JP5824412B2 - Graph data visualization device, method and program - Google Patents

Description

  The present invention relates to a graph data visualization apparatus, method, and program, and more particularly, to a graph data visualization apparatus, method, and program for visualizing graph data that includes a plurality of nodes and edges that connect the nodes.

  The technology for visualizing a network as a graph (hereinafter simply referred to as “visualization technology”) generally visualizes graph data that forms a network by the relationship between data and data by projecting it onto a low-dimensional phase space. Refers to that. The graph data can be visualized by expressing it with a node indicating the element and an edge connecting the nodes. For example, in the case of a web page with a hyperlink on the Internet, the graph can be visualized and displayed by representing each web page as a node and the hyperlink as an edge. In addition, for example, network display such as finance / communication / transport / social organization / gene information, graph display of data such as chemistry / biology / medicine, and graph display of text data and image data based on relevance Various applications such as a display of a combination, a combination display of related module groups (for example, an LSI design drawing of an IC chip), a label display used for an illustration display of a map or a reference book, and the like can be considered. Therefore, a graph visualization display technique using a mechanical algorithm by a computer is a technique in demand in a very wide range of fields.

<Conditions>
An important and greatest object in the graph visualization display technology is preferably to satisfy the following two conditions as much as possible on the graph visualization display device.

  [Condition 1] Arrange the nodes so as not to overlap each other.

  [Condition 2] Relevant nodes are connected to each other via edges and arranged in the vicinity.

  These conditions are shown in FIG. [Condition 1] is to prevent misreading of information due to overlapping display of different node information. [Condition 2] is to improve the visual information recognition system by arranging related nodes in the vicinity.

  In order to satisfy the above two conditions, it is necessary to obtain the arrangement coordinates of the node on the graph visualization display device.

<Related technologies>
[Basic technology]
Conventionally, a technique using a dynamic model has been widely used as a graph visualization display technique for satisfying the above conditions, and the following two are most frequently used all over the world.

  Spring model method: A method in which virtual springs are assumed between all nodes, and a coordinate update method is sequentially performed node by node. In general, the number of shortest path paths on the graph between the nodes is calculated as the natural length of the spring between the nodes (for example, see Non-Patent Document 1).

  Force-directed method: A repulsive force is applied between all nodes (for example, Coulomb repulsive force acting between molecules), an attractive force is applied between connected nodes (edges), and a coordinate update method is used as this attractive force. The total sum of repulsive forces is used for updating (for example, see Non-Patent Document 2).

  In any of the above two methods, a repulsive force acts between all the nodes, and it is possible to eliminate the overlap between nodes required by [Condition 1]. In addition, an attractive force works between the nodes to be connected, so that it is possible to place the connection node in the vicinity, which is required in [Condition 2].

  In the above two methods, when the attractive and repulsive functions are uniquely determined, the coordinates are set so that the objective function converges (maximum entropy is obtained) using a numerical calculation method such as the steepest descent method or Newton method. Update.

  However, in the above-described graph visualization display technology, it is often very difficult to satisfy [Condition 2] in order to embed graph data having a complicated network structure in a low dimension (particularly two dimensions). In particular, when there are a large number of edge-connected nodes (so-called high-order nodes), it becomes very difficult to arrange all the nodes to be connected in the vicinity, resulting in a problem that long edges are generated. .

To solve this problem, the edge length is usually made redundant, and the overall arrangement is made so as not to cause an extremely long edge. However, there is a limit to making the edge length redundant, and as an approach to solving this problem,
[Approach 1] Cutting edges (allowing extremely long edges);
[Approach 2] Divide the nodes;
A solution can be considered.

  In [Approach 1], as a representative method, there is a graph visualization calculation method using the LGL method (for example, see Non-Patent Document 3). In the LGL method, a minimum spanning tree is created from a graph data structure, and the entire structure is hierarchized by cutting the edges, thereby arranging nodes that are totally connected in the vicinity. However, in [Approach 1] including the LGL method, the relevance regarding the network structure is ignored in the first place, and the above [Condition 2] cannot be satisfied. Therefore, it is not included as a competitive technology of the present invention.

  Unlike [Approach 1], the method of dividing a node in [Approach 2] can store edge connection information. In the present invention, a method for efficiently performing “dividing a node” in [Approach 2] is presented.

Kamada, T., and Kawai, S .: An algorithm for drawing general undirected graphs, Information Processing Letters, 12, 31, 7-15 (1989). Fruchterman, T. M. J., Reingold, E. M .: Graph Drawing by Force-directed Placement, Software-Practice and Experience, 11, 21, 1129-1174 (1991). Adai, LGL: creating a map of protein function with an algorithm for visualizing very large biological networks Lyon, B .: The Opte Project (2005) http://www.opte.org/

  For the above-described graph visualization display technique, a fundamental requirement is that “nodes connected by edges are arranged in the vicinity without generating extremely long edges”. Specifically, graph data within a window displayed on the display device of a personal computer or within the size of image data that can be printed (in reality, hundreds to thousands of nodes) is displayed in the window. It is necessary to arrange so that the data structure of the graph can be understood sufficiently. At this time, it is required to satisfy the above two conditions “nodes do not overlap” and “relevant things are arranged in the vicinity”.

  Usually, when one node is connected to a plurality of nodes and the node belongs to a plurality of topics, the visualization result is destroyed for the node, and the readability cannot be satisfied. For example, as shown in FIG. 2, the influence of “site A” is large, and the connection between “site A” and “maternity”, “milk”, “toy”, etc. is difficult to understand. In addition, it is difficult to intuitively understand why "Pa League" and "tea" are nearby.

  The present invention has been made in view of the above points, and in the graph visualization display technology, the nodes do not overlap each other with respect to the visualization result in which the connection-related readability is not sufficiently satisfied for the high-order nodes, and An object of the present invention is to provide a graph data visualization apparatus, method, and program capable of satisfying the two conditions of being related in the vicinity and enhancing the readability of the connection relation between nodes.

In order to solve the above problems, the present invention (Claim 1) is a graph data visualization device for visualizing graph data composed of a plurality of nodes and edges connecting the nodes,
Wherein the memory means is read graph data, the number of edges connecting the said graph data (hereinafter, referred to as "order") based on the angle and the distribution of the length of the respective edges between the edges extending from a large node And a visualization means for dividing the set of nodes and mapping them into a two-dimensional space.

Further, according to the present invention (Claim 2), in the visualization means,
For the graph data, optimization calculation means for performing optimization calculation of the coordinates of the node according to a predetermined dynamic model,
From the optimization result of the optimization calculation means, the average value and distribution of edge lengths connected to each node are calculated, the length of the edge connected to each node and the angle of the vector centered on the node, A split node determining unit that calculates a distribution of lengths and determines a node set in which the angle and length of the vector deviate from the average value as split node candidates;
Node dividing means for dividing the divided node candidate from the graph data;
Means for executing the optimization calculation means for the graph data divided by the node dividing means.

  As described above, according to the present invention, when there are many extended edges in the graph visualization result of the graph data, the readability when arranging related nodes in the graph visualization display in the vicinity is improved. And maintaining the proximity by dividing the node.

It is a figure which shows the conditions in a graph visualization apparatus. It is an example of graph data. It is a block diagram of the graph data visualization apparatus in one embodiment of this invention. It is an example of the division node candidate selection of the division node determination process part in one embodiment of this invention. It is an example of the node division | segmentation by the node division | segmentation process part in one embodiment of this invention. It is a flowchart of the processing apparatus in one embodiment of this invention. It is FIG. (1) for demonstrating the node division | segmentation process in one embodiment of this invention. It is FIG. (2) for demonstrating the node division | segmentation process in one embodiment of this invention. It is FIG. (3) for demonstrating the node division | segmentation process in one embodiment of this invention.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

  FIG. 3 shows the configuration of the graph data visualization apparatus in one embodiment of the present invention. The configuration shown in the figure shows the configuration of a computer system as a graph data visualization device.

  The graph visualization device 10 shown in the figure includes a processing device (CPU) 11 that executes graph visualization display processing by program control, a main memory 12 that stores a program for controlling the processing device 11, and a graph generated by the processing device 11. A display device 13 that displays a visualized image of data and a storage device 14 that stores graph data to be processed are provided.

  The processing device 11 includes a node arrangement coordinate optimization processing unit 21, a split node determination processing unit 22, and a node split processing unit 23. In the figure, only the configuration for realizing the present embodiment is shown. Actually, in addition to the configuration shown in the figure, it is assumed that an input device such as a keyboard and a mouse for inputting various commands and data, various peripheral devices, an interface for a network, and the like are provided.

  The node arrangement coordinate optimization processing unit 21 of the processing device 11 performs optimization calculation of node coordinates in accordance with a predetermined dynamic model added based on the graph data.

  The split node determination processing unit 22 of the processing device 11 extracts split node candidates. Specifically, as shown in FIG. 4, a node having a long edge is extracted as a candidate for a split node (in the case of FIG. 4, site A).

  The node division processing unit 23 of the processing device 11 divides the node and the edge when the candidate for the division node is extracted by the division node determination processing unit 22. For example, in the example of FIG. 4, the site A is divided as shown in FIG.

  In addition to the above configuration, the graph visualization device 10 has a memory (not shown) used in the processing device 11 and stores intermediate calculation results.

  FIG. 6 is a flowchart of the processing apparatus according to the embodiment of the present invention.

  Step 201) The node arrangement coordinate optimization processing unit 21 reads graph data from the storage device 14.

  Step 202) The node arrangement coordinate optimization processing unit 21 calculates and updates the optimum arrangement of the node from the equation of motion according to a predetermined dynamic model, and stores it in a memory (not shown).

  Step 203) The split node determination processing unit 22 obtains the distribution of the lengths of the edges connected to each node when the nodes are arranged by the graph visualization calculation, and selects a node having a large average or variance as a candidate node. Extract and store in memory (not shown).

  Step 204) If there is no candidate node extracted in step 203, the process is terminated. If there is a candidate node, the process proceeds to step 205.

  Step 205) The node division processing unit 23 divides a candidate node, particularly a node having a high centrality, when receiving force from all directions. As a concrete method, when there is a bias in the length of the edge connected to an arbitrary node and there are many long edges, the nodes are divided by grouping the long edges facing the same direction. To do. In the example of FIG. 5, by dividing the node of “site A”, it becomes easy to understand the connection between “site A” and “maternity” “milk” “toy” and the like, and “pa league” and “ The reason why "tea" is nearby is also intuitively understandable. For example, it is an effective means for comparing visualization results of EC (Electronic Commerce) sites that handle all genres, such as purchase log data, and specialized EC sites.

  After the processing, the process proceeds to step 202, and the optimum arrangement is calculated again.

  If there are no extraction candidates in step 204 above, the division result (image data) is output to the display device 13.

  Hereinafter, the processing of the processing device 11 will be described in detail.

  7 to 9 are diagrams for explaining the node division processing according to the embodiment of the present invention.

  FIG. 7A shows the structure of the graph data. The graph data has items of ID, order, and connection destination. The order is the number of connected edges. FIG.7 (b) shows the graph visualization result performed based on the data of Fig.7 (a). FIG. 7C is an example of a calculation result of a distribution of average lengths of edges connected to each node from the visualization result of FIG. These calculation results are stored in a memory (not shown).

  When the node arrangement coordinate optimization processing unit 21 performs graph visualization calculation based on the graph data of FIG. 7A, a result as shown in FIG. 7B is obtained. As a result, the split node determination processing unit 22 determines a candidate node to be split based on the degree distribution of each node, the average value or variance of edges connected to each node, and the like. In this case, as shown in FIG. 7C, “ID: 5” having a large degree, average, and variance is selected. At this time, it may be determined simply from the order. This is because, when the degree (number of edges) is small, the variance or average becomes relatively large. Therefore, if the decision is made only by the variance or average, a node with a low degree is preferentially selected.

  As shown in FIG. 8D, the split node determination processing unit 22 calculates the distribution of the angle Θ and the edge length of each edge with respect to the selected node of “ID: 5”. Next, FIG. 8E illustrates the obtained edge angle Θ and the length of the edge. The split node determination processing unit 22 extends the edge long and extends in the same direction. Select “ID: 1”, “ID: 2”, “ID: 3” (ID surrounded by a dotted line). In FIG. 8F, in the node division processing unit 23, “ID: 5” is a node “ID: 5 ′” that connects the selected “ID: 1”, “ID: 2”, and “ID: 3” with an edge. And graph data divided into “ID: 5 ″” connecting the remaining nodes. The result of the visualization calculation performed by the node arrangement coordinate optimization processing unit 21 using the graph data of FIG. 8F obtained by dividing “ID: 5” is shown on the left side of FIG. At this time, depending on the purpose, as shown on the right side of FIG. 9G, the graph visualization calculation may be performed by connecting “ID: 5 ′” and “ID: 5 ″”.

  The processing of the node arrangement coordinate optimization processing unit 21, the split node determination processing unit 22, and the node split processing unit 23 of the processing device 11 is constructed as a program and stored in the main memory 12 of the graph visualization display device. Besides being executed, it can be installed and executed on a computer used as a graph visualization device, or distributed via a network.

  The present invention is not limited to the above-described embodiments, and various modifications and applications are possible within the scope of the claims.

DESCRIPTION OF SYMBOLS 10 Graph visualization apparatus 11 Processing apparatus 12 Main memory 13 Display apparatus 21 Node arrangement coordinate optimization process part 22 Split node determination process part 23 Node split process part

Claims (5)

A graph data visualization device for visualizing graph data composed of a plurality of nodes and edges connecting the nodes,
Wherein the memory means is read graph data, the number of edges connecting the said graph data (hereinafter, referred to as "order") based on the angle and the distribution of the length of the respective edges between the edges extending from a large node And a graph data visualization device characterized by having a visualization means for dividing a set of nodes and mapping them to a two-dimensional space. The visualization means includes:
For the graph data, optimization calculation means for performing optimization calculation of the coordinates of the node according to a predetermined dynamic model,
From the optimization result of the optimization calculation means, the average value and distribution of edge lengths connected to each node are calculated, the length of the edge connected to each node and the angle of the vector centered on the node, A split node determining unit that calculates a distribution of lengths and determines a node set in which the angle and length of the vector deviate from the average value as split node candidates;
Node dividing means for dividing the divided node candidate from the graph data;
Means for executing the optimization calculation means for the graph data divided by the node dividing means;
The graph data visualization apparatus according to claim 1, comprising: A graph data visualization method for visualizing graph data composed of a plurality of nodes and edges connecting the nodes,
Wherein the memory means is read graph data, the number of edges connecting the said graph data (hereinafter, referred to as "order") based on the angle and the distribution of the length of the respective edges between the edges extending from a large node Then, a graph data visualization method characterized by performing a visualization step of dividing a set of nodes and mapping to a two-dimensional space. In the visualization step,
For the graph data, an optimization calculation step for performing optimization calculation of the coordinates of the node according to a predetermined dynamic model,
From the optimization result of the optimization calculation step, the average value and distribution of the edge lengths connected to each node are calculated, the length of the edge connected to each node and the angle of the vector centered on the node, A split node determining step of calculating a distribution of lengths and determining a set of nodes whose vector angles and lengths deviate from the average value as split node candidates;
A node dividing step of dividing the divided node candidate from the graph data;
Is repeated until there are no more split node candidates.
The graph data visualization method according to claim 3. Computer
A graph data visualization program for functioning as each means of the graph data visualization device according to claim 1.

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