CN106846437B - A kind of time series data method for visualizing based on spiral figure - Google Patents

Abstract

The invention discloses a time series data visualization method based on a spiral graph, which includes the following steps: first, for a given phased time series, a circle is used to represent a state, and multiple concentric circles represent the phased time series contained State set; Secondly, the reachable path between states is represented by a spiral line, where the color and transparency of the spiral line are related to the type of path and the number of intersections between the path and other paths, and the transparency of the spiral line is based on the relationship between the spiral line and other spiral lines The number of intersections of the lines is calculated using the long-tail algorithm; finally, interactive actions are designed to meet the user's operational needs. Experiments on my country's railway train station data have verified the effectiveness of the model for visualization of phased time series data, and can provide decision support for users in selecting routes between state transitions. The invention solves the problem of effectively displaying paths of any time length in a limited space without increasing the length of the time axis, and assigns transparency to each path by adopting a transparency algorithm based on a long-tail function, reducing the path Cross-overlap brings clutter while effectively preserving data information.

Description

A Time Series Data Visualization Method Based on Spiral Graph

technical field

The invention relates to the field of information visualization, in particular to a time series data visualization method based on a spiral graph.

Background technique

In the daily behavior of human beings, time is the ubiquitous ruler. In today's era of rapid data growth, people generate a large amount of data in their activities, including time series data involving state changes. People often hope to get the pattern of data changing over time from time series data, but it is difficult to quickly obtain effective information from a large amount of data by visually observing it.

Visualization abstracts data into the form of charts, helping people understand obscure data and discover knowledge hidden in data through interaction. The more common visualization forms include line charts, pie charts, scatter plots, and recently more interactive Sankey diagrams, tree diagrams, etc. Different visualization forms are suitable for data with different characteristics. Visualization techniques have achieved remarkable results in displaying time series data, such as curve graphs, themed rivers, tree graphs, spiral graphs, etc. Among them, the spiral graph is an important form of displaying periodic time series data in visualization. The spiral graph can show the continuity of data in time and the change law in different time periods through continuous spiral lines, so it has been widely used in the field of processing periodic continuous data.

The phased time series data type is a special data type that describes the change of the state of an event over time. An event from the start time to the end time contains a total of n states, the event sequentially transitions from state 1 to state n, and the process of transitioning from state i to state i+1 is called phase i, and there are multiple possible reach path. The visualization of phased time series data needs to meet the following requirements: 1. Effectively display the time changes during the state transition process; 2. Good interaction, providing decision support for users to choose paths at various stages; 3. In a limited space Show scalable time length; 4. Satisfy people's aesthetic needs under the condition of ensuring data reliability.

An important feature of the data studied by the present invention is that the time-consuming paths between state transitions are uncertain, and existing visualization methods, such as parallel coordinates and Sankey diagrams, cannot effectively display an expandable time axis. Parallel coordinates and Sankey diagrams use a time axis to represent a state, and the connection between the states represents the reachable path, so when a certain route lasts for a long time, it will inevitably lead to the lengthening of the time axis related to it, which obviously does not conform to Aesthetic requirements for simple and beautiful visualization. The spiral diagram proposed by the present invention can better solve this problem.

Spiral charts are widely used to represent time series data that changes periodically. In 1998, Carils et al. presented a new visualization form for visualizing periodic time series data, and introduced several practical applications of spiral visualization. Different visualization styles can be arranged and laid out on the chart in the style of spiral charts, such as ink dot charts, 3D ring charts, and histograms. The size of these entities represents the size of the value. In 1999, Hewagamage et al. used 3D spiral form to display spatiotemporal data on geographical pictures. In 2001, Weber et al. focused on encoding temporal data using lines and colors. When the amount of data is large, it is proposed to use 3D helix to display the data. In 2002, Dragicevic et al. proposed a new way of visually displaying upcoming events——SpriaClock (spiral clock), which combines spiral diagrams and clock representations, and can better display a series of events that occur in time sequence. In 2005, Tominski et al. proposed to display the 3D helix diagram on the 3D map. It proposed a tunnel view to view more information hidden in the helix diagram for the information hiding brought by the 3D map, and proposed to color-code the helix diagram to display multiple The encoded form of the variable's data. In 2008, Tominski et al. proposed to use TTPC coding method to color-code the spiral graph, so that the values are more clearly identifiable for users. In 2012, Cheng et al. proposed a novel way of polar parallel coordinates to visualize time series data and compared it with traditional parallel coordinates. Polar parallel coordinates can display more coordinates, and can effectively display the periodic characteristics of time series data.

Contents of the invention

In view of the existing visualization forms such as parallel coordinates and Sankey diagrams, and the uncertainty of the time-consuming path between state transitions, the purpose of the present invention is to provide an effective and concise display of the path between state transitions in a limited space Methods of Information - A Spiral Graph-Based Method for Visualizing Time-Series Data.

The specific implementation steps are as follows:

A time series data visualization method based on a spiral graph, which performs the following specific steps in sequence:

Step 1: The input has a set of states S={s ₁ ,...s _i ,...s _n }, and a set of reachable paths between states L={L ₁ ,...L _i ,...L _{n -1} } phased time series data, where n is the number of states, s _i represents the i-th state, the process of transitioning from state i to state i+1 is called stage i, and _Li represents the reachable path of stage i ;

Step 2: Design the state ring according to the state attributes of the state set S, including the state ring radius set R={r ₁ ,...r _i ,...r _n }, the state ring width arcWidth, and the state ring color set Color＝{color ₁ ,...color _i ,...color _n }; the state ring coordinate axis designed according to the state cycle T, wherein, the element r _i in the radius set R represents the outer radius of the state s _i ring, The element color _i in the Color set represents the color of the state s _i , and the state set S is represented as a series of concentric rings with the center of (x _o , y _o );

Step 3: According to the path set L and the state set S, use elliptical sub-lines to complete the line drawing of the path, where the path of each stage in the path set L includes the following attributes: the start time of the path startTime, the arrival time arriveTime, and the elapsed time t. The detailed operation steps are as follows:

Step 3.1: According to the starting time startTime _ik of each path _{li ik} (i=1,2,...n-1; k=1,2,...p _i ; p _i =|L _i |), Arrival time arriveTime _ik , the coordinates of the starting position on the ring of state s _i are (Sx _ik , Sy _ik ), and the coordinates of the arrival position on the ring of state s _i+1 are (Tx _ik , Ty _ik );

Step 3.2: According to the duration t _ik of the path l _ik and the period T of the state circle, obtain the path spiral span △radian _ik =(t _ik /T)*2π, and design the path li _ik as segment _ik =( t _ik /T)*360 segments of elliptical sub-lines;

Step 3.3: Phase i radius span △r _i =r _i+1 -arcWidth-r _i is divided into segment _ik segments, each segment radius span is △r _ik =△r _i /segment _ik , then the ellipse sub-line seg _ikj (j= 1,2,...segment _ik ) has a minor semi-axis a _ikj =ri +△r _ik *(j-1), a major _semi -axis b _ikj = _ri +△r _ik *j, and the ellipse The center of the circle is the same as the center of the state ring;

Step 3.4: Draw path lines according to the above steps.

Step 4: Map the type of path l _ik to the interval [0,1] to obtain l_type _ik , and use l_type _ik as an argument of the unary function y=ax+b, and the obtained y is the color color _ik of _{li ik} ;

Step 5: According to the intersection number crossNum _ik of the path l _ik in stage i and other paths in the stage, use the long-tail function Obtain the transparency transp _ik of the path, where crossNum _ik is the independent variable and transp _ik is the dependent variable;

Step 6: Conduct interaction design.

With such processing, the method of the present invention uses a circle to represent a state, and a spiral line represents a reachable path between states. The model can effectively display paths of any length in a limited space without increasing the length of the time axis. The transparency algorithm based on the long-tail function is used to assign transparency to each path according to the number of intersections between a path and other paths, thereby reducing the clutter caused by overlapping paths and effectively retaining data information. It also provides functions such as path filtering, highlighting, viewing detailed information, zooming, etc., and realizes flexible interactive operations.

Compared with prior art, positive effect of the present invention is:

First, the existing visualization methods for representing time series cannot ensure that the reachable paths between states are represented in a limited and definite space. However, the present invention sets the state in the form of a ring, the radius of each ring is determined, and the path that can be reached between the states is determined in the space between the initial state ring and the end state ring, so it can handle any The length of the path is displayed in time.

2. More path curves displayed in a limited space produce more intersections. We found that using a transparency setting algorithm based on long-tail functions can effectively reduce the number of intersections, and can display all the intersections completely and clearly through some interactive means. reachable path.

Traditional time series visualization methods cannot display all paths in a limited space. However, the present invention finds that the time series data visualization method based on the spiral graph can efficiently solve this problem, and can completely display all the required information, and ensure the cleanliness and convenience of displaying the graph.

Description of drawings

Fig. 1 is the working block diagram of main steps of the present invention.

Fig. 2 is an example diagram of state s _i .

Figure 3 is an example diagram of multiple state visualizations.

Fig. 4 is an example diagram of visualization of multiple state transition paths.

Fig. 5 is a parameter explanatory diagram.

Figure 6 is an example diagram of the transparency setting of the spiral line.

Figure 7 is the result graph of the final data display of the experimental results.

In view of the restrictions on color expression in the drawings of the patent specification, the following explanations are specially made:

The color of the circle in Figure 1 is color _i ;

The colors of the rings in Figure 2 are color ₁ , color ₂ , and color ₃ from the inside to the outside;

The color of the spiral l _1k in stage 1 in Figure 3 is the transition color from color ₁ to color ₂ in Figure 2; the color of the spiral l _2k in stage 2 is the transition color from color ₂ to color ₃ in Figure 2.

In Fig. 7, the color of Chengdu circle is color ₁ , the color of Xi'an circle is color ₂ , and the color of Zhengzhou circle is color ₃ ; the color of the train from Chengdu to Xi'an is the transition color between color ₁ and color ₂ ; the color of the train from Xi'an to Zhengzhou is color ₂ and color 3 The transition color of color ₃ .

Detailed ways

The specific implementation steps are as follows:

Step 1: The input has a set of states S={s ₁ ,...s _i ,...s _n }, and a set of reachable paths between states L={L ₁ ,...L _i ,...L _{n -1} } phased time series data, where n is the number of states, s _i represents the i-th state, the process of transitioning from state i to state i+1 is called stage i, and _Li represents the reachable path of stage i ;

Step 2: Design the state ring according to the attributes of the state set S, including the state ring radius set R={r ₁ ,...r _i ,...r _n }, the state ring width arcWidth, and the state ring color set Color＝{color ₁ ,...color _i ,...color _n }; the state ring coordinate axis designed according to the state cycle T, wherein, the element r _i in the radius set R represents the outer radius of the state s _i ring, The element color _i in the Color set represents the color of the state s _i , and the state set S is represented as a sequence of concentric rings, the center of which is (x _o , y _o );

Step 3: According to the path set L and the state set S, use elliptical sub-lines to complete the line drawing of the path. The path in each stage in the path set L includes the following attributes: the start time of the path startTime, the arrival time arriveTime, and the elapsed time t.

The starting position (Sx _ik , Sy _ik ) of a reachable path l _ik (start time startTime _ik , arrival time arriveTime _ik , duration t _ik ) of stage i is The arrival position (Tx _ik , Ty _ik ) is

The path l _ik is visualized in the form of a spiral line, which is composed of segment _ik segment sub-lines, each sub-line is composed of a section of elliptical arc seg _ikj , and the minor semi-axis a _ikj of each elliptical arc = r _i + △ r _ik *(j-1 ) and b _ikj of the long semi-axis = r _i +△r _ik *j, the end position of seg _ikj (Tx _ikj , Ty _ikj ) is the starting position of seg _ik(j+1) (Sx _ik(j+1) , Sy _ik(j+1) ) is Where Δagl _ik = Δradian _ik /segment _ik .

Step 4: The type of path l _ik is mapped to the interval [0,1] as l_type _ik , and l_type _ik is used as the independent variable of the unary function y=ax+b to obtain the color color ik of the dependent variable _{li ik} .

Since the color of state s _i is color _i and the color of state s _i+1 is color _i+1 , then the color of li _ik can be obtained as color _ik =(color _i+1 -color _i )*l_type _ik +color _i .

Step 5: According to the algorithm To find out whether the path l _ik and the path l _ip intersect, you can find the number crossNum _ik of intersections between the path l _ik and other paths in stage i, and use the long-tail function Find the transparency transp _ik of the path. By setting the maximum transparency transpMax _i and the minimum transparency transpMin _i of the path, and obtaining the maximum crossNumMax _i and the minimum crossNumMin i of the path intersection points in stage _i , then

Step 6: Perform interactive design, including: highlighting the paths in each time interval in stage i by segment, highlighting a path and displaying the path details.

The present invention designs a method that can effectively display any length of time and any number of paths in a limited space. The paths between states exist between the state rings, and according to the number of intersections between paths, according to the long tail The function judges the transparency of the path to improve the clutter caused by a large number of paths to the user.

In order to verify the effectiveness of the present invention, the staged time series visualization model based on the spiral graph is applied to Chinese railway data, aiming to provide decision support for users to choose the route that needs to transfer.

The experimental data comes from the China Railway Ticketing Network www.12306.cn, and the event is defined as the itinerary from Chengdu to Zhengzhou via Xi'an. Then the state set S is {Chengdu, Xi'an, Zhengzhou}, and l _1k (k=1,2,...,11), l _2k (k=1,2,...,68), that is, from Chengdu to Xi'an There are 11 trains available, and 68 trains from Xi'an to Zhengzhou. Train data contains departure time, arrival time, duration, and frequency. According to the time characteristics of the train data, the period of the state is set to 24 hours. In particular, in the train data, since the departure time of trains is not evenly distributed in 24 hours, combining the distribution of departure time and people's travel habits, the period T is divided into 8 segments with a duration of 3 hours.

Claims (1)

1. A time series data visualization method based on a spiral graph, which can effectively visualize phased time series data in a limited space, and execute the following specific steps sequentially: Step 1: The input has a set of states S={s ₁ ,...s _i ,...s _n }, and a set of reachable paths between states L={L ₁ ,...L _i ,...L _{n -1} } phased time series data, where n is the number of states, s _i represents the i-th state, the process of transitioning from state i to state i+1 is called stage i, and _Li represents the reachable path of stage i ; Step 2: Design the state ring according to the state attributes of the state set S, including the state ring radius set R={r ₁ ,...r _i ,...r _n }, the state ring width arcWidth, and the state ring color set Color＝{color ₁ ,...color _i ,...color _n }; the state ring coordinate axis designed according to the state cycle T, wherein, the element r _i in the radius set R represents the outer radius of the state s _i ring, The element color _i in the Color set represents the color of the state s _i , and the state set S is represented as a series of concentric rings with the center of (x _o , y _o ); Step 3: According to the path set L and the state set S, use elliptical sub-lines to complete the line drawing of the path, where each path in the path set L includes the following attributes: start time startTime of the path, arrival time arriveTime, elapsed time t, completion Path drawing; detailed steps are as follows: Step 3.1: According to the starting time startTime _ik of each path _{li ik} (i=1,2,...n-1; k=1,2,...p _i ; p _i =|L _i |), Arrival time arriveTime _ik , the coordinates of the starting position on the ring of state s _i are (Sxi _ik ,Sy _ik ), and the coordinates of the arrival position on the ring of state s _i+1 are (Tx _ik ,Ty _ik ); where: The starting position (Sx _ik ,Sy _ik ) of a reachable path _{li ik} in stage i is The arrival position (Tx _ik , Ty _ik ) is Step 3.2: According to the duration t _ik of the path l _ik and the period T of the state circle, obtain the path spiral span △radian _ik =(t _ik /T)*2π, and design the path li _ik as segment _ik =( t _ik /T)*360 segments of elliptical sub-lines; Step 3.3: Stage i ring width △r _i =r _i+1 -arcWidth-r _i is divided into segment _ik segments, each sub-line width is △r _ik =△r _i /segment _ik , then the ellipse sub-line seg _ikj (j =1,2,...,segment _ik ) has a minor semi-axis a _ikj =ri +△r _ik *(j-1), a major _semi -axis b _ikj = _ri +△r _ik *j, and The center of the ellipse is the same as the center of the state ring; The end position of seg _ikj (Tx _ikj , Ty _ikj ) is the starting position of seg _ik(j+1) (Sx _ik(j+1) , Sy _ik(j+1) ) is Where △agl _ik = △radian _ik /segment _ik ; Step 3.4: Draw path lines according to the above steps; Step 4: The type of path l _ik is mapped to the interval [0,1] as l_type _ik , the color of state s _i is color _i , and the color of state s _i+1 is color _i+1 , then the color of l _ik can be obtained For color _ik = (color _i+1 -color _i )*l_type _ik +color _i ; Step 5: Calculate the number of paths crossNum _ik intersecting with path l _ik in stage i, using the long-tail function Find the transparency transp _ik of the path, where crossNum _ik is the independent variable and transp _ik is the dependent variable; according to the algorithm To find out whether the path l _ik and the path l _ip intersect, you can find the number crossNum _ik of intersections between the path l _ik and other paths in stage i, and use the long-tail function Obtain the transparency transp _ik of the path; by setting the maximum transparency transpMax _i and the minimum transparency transpMin _i of the path, and obtain the maximum crossNumMax _i and the minimum crossNumMin i of the path intersection points in stage _i , then Step 6: Conduct interaction design.