs of neighbors from different classes.
- (1)
- Intra-class absorption:
- (2)
- Inter-class expulsion:
3. Supervised Kernel Locality-Based Discriminant Neighborhood Embedding
3.1. Main Idea
3.2. Mathematics
4. Biometrics Application: Results and Analysis
4.1. Experimental Results with the Sheffield Face Database
4.2. Experimental Results with the Yale Face Database
4.3. Experimental Results with the ORL Database
4.4. Experimental Results with the Head Pose Database
4.5. Experimental Results with the Finger Vein Database.
4.6. Experimental Results with the Finger Knuckle Print Database
4.7. Classification Performance and Computational Cost
5. Conclusions and Future Research
Author Contributions
Funding
Conflicts of Interest
References
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Database | Sheffield Face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Tn | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 15 | 16 | 17 |
PCA | 45.1 | 47.94 | 49.68 | 49 | 49.64 | 51.15 | 52.5 | 54.54 | 85.5 | 93 | 92 |
(18) | (18) | (18) | (18) | (30) | (26) | (30) | (26) | (18) | (28) | (10) | |
KPCA | 45.2 | 48.2 | 50.31 | 50.33 | 50.7 | 51.92 | 54.15 | 55.9 | 87.5 | 93 | 92 |
(18) | (22) | (30) | (38) | (42) | (58) | (50) | (69) | (38) | (30) | (14) | |
UDP | 45.33 | 48.1 | 48.43 | 51.66 | 50.71 | 51.9 | 55.41 | 57.27 | 87 | 95 | 92.5 |
(10) | (22) | (30) | (30) | (45) | (66) | (54) | (50) | (90) | (86) | (14) | |
LPP | 45.55 | 48.2 | 52.81 | 50.66 | 56.07 | 52.3 | 54.16 | 55.9 | 90 | 93.33 | 95 |
(14) | (26) | (12) | (34) | (38) | (54) | (46) | (62) | (74) | (42) | (34) | |
LDA | 45.2 | 50.29 | 48.43 | 58.66 | 56.07 | 59.23 | 60 | 61.36 | 92.5 | 93 | 97.5 |
(18) | (26) | (14) | (34) | (22) | (6) | (42) | (50) | (22) | (30) | (18) | |
DNE | 45.2 | 48.23 | 50.31 | 51.33 | 51.78 | 51.9 | 54.58 | 56.36 | 87.5 | 93.33 | 92.5 |
(18) | (34) | (14) | (74) | (58) | (42) | (74) | (78) | (38) | (30) | (20) | |
LDNE | 45.27 | 50.58 | 56.87 | 58.66 | 65 | 73.07 | 76.66 | 76.81 | 90 | 96.1 | 97.5 |
(22) | (9) | (14) | (14) | (14) | (34) | (18) | (14) | (22) | (14) | (18) | |
SKLDNE | 46.38 | 52.94 | 59.06 | 62.66 | 69.64 | 78.46 | 83.75 | 80.45 | 93.75 | 98.33 | 100 |
(10) | (10) | (14) | (10) | (14) | (30) | (10) | (10) | (34) | (10) | (10) |
Database | Yale Face | ||||
---|---|---|---|---|---|
Tn | 1 | 6 | 7 | 8 | 9 |
PCA | 51.66 | 81.66 | 88.88 | 86.6 | 93 |
(29) | (22) | (26) | (26) | (10) | |
KPCA | 50 | 83.3 | 91 | 86.66 | 93.3 |
(10) | (30) | (30) | (90) | (10) | |
UDP | 49.16 | 81.66 | 88.8 | 90 | 92.9 |
(25) | (50) | (54) | (28) | (18) | |
LPP | 51 | 85 | 91.1 | 96.66 | 93.3 |
(22) | (26) | (30) | (34) | (18) | |
LDA | 50 | 81.66 | 91.1 | 93.3 | 93.3 |
(22) | (18) | (22) | (98) | (50) | |
DNE | 51.66 | 83.3 | 91 | 90 | 93 |
(30) | (30) | (30) | (66) | (10) | |
LDNE | 60 | 83.3 | 88.88 | 93.33 | 100 |
(19) | (50) | (57) | (48) | (42) | |
SKLDNE | 60.83 | 85 | 95.55 | 96.66 | 100 |
(22) | (38) | (62) | (46) | (26) |
Database | ORL Face | |||||
---|---|---|---|---|---|---|
Tn | 1 | 4 | 5 | 6 | 7 | 8 |
PCA | 78.75 | 85.41 | 87.5 | 95.62 | 95.83 | 95.9 |
(30) | (30) | (26) | (20) | (10) | (10) | |
KPCA | 81.56 | 87 | 89 | 96.2 | 96.66 | 96.25 |
(46) | (54) | (66) | (34) | (34) | (20) | |
UDP | 80 | 86.66 | 89.5 | 94.75 | 96.6 | 96 |
(54) | (90) | (98) | (38) | (18) | (14) | |
LPP | 80.62 | 87.5 | 90 | 95 | 95.8 | 97.5 |
(58) | (86) | (94) | (34) | (30) | (62) | |
LDA | 80.93 | 87.91 | 90 | 96.25 | 95.83 | 96 |
(54) | (34) | (38) | (22) | (34) | (18) | |
DNE | 81.56 | 87.08 | 89 | 96.2 | 96.66 | 96.25 |
(46) | (54) | (66) | (34) | (34) | (10) | |
LDNE | 85 | 92 | 92 | 95.6 | 95 | 96.5 |
(26) | (62) | (78) | (30) | (24) | (54) | |
SKLDNE | 85.93 | 93.33 | 94 | 96.87 | 97.5 | 100 |
(38) | (61) | (50) | (66) | (22) | (18) |
Database | Head Pose | |||||
---|---|---|---|---|---|---|
Tn | 30 | 70 | 90 | 110 | 120 | 130 |
PCA | 66.21 | 63.69 | 50.16 | 79.73 | 83.6 | 82.67 |
(30) | (26) | (26) | (26) | (74) | (26) | |
KPCA | 66.38 | 64.31 | 59.37 | 84.86 | 86.22 | 85.71 |
(30) | (70) | (30) | (90) | (22) | (62) | |
UDP | 65.83 | 64.39 | 58.75 | 85.52 | 87.21 | 85.71 |
(6) | (22) | (34) | (98) | (94) | (78) | |
LPP | 68.01 | 64.4 | 59.7 | 85.39 | 88.36 | 87.85 |
(30) | (82) | (26) | (90) | (62) | (50) | |
LDA | 68.21 | 65.14 | 60 | 86.57 | 87.04 | 88.57 |
(6) | (18) | (22) | (98) | (98) | (46) | |
DNE | 66.28 | 64.5 | 58.5 | 84.63 | 86.22 | 85.71 |
(30) | (70) | (30) | (90) | (74) | (62) | |
LDNE | 69.7 | 66.2 | 59 | 96.9 | 98 | 98.02 |
(20) | (19) | (18) | (24) | (18) | (18) | |
SKLDNE | 70.7 | 67.06 | 60.83 | 98.94 | 99.01 | 99.28 |
(30) | (18) | (22) | (22) | (18) | (14) |
Database | Finger Vein | ||||||
---|---|---|---|---|---|---|---|
Tn | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
PCA | 79.66 | 89.37 | 94.85 | 96.3 | 96.41 | 99 | 99.54 |
(30) | (34) | (34) | (26) | (26) | (26) | (27) | |
KPCA | 79.33 | 88.75 | 94.57 | 96.33 | 96.4 | 99.2 | 99.5 |
(30) | (30) | (30) | (30) | (26) | (26) | (27) | |
UDP | 80 | 90.75 | 95.85 | 96.8 | 97 | 99 | 99.5 |
(30) | (30) | (30) | (34) | (30) | (34) | (30) | |
LPP | 79.66 | 89.5 | 94.85 | 96.83 | 96.6 | 99 | 99.56 |
(30) | (22) | (34) | (26) | (22) | (34) | (34) | |
LDA | 79.66 | 91.75 | 96.71 | 97.16 | 98.2 | 99.5 | 99.55 |
(30) | (26) | (30) | (30) | (30) | (22) | (29) | |
DNE | 81 | 90.12 | 95.42 | 97 | 96.8 | 99.15 | 100 |
(90) | (90) | (62) | (86) | (66) | (54) | (86) | |
LDNE | 80.75 | 94.17 | 96.85 | 97.5 | 96.4 | 99.25 | 99.2 |
(86) | (38) | (62) | (76) | (74) | (66) | (42) | |
SKLDNE | 81.22 | 95.38 | 97.71 | 98.5 | 99.2 | 99.75 | 100 |
(54) | (26) | (26) | (34) | (34) | (26) | (26) |
Database | Finger Knuckle | ||||||||
---|---|---|---|---|---|---|---|---|---|
Tn | 1 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
PCA | 50.18 | 67.5 | 68.28 | 59.66 | 75.2 | 92 | 94 | 93 | 97.5 |
(30) | (78) | (94) | (30) | (26) | (82) | (90) | (38) | (40) | |
KPCA | 52.9 | 61.87 | 63.42 | 59.66 | 80.2 | 87.75 | 89.66 | 93 | 97.15 |
(50) | (60) | (39) | (37) | (30) | (25) | (26) | (27) | (20) | |
UDP | 56.18 | 65.25 | 67.14 | 63.88 | 82.2 | 92 | 93.3 | 96.5 | 97 |
(62) | (98) | (90) | (90) | (98) | (98) | (90) | (70) | (35) | |
LPP | 55 | 71 | 72 | 67.5 | 82.2 | 92.5 | 94.2 | 96 | 98 |
(62) | (94) | (94) | (98) | (94) | (98) | (98) | (74) | (86) | |
LDA | 53 | 72.12 | 72.14 | 68.83 | 84.8 | 92.7 | 94.33 | 97 | 98 |
(62) | (94) | (98) | (98) | (90) | (74) | (90) | (82) | (26) | |
DNE | 53.81 | 67.5 | 68.3 | 65.33 | 80.4 | 92 | 94 | 93 | 97 |
(98) | (88) | (94) | (94) | (94) | (82) | (90) | (38) | (20) | |
LDNE | 53.9 | 76.75 | 78 | 72.70 | 84.6 | 92.75 | 94.66 | 93.3 | 97.2 |
(86) | (87) | (86) | (94) | (76) | (34) | (58) | (46) | (26) | |
SKLDNE | 56.36 | 79.37 | 81.42 | 80.16 | 90.6 | 98 | 98.66 | 99 | 100 |
(22) | (86) | (98) | (90) | (66) | (66) | (26) | (22) | (18) |
Method | SKLDNE | LDNE | DNE | KPCA | LDA | LPP | UDP | PCA |
---|---|---|---|---|---|---|---|---|
Time (s) | 0.35 | 0.4 | 0.37 | 0.012 | 0.04 | 0.36 | 0.06 | 0.02 |
Method | 16 × 16 | 32 × 32 | 64 × 64 |
---|---|---|---|
MLP | 64.76 | 84.76 | 86.19 |
DBNs + MLP | 88.57 | 89.05 | 90.95 |
SKLDNE | 100 | 100 | 100 |
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Share and Cite
Khalili Mobarakeh, A.; Cabrera Carrillo, J.A.; Castillo Aguilar, J.J. Robust Face Recognition Based on a New Supervised Kernel Subspace Learning Method. Sensors 2019, 19, 1643. https://doi.org/10.3390/s19071643
Khalili Mobarakeh A, Cabrera Carrillo JA, Castillo Aguilar JJ. Robust Face Recognition Based on a New Supervised Kernel Subspace Learning Method. Sensors. 2019; 19(7):1643. https://doi.org/10.3390/s19071643
Chicago/Turabian StyleKhalili Mobarakeh, Ali, Juan Antonio Cabrera Carrillo, and Juan Jesús Castillo Aguilar. 2019. "Robust Face Recognition Based on a New Supervised Kernel Subspace Learning Method" Sensors 19, no. 7: 1643. https://doi.org/10.3390/s19071643