Graph evaluation device, processing device, graph evaluation method, processing method and program

Abstract

To evaluate the reproducibility of data using a graph represented by using nodes and edges.SOLUTION: A graph evaluation apparatus includes an evaluation index calculation processing unit which calculates an index for evaluating a graph model represented by a graph structure represented with nodes and edges and a probability parameter indicating occurrence probability of the graph structure for each node pass-through pattern. The evaluation index calculation processing unit includes: a likelihood calculation unit which calculates likelihood of past-result pass-through pattern which is past-result node pass-through pattern in the graph mode, on the basis of the probability parameter for each node pass-through pattern; and an evaluation index calculation unit which calculates a first evaluation index for evaluation the reproducibility of the past-result pass-through pattern on the basis of the likelihood of the past-result pass-through pattern.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a graph evaluation device, a graph evaluation method, and a program for evaluating a graph represented using nodes and edges, and to a processing device and a processing method for processing the information obtained thereby. [Background technology]

[0002] A graph is a collection of nodes and edges, and it can model the relationships (networks) between nodes. Such graphs can represent elements (nodes) and connections (edges) in networks such as transportation networks and logistics networks. Based on these graphs, analyses such as efficiency and productivity can be performed.

[0003] For example, in the steelmaking process, the final product is obtained through the processing of intermediate materials in numerous steps. To improve productivity, it is important to maximize the utilization rate of equipment in each step, and to improve equipment utilization, it is necessary to accurately predict and control the inventory status of storage areas where intermediate materials are temporarily stored between equipment. For example, if there is a shortage of materials in the front storage area where the materials to be processed by the equipment are stored, the equipment will not have enough materials to be processed, causing the equipment to shut down. Also, if the rear storage area where the processed materials processed by the equipment are stored becomes full, it will become impossible to discharge the processed materials from the equipment, leading to a decrease in equipment utilization. Therefore, by visualizing the logistics in the steelmaking process using graphs, it is possible to identify equipment, storage areas, and conveying equipment that are bottlenecks, and to consider the measures necessary to improve productivity.

[0004] If all the configurations and connections of the network being graphed are represented directly in the graph, the more complex the network, the more cumbersome the graph becomes, and its readability decreases. Furthermore, if a simulation is performed based on the created graph, the simulation load increases. For this reason, graphs are simplified by aggregating or deleting nodes to prevent the loss of information.

[0005] For example, there is a network analysis technique that unearths characteristic subgraphs from large graphs. As a method of network analysis, for example in the field of graph theory, a method has been proposed to simplify graphs by maximizing the modularity, an indicator representing the quality of clustering, in the Min-cut method, which divides nodes so that the number of edges within a cluster is maximized and the number of edges between clusters is minimized. Patent Document 1 discloses a method in which nodes that have only one edge in the input graph data are considered to be in the same cluster as the node and adjacent nodes, and are aggregated into a single node. Patent Document 2 discloses a method in which the nodes of a graph are divided into N groups, the graph is classified into clusters from these N groups according to modularity, and multiple nodes that belong to the same cluster are aggregated into a single node.

[0006] Furthermore, process mining is a technique that estimates the structure of a process as a network from historical data. In process mining, methods for simplifying the network are also being considered; for example, Non-Patent Document 1 proposes a method for deleting or aggregating infrequently occurring nodes or edges. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Japanese Patent Publication No. 2013-156698 [Patent Document 2] Japanese Patent Publication No. 2017-204161 [Non-patent literature]

[0008] [Non-Patent Document 1] Christian W. Gueunther and Wil M.P. van der Aalst “Fuzzy Mining - Adaptive Process Simplification Based on Multi-perspective Metrics”, Business Process Management. BPM 2007. Lecture Notes in Computer Science, vol 4714. [Searched on September 22, 2022], Internet <URL:https: / / doi.org / 10.1007 / 978-3-540-75183-0_24> [Summary of the Invention] [Problem to be Solved by the Invention]

[0009] However, the network analysis techniques described in the above Patent Document 1, Patent Document 2, etc. focus only on the relationship between two nodes, and aggregate the graph structure according to an index representing the quality of clustering. For this reason, graphs simplified by the methods described in the above Patent Document 1, Patent Document 2, etc. do not consider the passing order of nodes. When the original graph represents a network with an order of passage and flow, such as a logistics network, information loss of the original graph occurs.

[0010] Further, in the process mining techniques described in the above Non-Patent Document 1, etc., nodes and edges are deleted or aggregated without considering the roles of the nodes. For this reason, when the original graph represents a network with an order of passage and flow such as a logistics network, the graph simplified by the method described in the above Non-Patent Document 1 may lack actually possible flows or aggregate nodes with different roles, resulting in a large deviation from the graph representing the actual network.

[0011] Thus, in graphs representing networks, the degree to which a simplified graph retains information from the original graph (i.e., the reproducibility of the data by the graph) may be low. If a simplified graph fails to retain information from the original graph, it may be impossible to correctly recognize the network state using the simplified graph, or the accuracy of the analysis may decrease. For this reason, there is a need for a method to evaluate the reproducibility of data by a simplified graph.

[0012] Therefore, the present invention has been made in view of the above problems, and the object of the present invention is to provide a graph evaluation device, a graph evaluation method and a program capable of evaluating the reproducibility of data using a graph represented with nodes and edges, and a processing device and a processing method for processing the information obtained thereby. [Means for solving the problem]

[0013] To solve the above problems, according to one aspect of the present invention, a graph evaluation device is provided which includes an evaluation index calculation processing unit that calculates an index for evaluating a graph model represented by a graph structure represented using nodes and edges and probability parameters representing the probability of occurrence for each node passage pattern of the graph structure, the evaluation index calculation processing unit having a likelihood calculation unit that calculates the likelihood of the actual passage pattern, which is the actual node passage pattern in the graph model, based on the probability parameters for each node passage pattern, and an evaluation index calculation unit that calculates a first evaluation index for evaluating the reproducibility of the actual passage pattern based on the likelihood of the actual passage pattern.

[0014] The probability parameter is a value set to maximize the likelihood of the actual passing pattern, and the evaluation indicator calculation unit may calculate the maximum likelihood or maximum log-likelihood of the actual passing pattern as the first evaluation indicator.

[0015] The probability parameter is a value set to maximize the likelihood of the actual passing pattern based on the number of occurrences of the actual passing pattern included in the smoothed node passing pattern, and the evaluation index calculation unit may calculate the maximum likelihood or maximum log-likelihood of the actual passing pattern based on the number of occurrences of each node passing pattern after smoothing.

[0016] The evaluation index calculation processing unit may include a performance passage pattern generation unit that generates performance passage patterns from performance data, a node passage pattern generation unit that generates node passage patterns based on the graph structure of the graph model, and a probability parameter setting unit that sets probability parameters for each node passage pattern of the graph model.

[0017] The evaluation index calculation unit may calculate a second evaluation index that represents the complexity of the graph model based on the number of node traversal patterns included in the graph model and the weight coefficients.

[0018] The evaluation index calculation unit may calculate the sum of the first evaluation index and the second evaluation index as the evaluation index for the graph model.

[0019] The graph evaluation device may include a search unit that searches for the optimal graph model that best suits the purpose based on evaluation metrics, the reproducibility and complexity of the graph model. In this case, the evaluation metric calculation processing unit calculates evaluation metrics for each of several different graph models, and the search unit selects the graph model with the smallest evaluation metric among the several graph models as the optimal graph model.

[0020] The evaluation index calculation processing unit may output to the processing unit at least one of the following: the graph structure of the graph model for which the first evaluation index was calculated, the probability parameters, or an index for evaluating the graph model.

[0021] Furthermore, in order to solve the above problems, according to another aspect of the present invention, a processing device is provided that receives at least one of the following: the graph structure of the graph model calculated by the graph evaluation device described above, probability parameters, or an index for evaluating the graph model, and processes the received information.

[0022] Furthermore, in order to solve the above problems, according to another aspect of the present invention, a graph evaluation method by a graph evaluation device is provided, comprising: a likelihood calculation step of calculating the likelihood of actual passing patterns, which are actual node passing patterns, based on the probability parameter for each node passing pattern, for a graph model represented by a graph structure represented using nodes and edges and probability parameters representing the probability of occurrence for each node passing pattern of the graph structure; and a first evaluation index calculation step of calculating an evaluation index, which includes a first evaluation index for evaluating the reproducibility of actual passing patterns by the graph model, based on the likelihood of the actual passing patterns, as an index for evaluating the graph model.

[0023] Furthermore, in order to solve the above problems, according to another aspect of the present invention, a processing method is provided which receives at least one of the graph structure, probability parameters, or indicators for evaluating the graph model calculated by the graph evaluation method described above, and processes the received information.

[0024] Furthermore, in order to solve the above problems, according to another aspect of the present invention, a program is provided for a computer to perform the following actions for a graph model represented by a graph structure represented using nodes and edges and probability parameters representing the probability of occurrence for each node passage pattern of the graph structure: calculate the likelihood of the actual passage pattern, which is the actual node passage pattern, based on the probability parameters for each node passage pattern; and calculate a first evaluation index for evaluating the reproducibility of the actual passage pattern by the graph model, based on the likelihood of the actual passage pattern, as an index for evaluating the graph model. [Effects of the Invention]

[0025] As described above, the present invention makes it possible to evaluate the reproducibility of data using graphs represented with nodes and edges. The information obtained in this process can be used for presenting the evaluation results of the graph, analyzing the network, and performing simulations. [Brief explanation of the drawing]

[0026] [Figure 1] This is an explanatory diagram showing examples of a graph representing a logistics network and a simplified graph. [Figure 2] This flowchart illustrates the method for evaluating the reproducibility of data using graphs in the present invention. [Figure 3] This is a functional block diagram of a graph evaluation device according to the first embodiment of the present invention. [Figure 4] This flowchart shows an example of a graph evaluation method according to the same embodiment. [Figure 5] This is an explanatory diagram showing an example of actual data for a coil logistics network. [Figure 6] This graph shows an example of the original graph and a simplified graph created from the actual data in Figure 5. [Figure 7] As an example of graph structure data, this is an explanatory diagram showing the adjacency matrix, which is a matrix representation of the graph structure of graph A. [Figure 8] As an example of a performance-based success pattern, this table shows the performance-based success pattern in Graph A. [Figure 9] As an example of a node traversal pattern, this table shows the node traversal patterns in Graph B. [Figure 10] This table shows the maximum likelihood estimates calculated as probability parameters for each node traversal pattern in Graph B. [Figure 11] The table below shows the results of calculating the likelihood and log-likelihood of the actual passing patterns for Graph B. [Figure 12] This is a functional block diagram of a graph evaluation device according to a second embodiment of the present invention. [Figure 13]This flowchart shows an example of a graph evaluation method according to the same embodiment. [Figure 14] This is an explanatory diagram showing an example of a group of simplified graphs (graphs C to I) obtained as neighborhood solutions to graph B. [Figure 15] Graphs A through I are bar graphs showing the values ​​of the evaluation metrics. [Figure 16] This block diagram shows an example of a hardware configuration diagram for an information processing device that functions as a graph evaluation device according to the present invention. [Modes for carrying out the invention]

[0027] Preferred embodiments of the present invention will be described in detail below with reference to the attached drawings. In this specification and drawings, components having substantially the same functional configuration are denoted by the same reference numerals, and redundant descriptions will be omitted.

[0028] [1. Overview] This invention relates to a method for evaluating a graph model represented by a graph structure using nodes and edges, and probability parameters representing the probability of occurrence for each node traversal pattern of the graph structure.

[0029] For example, by visualizing the logistics network in the steelmaking process as a graph, which shows the stages through which products (intermediate materials) are distributed, including equipment, storage areas, and transport devices, it becomes possible to identify processes that are bottlenecks causing a decrease in production volume, such as a decline in equipment utilization. Figure 1 shows an example of Graph Go, which represents the logistics network, and a simplified graph Gs, which is a simplified version of Graph Go. Graph Go on the left side of Figure 1 directly represents the connections (edges) in logistics between all the target elements (nodes), such as equipment, storage areas, and transport devices. In complex networks like the logistics network of the steelmaking process, Graph Go accurately represents the information but becomes cumbersome, making it difficult to identify bottleneck processes at a glance. Therefore, by deleting or aggregating nodes and edges to simplify the elements and connections of the network represented by Graph Go and modeling them, the visibility of bottleneck processes and processes that affect them is improved.

[0030] For example, as shown on the right side of Figure 1, a simplified graph Gs is created by simplifying graph Go using nodes (○, □, ◇) representing the processes that are bottlenecks and the processes that affect them, and edges that show the connections between these nodes. The thickness of the edge lines represents the volume of goods being transported, with thicker lines indicating a higher volume of goods. Using such a simplified graph Gs, it is possible to easily identify processes where goods are concentrated and to consider countermeasures to eliminate the bottleneck.

[0031] Here, since the simplified graph Gs is created by aggregating and deleting nodes and edges, there is a possibility that information from the original graph Go may be lost or that it may contain information that is not actually possible. If the simplified graph Gs does not retain the information from the original graph Go, it may not be possible to correctly recognize the state of the network using the simplified graph Gs, or the accuracy of the analysis may decrease. Therefore, the present invention proposes a method for evaluating the reproducibility of a graph model represented by the graph structure of the graph to be evaluated (e.g., the simplified graph Gs) represented using nodes and edges, and probability parameters that represent the probability of occurrence for each node traversal pattern of the said graph structure.

[0032] Figure 2 shows the flow of the method for evaluating the reproducibility of the graph model in the present invention.

[0033] First, as shown in Figure 2, the likelihood of the actual passage patterns in the graph model is calculated (S10) based on probability parameters that represent the probability of occurrence for each node passage pattern in the graph model. The graph model to be evaluated is represented by a graph structure using nodes and edges, and probability parameters that represent the probability of occurrence for each node passage pattern in the graph structure. A node passage pattern is a path represented by nodes and edges, and for example, in a logistics network, it shows the order in which goods pass through the process. In other words, a node passage pattern can also be said to be a path that exists in the graph structure. The probability parameter indicates the probability that a node passage pattern in the graph model can actually occur. The value of the probability parameter can be set arbitrarily, and for example, a value set to maximize the likelihood of the actual passage pattern (i.e., the maximum likelihood estimate) may be used. In step S10, the likelihood of the actual passage pattern is calculated based on the probability parameters for each node passage pattern represented by the graph model.

[0034] Next, based on the likelihood of the actual route pattern calculated in step S10, a first evaluation index is calculated to evaluate the reproducibility of the graph model as an index for evaluating the graph model (S20). Here, the reproducibility of the graph model refers to the degree to which the original actual data is maintained when actual data is shown based on the graph model. The actual data is data that includes route information (see Figure 5 described later) that shows actual routes in the actual network to be represented by the graph structure (graph). Note that the actual data shown based on the graph model and the original actual data may be the same or different. The first evaluation index can be expressed as, for example, the maximum likelihood, the maximum log-likelihood, etc. By calculating the first evaluation index for the graph model of the simplified graph Gs, for example, the degree of information loss can be determined from the difference from the first evaluation index of the original graph Go, and a graph model with higher reproducibility can be identified from the difference with the first evaluation index of other graph models.

[0035] The following will provide a detailed explanation of a graph evaluation device and a graph evaluation method according to one embodiment of the present invention.

[0036] [2. First Embodiment] [2-1. Graph Evaluation Device] First, a graph evaluation device 100 according to the first embodiment of the present invention will be described based on Figure 3. Figure 3 is a functional block diagram of the graph evaluation device 100 according to this embodiment. As shown in Figure 3, the graph evaluation device 100 according to this embodiment includes a performance data acquisition unit 110, a graph acquisition unit 120, and an evaluation index calculation processing unit 130.

[0037] (Performance Data Acquisition Department) The performance data acquisition unit 110 acquires performance data from the performance data storage unit 210, which stores performance data in the network. The performance data storage unit 210 stores the order in which processes are passed, represented by the nodes and edges of a graph, as performance data. For example, the performance data storage unit 210 stores the order in which coils manufactured in the steelmaking process pass through as performance data (see Figure 5, described later). The performance data acquisition unit 110 outputs the acquired performance data to the graph acquisition unit 120.

[0038] (Graph acquisition section) The graph acquisition unit 120 acquires graph structure data representing the graph structure of the graph model to be evaluated. The graph structure is information that represents the relationships between nodes using nodes and edges. The graph structure represents a directed graph represented by nodes and edges.

[0039] The graph acquisition unit 120 may, for example, acquire pre-created graph structure data from the graph structure data storage unit 220. The graph structure data storage unit 220 stores multiple different graph structure data. These graph structure data represent the graph structures of multiple different graph models, simplified by aggregating or deleting nodes and edges of the graph representing the network. The graph structure data stored in the graph structure data storage unit 220 may be created by the user, or it may be automatically created from the graph structure of the original graph by executing a program that aggregates or deletes nodes and edges of the graph.

[0040] Alternatively, the graph acquisition unit 120 may acquire graph structure data by creating a graph structure of a graph model by aggregating or deleting nodes and edges based on the graph structure of the original graph obtained from the actual data acquisition unit 110.

[0041] The graph acquisition unit 120 may acquire, for example, an adjacency matrix (see Figure 7, described later) which is a matrix representation of the graph structure, as graph structure data. The graph acquisition unit 120 outputs the acquired graph structure data to the evaluation index calculation processing unit 130.

[0042] (Evaluation indicator calculation processing unit) The evaluation index calculation processing unit 130 calculates a first evaluation index for evaluating the reproducibility of the graph model as an index for evaluating the graph model. First, the evaluation index calculation processing unit 130 sets probability parameters for each node passage pattern for the graph structure data acquired by the graph acquisition unit 120. The probability parameters may be set to any value, for example, a value set to maximize the likelihood of the actual passage pattern.

[0043] The value of the probability parameter that maximizes the likelihood of the actual passage pattern can be calculated, for example, using the maximum likelihood estimation method. Specifically, the evaluation index calculation processing unit 130 first creates the actual node passage patterns (i.e., actual passage patterns) shown in the original graph from the actual data acquired by the actual data acquisition unit 110. Then, the evaluation index calculation processing unit 130 calculates the probability of these actual passage patterns occurring in each node passage pattern of the graph model and uses this as the value of the probability parameter for each node passage pattern.

[0044] After setting the probability parameters for each node passage pattern in this manner, the evaluation index calculation processing unit 130 calculates the likelihood of the actual passage pattern in the graph model based on the set probability parameters. The likelihood of the actual passage pattern can be expressed as the value obtained by dividing the probability parameter for each node passage pattern of the actual passage pattern by the number of types of patterns included in that node passage pattern. The likelihood may also be the log-likelihood.

[0045] The evaluation indicator calculation processing unit 130 then calculates a first evaluation indicator for evaluating the reproducibility of the graph model based on the likelihood of the calculated actual passage pattern. The evaluation indicator calculation processing unit 130 may calculate the first evaluation indicator only for the graph model, or it may calculate the first evaluation indicator for both the graph model and the original graph. When the probability parameter is set to a value that maximizes the likelihood of the actual passage pattern, the evaluation indicator calculation processing unit 130 may calculate, for example, the maximum likelihood or its logarithm, the maximum log-likelihood, as the first evaluation indicator.

[0046] The evaluation index calculation processing unit 130 that performs such processing includes, for example, as shown in Figure 3, a performance passage pattern generation unit 131, a node passage pattern generation unit 133, a probability parameter setting unit 135, a likelihood calculation unit 137, and an evaluation index calculation unit 139.

[0047] The performance traversal pattern generation unit 131 generates a set of performance traversal patterns from the performance data acquired by the performance data acquisition unit 110. The node traversal pattern generation unit 133 generates node traversal patterns of the graph model based on the graph structure data acquired by the graph acquisition unit 120. The probability parameter setting unit 135 sets probability parameters for each node traversal pattern of the graph model generated by the node traversal pattern generation unit 133. The likelihood calculation unit 137 calculates the likelihood of the performance traversal patterns using the probability parameters set by the probability parameter setting unit 135. The evaluation index calculation unit 139 calculates an index for evaluating the graph model. For example, the evaluation index calculation unit 139 calculates a first evaluation index of the graph model based on the likelihood of the performance traversal patterns calculated by the likelihood calculation unit 137.

[0048] The evaluation index calculation processing unit 130 outputs an index for evaluating the calculated graph model (in this embodiment, the first evaluation index) to the display device 300. The evaluation index calculation processing unit 130 only needs to output at least one of the following to the display device 300: the graph structure of the calculated graph model, the probability parameters, or the index for evaluating the graph model. Therefore, the evaluation index calculation processing unit 130 may output the created graph structure to the display device 300, or it may output both the graph structure and the evaluation index to the display device 300.

[0049] The display device 300 is, for example, a display and is communicatively connected to the graph evaluation device 100. The display device 300 outputs a first evaluation index calculated by the graph evaluation device 100 to, for example, a user who evaluates the graph model. This allows the user to quantitatively evaluate the reproducibility of the graph model based on the first evaluation index of the graph model. Furthermore, by outputting the graph structure to the display device 300, the user can easily grasp the state of the network at each point in time from the graph displayed on the display device 300.

[0050] The graph evaluation device 100 may perform processing at predetermined timings, such as when performance data is updated or at regular intervals, to acquire performance data, create a graph structure based on evaluation indicators, and output it to the display device 300. This allows the user to check the latest graph structure. Therefore, it is possible to perform real-time network analysis, such as identifying processes that are bottlenecks.

[0051] In this embodiment, the graph evaluation device 100 outputs information such as the first evaluation index to the display device 300 as shown in Figure 3, but the present invention is not limited to this example. For example, the graph evaluation device 100 may output information to a processing device that processes the information output from the evaluation index calculation processing unit 130. The processing device receives at least one of the graph structure of the graph model calculated by the graph evaluation device 100, probability parameters, or an index for evaluating the graph model, and processes the received information.

[0052] The processing device is a device (see Figure 16 below) that is connected directly to the graph evaluation device 100 or via a communication network, and is an output device 923, removable recording medium 925, external device 927, or an external information processing device 931 connected via the communication network 929 in Figure 16. The display device 300 shown in Figure 3 is an example of a processing device and corresponds to the output device 923 in Figure 16. The display device 300 processes the information received from the graph evaluation device 100 and displays graphs and evaluation indicators on the screen. Alternatively, the processing device may be an analysis device that analyzes a logistics network or a simulation device that simulates logistics. The analysis device and simulation device may be an external information processing device 931 connected via the communication network 929 in Figure 16.

[0053] Furthermore, the graph evaluation device 100 according to the present invention only needs to have the function of calculating an index (in this embodiment, a first evaluation index) for evaluating a graph model, and therefore only needs to be equipped with at least the likelihood calculation unit 137 and the evaluation index calculation unit 139 of the evaluation index calculation processing unit 130. In this embodiment, the graph evaluation device 100 evaluates a graph model generated by setting probability parameters for each node passage pattern using the probability parameter setting unit 135 on the graph structure acquired by the graph acquisition unit 120. However, the present invention is not limited to this example, and the graph evaluation device 100 may evaluate a graph model generated by another device. Therefore, the actual data acquisition unit 110, the graph acquisition unit 120, the actual passage pattern generation unit 131, the node passage pattern generation unit 133, and the probability parameter setting unit 135 may be composed of one or more devices different from the graph evaluation device 100.

[0054] It is possible to create computer programs to realize each function of the graph evaluation device 100 and implement them on a personal computer or the like. Furthermore, a computer-readable recording medium containing such computer programs can also be provided. Examples of recording media include magnetic disks, optical disks, magneto-optical disks, and flash memory. Alternatively, the above-mentioned computer programs may be distributed without using a recording medium, for example, via a network.

[0055] [2-2. Graph Evaluation Method] Next, the graph evaluation method according to this embodiment will be described based on Figure 4. Figure 4 is a flowchart showing an example of the graph evaluation method according to this embodiment. In the following explanation, we will consider the logistics network of coils manufactured in the steelmaking process as a specific example. The graph representing this logistics network shows the order in which the coils pass through the processes (equipment, storage area, conveying equipment) during the manufacturing process.

[0056] (S100: Acquire performance data) First, as shown in Figure 4, the performance data acquisition unit 110 acquires performance data from the performance data storage unit 210 (S100). The performance data storage unit 210 stores performance data in the network. Figure 5 shows an example of performance data for a coil logistics network.

[0057] The performance data shown in Figure 5 represents the three processes that the coil passes through in sequence, and the coil identification number (CoilNo) is associated with the first, second, and third processes that the coil passes through. For example, coil number C0000 indicates that the coil passes through the processes in the order of process A (node ​​A), process AGV1 (node ​​AGV1), and process C (node ​​C). The performance data acquisition unit 110 acquires a predetermined number or period of performance data from the performance data storage unit 210 and outputs it to the graph acquisition unit 120.

[0058] (S110: Graph structure data acquisition) Next, the graph acquisition unit 120 acquires graph structure data representing the graph structure of the graph model to be evaluated (S110). The graph structure represents a directed graph that shows the relationships between nodes using nodes and edges. The graph acquisition unit 120 may, for example, acquire pre-created graph structure data from the graph structure data storage unit 220. Alternatively, the graph acquisition unit 120 may acquire graph structure data by creating the graph structure of the graph model by aggregating or deleting nodes and edges based on the graph structure of the original graph obtained from the actual data acquisition unit 110. The actual data acquisition unit 110 may also acquire graph structure data of the original graph that shows the elements and connections as they are.

[0059] For example, consider Graph A (the original graph), shown in Figure 6, which directly represents all the elements and connections of the actual data in Figure 5, and Graph B (the simplified graph), which is a simplified model of Graph A. In Graphs A and B, the numbers indicated corresponding to the edges connecting the nodes represent the number of coils that moved between the nodes (processes) connected by the edges. Graph B is a simplified graph represented by a graph structure in which nodes AGV1 and AGV2 of Graph A are aggregated. A simplified graph is a graph with fewer nodes or edges than the original graph.

[0060] In step S110, the graph acquisition unit 120 acquires graph structure data G representing the relationships between nodes and edges of graphs A and B. As an example of graph structure data G, Figure 7 shows an adjacency matrix, which is a matrix representation of the graph structure of graph A in Figure 6. Note that the format of graph structure data G is not limited to an adjacency matrix; any information that can reconstruct the graph structure is acceptable. Furthermore, if the node passage patterns reconstructed from the graph structure do not reproduce any of the passage patterns included in the actual data acquired in step S100, the first evaluation index, which will be described later, cannot be calculated correctly. For this reason, the graph structure data G is designed to reproduce at least one passage pattern included in the actual data acquired in step S100.

[0061] The graph acquisition unit 120 outputs the acquired graph structure data to the evaluation index calculation processing unit 130.

[0062] (S120-S160: Calculation of the first evaluation index) The evaluation index calculation processing unit 130 then calculates a first evaluation index for evaluating the reproducibility of the graph model.

[0063] First, the actual passage pattern generation unit 131 generates a node passage pattern (actual passage pattern) of the original graph from the actual data acquired by the actual data acquisition unit 110 (S120).

[0064] For example, in the actual data shown in Figure 5, the pattern in which a coil identified by each actual data point passes through a process is denoted as the passage pattern e. The passage pattern e is information that connects the first, second, and third processes through which the coil passes. For example, the passage pattern e1 for coil number C0000 is represented as "A-AGV1-C". The set of passage patterns e is given by E = {e1,···,e}. I Let's assume}. Note that I represents the number of acquired actual data points (i.e., the number of coils). In the example in Figure 5, I = 50.

[0065] The performance pass pattern generation unit 131 generates a set of performance pass patterns P={p1,···,p} from the performance data acquired by the performance data acquisition unit 110. J Generate}. Here, the number of occurrences for each performance pattern is N={N0,···,N}. J}∈R J Let J be the number of actual passage patterns created from the actual data. For example, when the actual data in Figure 5 is obtained in step S100, the actual passage pattern generation unit 131 obtains six actual passage patterns p1 to p6 (i.e., J=6) as actual passage patterns included in graph A in Figure 6, as shown in Figure 8. The set of actual passage patterns is P={A-AGV1-C, A-AGV2-C, A-AGV2-E, B-AGV3-D, B-AGV4-D, B-AGV5-D}. In this case, the number of occurrences of each actual passage pattern is N={10, 5, 5, 10, 10, 10}. In this way, by grouping the actual passage patterns by type, the number of actual passage patterns J can be reduced, thereby reducing the computational load.

[0066] Next, the node passage pattern generation unit 133 generates a node passage pattern for the graph model based on the graph structure data acquired by the graph acquisition unit 120 in step S110 (S130). The node passage pattern generation unit 133 generates a node passage pattern for the graph model by, for example, enumerating paths from a start point to an end point in a directed graph having a start point and an end point, as determined by the graph structure data.

[0067] Here, let the set of node passage patterns be Q={q1,···,q K}, where K is the number of node passage patterns in a graph model created based on graph structure data. For example, the node passage patterns included in the graph structure of Graph B in FIG. 6 are the 5 actual passage patterns q1 to q5 (i.e., K=5) shown in FIG. 9. The set of these node passage patterns is Q={A-<AGV1,AGV2>-C,A-<AGV1,AGV2>-E,B-AGV3-D,B-AGV4-D,B-AGV5-D}.

[0068] Then, the probability parameter setting unit 135 sets a probability parameter for each node passage pattern of the graph model (S140). The probability parameter of the graph model θ={θ1,···,θ K}∈R K can be set to any arbitrary value; for example, the occurrence probability of each node passage pattern among actual passage patterns may be set. In the present invention, in order to obtain a graph model that can best reproduce the actual passage patterns, the probability parameter θ is set to a value that maximizes the likelihood of the actual passage patterns based on the maximum likelihood estimation method (i.e., the maximum likelihood estimate) θ ML is used. The maximum likelihood estimate θ used as the probability parameter θ ML h(j) is represented by the following formula (1).

[0069] [Formula]

[0070] Note that in the above formula (1), for node passage pattern q k let C={c1,···,c K}∈R K be the number of types of actual passage patterns included in node passage pattern q k let E K be the set of actual passage patterns included in the node passage pattern, and the number of actual passage patterns is represented by |E K |. Further, for an actual passage pattern p jThe node passage pattern q contains the relevant historical passage pattern from index j. k Let h(j) be a function that returns the index k of the given index j. That is, function h(j) returns the actual passage pattern p of the input index j. j q, the corresponding node traversal pattern k Output the index k.

[0071] Here, depending on the graph structure of the graph model's graph structure data G, there may be node passage patterns that cannot reproduce the actual passage patterns. For example, such a graph structure can occur in a graph model that aggregates many nodes. In this case, it becomes impossible to compute the function h(j), and the maximum likelihood estimate θ used as the probability parameter θ is not found. ML It will also become impossible to calculate this.

[0072] Therefore, by performing smoothing in advance using Laplace smoothing, etc., even if the actual passing pattern cannot be reproduced, the maximum likelihood estimate θ can be obtained. ML It may be possible to make it possible to calculate the function h(j). Specifically, for index j for which the function h(j) cannot be calculated, the function h(j) should return 0. In other words, the function h(j) should return the actual passage pattern p of the input index j. j q, the corresponding node traversal pattern k If an index k exists, it outputs that index k; however, if there is no node passage pattern corresponding to the actual passage pattern of the input index j, it outputs 0. In this case, the maximum likelihood estimate θ ML h(j) This can be expressed by the following equation (2).

[0073]

number

[0074] Furthermore, the smoothing method may be any smoothing method other than Laplace smoothing.

[0075] Figure 10 shows the maximum likelihood estimate θ as the probability parameter θ for each node passage pattern in Graph B of Figure 6. ML h(j) The results calculated based on the above equation (2) are shown. As shown in Figure 10, the maximum likelihood estimates θ for each of the five node passage patterns shown in Figure 9 are shown. ML h(j) This is how the maximum likelihood estimate θ is calculated. ML h(j) By calculating and setting this as the probability parameter θ, we can obtain a graph model that best reproduces the actual transaction patterns.

[0076] After setting the probability parameters for each node passage pattern in this manner, the likelihood calculation unit 137 calculates the likelihood of the actual passage pattern in the graph model based on the probability parameters set by the probability parameter setting unit 135 (S150). The likelihood of the actual passage pattern can be expressed as the value obtained by dividing the probability parameter for each node passage pattern of the actual passage pattern by the number of types of patterns included in that node passage pattern. The likelihood may also be the log-likelihood.

[0077] Figure 11 shows the results of calculating the likelihood and log-likelihood of the actual passage patterns for Graph B in Figure 6. The passage patterns shown in Figure 11 represent all node passage patterns included in Graph B in Figure 6, indicating that the seven actual passage patterns are reproduced. For each reproduced actual passage pattern, the number of occurrences of the actual passage pattern in the actual data obtained in step S100 and the node passage pattern q output by the function h(j) are shown. k The index k, and the number of types of actual pass patterns included in the corresponding node pass pattern C. h(j) The values ​​shown in Figure 11 are obtained. Note that in the table shown in Figure 11, h(j)=0 for the reproduced actual passage pattern "A-AGV1-E". In this case, c0 indicates the number of index j values ​​for which h(j)=0. The probability parameters (maximum likelihood estimates θ) shown in Figure 10 are obtained. ML h(j) ) and the number of types of actual passage patterns included in the corresponding node passage pattern C h(j)From this, the likelihood and log-likelihood of the actual performance pattern are calculated.

[0078] The likelihood or log-likelihood of the actual passage pattern calculated in step S150 represents the extent to which the actual data is likely to occur in each node passage pattern included in the model structure of the graph model being evaluated.

[0079] Subsequently, the evaluation index calculation unit 139 calculates a first evaluation index of the graph model (S160) based on the likelihood of the actual passing pattern calculated by the likelihood calculation unit 137 in step S150. For example, the evaluation index calculation unit 139 may calculate the maximum likelihood or the maximum log-likelihood as the first evaluation index. The maximum likelihood ML is expressed by the following equation (3-1), and the maximum log-likelihood MLL is expressed by the following equation (3-2). In the following equations (3-1) or (3-2), the maximum likelihood estimate θ is used as the probability parameter θ. ML h(j) Although this method is used, the value of the probability parameter θ can be set arbitrarily. For example, the maximum likelihood estimate θ ML h(j) Alternatively, the value of the probability parameter θ may be a value obtained by learning from actual data from a period other than the analysis period, or a value set by the user may be used.

[0080]

number

[0081] For example, if we calculate the maximum likelihood ML using the above formula (3-1) from the likelihood of the actual passing pattern for graph B in Figure 6 shown in Figure 11, we get 8.122667668864 × 10 -6 Therefore, if the maximum likelihood ML is used as the first evaluation metric, the first evaluation metric in Graph B is 8.122667668864 × 10 -6 This is the result. Furthermore, using the log-likelihood of the actual passing pattern for Graph B in Figure 6, as shown in Figure 11, the maximum log-likelihood MLL can be calculated using the above formula (3-2), which is -92.646. In other words, when the maximum log-likelihood MLL is used as the first evaluation metric, the first evaluation metric for Graph B is -92.646.

[0082] Furthermore, if smoothing is performed on the number of occurrences of node passage patterns in step S140, the evaluation index calculation unit 139 calculates the maximum likelihood or maximum log-likelihood based on the number of occurrences of each node passage pattern after smoothing. The evaluation index calculation unit 139 outputs the first evaluation index of the calculated graph model to the display device 300.

[0083] The graph evaluation method according to this embodiment has been described above.

[0084] [2-3. Evaluation of reproducibility using evaluation metrics] A user evaluating a graph model can quantitatively assess the reproducibility of the graph model based on the first evaluation index of the graph model output to the display device 300. Using the first evaluation index, the following evaluations can be performed, for example:

[0085] (a. Reproducibility of the original graph's data using a simplified graph) For example, the first evaluation metric can be used to evaluate the reproducibility of the data in the original graph by the simplified graph. Using the first evaluation metric, for example, it is possible to evaluate how well graph B (simplified graph) shown in Figure 6 reproduces the original graph A, which directly represents the actual data. In this case, the maximum likelihood estimate θ is set as the probability parameter θ of the graph model so that the graph model of graph B can reproduce the actual passage pattern best. ML It is best to use the following: the maximum likelihood estimate θ calculated based on the graph structure and actual data D. ML Using the probability parameter θ, the reproducibility of the actual data D by the graph model represented by the graph structure and probability parameter θ is evaluated using the first evaluation index.

[0086] In this case, the best first evaluation metric is the value of the original graph, which does not aggregate or delete nodes or edges. Therefore, by checking how much the first evaluation metric calculated for the graph model of the simplified graph deteriorates compared to the first evaluation metric calculated for the graph model of the original graph, it is possible to relatively evaluate the reproducibility of the data of the original graph by the simplified graph.

[0087] For example, if the maximum log-likelihood is used as the first evaluation metric, the maximum log-likelihood of the original graph will be the largest, and the maximum log-likelihood of the simplified graph will be smaller than that of the original graph. As a specific example, suppose that the maximum log-likelihoods obtained for the original graph and simplified graphs a to f are as shown in Table 1 below.

[0088] [Table 1]

[0089] In the example shown in Table 1, simplified graph f, which has the largest maximum log-likelihood among the simplified graphs, can be said to have the highest reproducibility of the data from the original graph and to have performed appropriate node aggregation and deletion. On the other hand, simplified graph c, which has a significantly small maximum log-likelihood, is considered to have low reproducibility of the data from the original graph and is likely to have failed to preserve the information from the original graph. Thus, the first evaluation metric can be used to evaluate the reproducibility of the data from the original graph by the simplified graph.

[0090] (b. Assessment of changes in network conditions) Furthermore, for example, the status of a network can be evaluated using a first evaluation index of a graph model representing the network. For instance, a first evaluation index can be calculated based on actual data obtained at predetermined intervals (e.g., every month) using a graph model of the graph structure representing the network. If the first evaluation index drops significantly from the time-series data obtained in this way, it can be inferred that the order or flow of elements passing through the graph representing the network has changed (for example, the logistics situation in a logistics network has changed), and that an anomaly may have occurred in the network.

[0091] At this time, the maximum likelihood estimate θ is set as the probability parameter θ of the graph model so that the graph model representing the network can best reproduce the actual passage patterns obtained in that network. ML It is best to use the following: the maximum likelihood estimate θ calculated based on the graph structure and actual data D. ML Using the probability parameter θ, the reproducibility of the graph structure and the graph model represented by the probability parameter θ to other historical data D' is evaluated using the first evaluation index.

[0092] For example, based on a graph model representing a logistics network, the maximum log-likelihood is calculated as the first evaluation metric from monthly performance data, as shown in Table 2. Here, if April 2022 is used as the base month, the maximum likelihood estimate θ is calculated using performance data obtained in April 2022. MLA graph model of the logistics network is created using probability parameter θ. Then, changes in logistics within the logistics network are evaluated by assessing how well the first evaluation metric reproduces the actual data from other months in this graph model. For example, in Table 2, the first evaluation metric has decreased since September 2022. This suggests that the reproducibility of the actual data has decreased in the graph model used as a baseline for April 2022, indicating that changes have occurred in logistics. From this, it is possible to detect the possibility of an anomaly occurring in the logistics network. Furthermore, changes in the logistics network may also indicate the need to change the baseline graph model.

[0093] [Table 2]

[0094] (c. Evaluation of reproducibility using the modified graph model) Furthermore, for example, when the probability parameters of the graph model are arbitrarily changed, the reproducibility of the graph model to the actual data can be evaluated using the first evaluation index. That is, the maximum likelihood estimate θ calculated based on the graph structure and the actual data D. ML For a graph model with probability parameter θ, the reproducibility of the actual data D by the graph model after arbitrarily changing the probability parameter θ is evaluated using the first evaluation index.

[0095] For example, in a graph model representing a logistics network, the probability parameter θ is the maximum likelihood estimate calculated based on the graph structure and actual data D. ML Assume that a value for θ is set. In this case, the operator changes at least a portion of the value of the probability parameter θ to match the ideal logistics conditions in reality, and calculates the first evaluation index of the graph model represented by the changed parameter for the actual data D. By observing the changes in the first evaluation index calculated in this way, it is possible to evaluate the graph model to reflect the operator's intentions.

[0096] Furthermore, the above model structure and the maximum likelihood estimate θ ML In a graph model representing a logistics network expressed by (probability parameter θ), at least a portion of the probability parameter θ is changed to a value set based on the production plan, and the first evaluation index of the graph model represented by the changed parameter is calculated for actual data D. The difference between the production plan and actual results can be evaluated by the change in the first evaluation index calculated in this way.

[0097] The graph evaluation method according to the first embodiment has been described above. According to the graph evaluation method according to this embodiment, for a graph model represented by a graph structure represented using nodes and edges and probability parameters representing the probability of occurrence for each node passage pattern of the graph structure, the likelihood of the actual passage pattern is calculated based on the probability parameters of the node passage pattern. Then, a first evaluation index, such as the maximum log-likelihood, is calculated based on the calculated likelihood of the actual passage pattern. By using such a first evaluation index, it becomes possible to quantitatively evaluate the reproducibility of the graph model. As a result, for example, it becomes possible to evaluate the reproducibility of the data of the original graph using a simplified graph, to detect changes in the network status from the reproducibility of the graph model based on reference actual data, and to evaluate whether the changes to be implemented are appropriate from the reproducibility of the modified graph model. Furthermore, by creating a graph based on the first evaluation index, it is also possible to create a graph with high reproducibility.

[0098] [3. Second Embodiment] Next, a graph evaluation device and a graph evaluation method using the same according to a second embodiment of the present invention will be described. In this embodiment, an evaluation index for the graph model is calculated based on a first evaluation index for evaluating the reproducibility of the graph model calculated in the first embodiment, and a second evaluation index that represents the complexity of the graph model by the number of node traversal patterns included in the graph model and a weight coefficient. Furthermore, based on the calculated evaluation index, the optimal graph model that best matches the objective is searched for. By creating a graph based on these evaluation indexes, it is possible to create a graph that balances reproducibility and complexity according to the evaluation index.

[0099] [3-1. Graph Evaluation Device] First, a graph evaluation device 100 according to a second embodiment of the present invention will be described based on Figure 12. Figure 12 is a functional block diagram of the graph evaluation device 100 according to this embodiment. In the following description, a detailed explanation of the functional configuration, similar to that of the first embodiment, will be omitted.

[0100] As shown in Figure 12, the graph evaluation device 100 according to this embodiment includes a performance data acquisition unit 110, a graph acquisition unit 120, an evaluation index calculation processing unit 130, and a search unit 140.

[0101] (Performance Data Acquisition Department) The performance data acquisition unit 110 acquires performance data from the performance data storage unit 210, which stores performance data in the network. The performance data acquisition unit 110 functions in the same way as the performance data acquisition unit 110 of the first embodiment. The performance data acquisition unit 110 outputs the acquired performance data to the graph acquisition unit 120.

[0102] (Graph acquisition section) The graph acquisition unit 120 acquires graph structure data representing the graph structure of the graph model to be evaluated. The graph acquisition unit 120 functions similarly to the graph acquisition unit 120 of the first embodiment. The graph acquisition unit 120 may, for example, acquire pre-created graph structure data from the graph structure data storage unit 220. Alternatively, the graph acquisition unit 120 may acquire graph structure data by creating the graph structure of the graph model by aggregating or deleting nodes and edges based on the graph structure of the original graph obtained from the actual data acquisition unit 110. The graph acquisition unit 120 may, for example, acquire an adjacency matrix (see Figure 7 described later), which is a matrix representation of the graph structure, as graph structure data. The graph acquisition unit 120 outputs the acquired graph structure data to the evaluation index calculation processing unit 130.

[0103] (Evaluation indicator calculation processing unit) The evaluation index calculation processing unit 130 calculates an index for evaluating the graph model. In this embodiment, the evaluation index calculation processing unit 130 calculates a first evaluation index for evaluating the reproducibility of the graph model and a second evaluation index representing the complexity of the graph model, and calculates an evaluation index for the graph model based on the first and second evaluation indexes. The evaluation index may be expressed, for example, as the sum of the first and second evaluation indexes.

[0104] The evaluation index calculation processing unit 130 calculates the first evaluation index in the same manner as in the first embodiment. That is, the evaluation index calculation processing unit 130 first sets probability parameters for each node passage pattern for the graph structure data acquired by the graph acquisition unit 120. Next, the evaluation index calculation processing unit 130 calculates the likelihood of the actual passage pattern in the graph model based on the set probability parameters. Then, the evaluation index calculation processing unit 130 calculates a first evaluation index for evaluating the reproducibility of the graph model based on the calculated likelihood of the actual passage pattern.

[0105] Furthermore, the evaluation index calculation processing unit 130 calculates a second evaluation index by multiplying the number of free parameters, which is set based on the number of node traversal patterns included in the graph model, by a weight coefficient. The number of free parameters is the value obtained by subtracting 1 from the number of node traversal patterns K included in the graph model. The weight coefficient can be set as appropriate by the user, for example, and may be set based on a balance with the first evaluation index. Then, the evaluation index calculation processing unit 130 adds the first evaluation index and the second evaluation index together to obtain the evaluation index.

[0106] The evaluation index calculation processing unit 130 that performs such processing includes, for example, as shown in Figure 12, a performance passage pattern generation unit 131, a node passage pattern generation unit 133, a probability parameter setting unit 135, a likelihood calculation unit 137, and an evaluation index calculation unit 139.

[0107] The actual passage pattern generation unit 131, the node passage pattern generation unit 133, the probability parameter setting unit 135, and the likelihood calculation unit 137 function in the same manner as in the first embodiment. That is, the actual passage pattern generation unit 131 generates a set of actual passage patterns from actual data acquired by the actual data acquisition unit 110. The node passage pattern generation unit 133 generates node passage patterns of the graph model based on graph structure data acquired by the graph acquisition unit 120. The probability parameter setting unit 135 sets probability parameters for each node passage pattern of the graph model generated by the node passage pattern generation unit 133. The likelihood calculation unit 137 calculates the likelihood of the actual passage patterns using the probability parameters set by the probability parameter setting unit 135.

[0108] The evaluation index calculation unit 139 calculates an index for evaluating the graph model. In this embodiment, the evaluation index calculation unit 139 calculates a first evaluation index, a second evaluation index, and an evaluation index as indicators for evaluating the graph model. Specifically, the evaluation index calculation unit 139 calculates a first evaluation index of the graph model based on the likelihood of the actual passage patterns calculated by the likelihood calculation unit 137. The evaluation index calculation unit 139 also calculates a second evaluation index by multiplying the number of free parameters, which is set based on the number of node passage patterns included in the graph model, by a weight coefficient. Then, the evaluation index calculation unit 139 adds the first evaluation index and the second evaluation index together to calculate the evaluation index of the graph model.

[0109] The evaluation index calculation processing unit 130 outputs the calculated evaluation index to the search unit 140. The evaluation index calculation processing unit 130 may also output the calculated evaluation index, its graph structure, and probability parameters to the display device 300, as previously described. In this case, the evaluation index calculation processing unit 130 may output the first and second evaluation indexes to the display device 300 in addition to the evaluation index, or it may output only the first evaluation index to the display device 300. As previously described, the display device 300 outputs, for example, at least one of the graph structure, probability parameters, or indexes for evaluating the graph model calculated by the graph evaluation device 100 to a user evaluating the graph model. The user can, for example, quantitatively evaluate the balance between the reproducibility and complexity of the graph model from the evaluation index.

[0110] (Exploration Department) The search unit 140 searches for the optimal graph model that best matches the objective based on the evaluation indicators, the reproducibility and complexity of the graph model. The search unit 140 continues searching for graph models until predetermined termination conditions are met. For example, the search may be terminated when the evaluation indicators are improved compared to the original graph, or when the fluctuations in the evaluation indicators converge after repeatedly performing the search while changing the graph structure of the graph model. The search unit 140 outputs the graph model that satisfies the predetermined termination conditions as the optimal graph model to the display device 300.

[0111] The search unit 140 stores the best evaluation index calculated by the evaluation index calculation processing unit 130 for each of the multiple graph structures created by the graph acquisition unit 120 through repeated edge deletion and other operations, as the evaluation index value for that search stage. Note that the evaluation index for which the value is stored may be only the best one, or a predetermined number of the highest-ranking evaluation indices may be stored. Therefore, the search unit 140 can output to the display device 300 one or more graph models obtained up to the point when a predetermined termination condition is met, in which the evaluation index values ​​are a predetermined number (1 or more) from the highest-ranking ones. In addition, the number of graph structures that the search unit 140 has the graph acquisition unit 120 create in a single search may be one or multiple.

[0112] Furthermore, the graph evaluation device 100 according to the present invention only needs to have the function of calculating indices for evaluating a graph model (in this embodiment, a first evaluation index, a second evaluation index, and an evaluation index), and therefore only needs to be equipped with at least the likelihood calculation unit 137 and the evaluation index calculation unit 139 of the evaluation index calculation processing unit 130. In other words, the graph evaluation device 100 according to this embodiment may also evaluate a graph model generated by another device, similar to the first embodiment. In addition, the graph evaluation device 100 may further include a search unit 140 in order to search for the optimal graph model. Accordingly, the actual data acquisition unit 110, the graph acquisition unit 120, the actual passage pattern generation unit 131, the node passage pattern generation unit 133, the probability parameter setting unit 135, and the search unit 140 may be composed of one or more devices different from the graph evaluation device 100.

[0113] Similar to the first embodiment, in this embodiment as well, it is possible to create a computer program to realize each function of the graph evaluation device 100 and implement it on a computer equipped with a processor, such as a personal computer. Furthermore, a computer-readable recording medium on which such a computer program is stored can also be provided. Examples of recording media include magnetic disks, optical disks, magneto-optical disks, and flash memory. Alternatively, the above-mentioned computer program may be distributed, for example, via a network, without using a recording medium.

[0114] [3-2. Graph Evaluation Method] Next, the graph evaluation method according to this embodiment will be described based on Figure 13. Figure 13 is a flowchart showing an example of the graph evaluation method according to this embodiment. In the following description, a detailed explanation of the process similar to that of the first embodiment will be omitted. In the following description, as a specific example, we will consider a logistics network for coils manufactured in a steelmaking process, similar to that of the first embodiment.

[0115] (S201: Acquisition of performance data) First, as shown in Figure 13, the performance data acquisition unit 110 acquires performance data from the performance data storage unit 210 (S201). Step S201 can be performed in the same way as step S100 in Figure 4. Similar to the first embodiment, the performance data acquisition unit 110 acquires a predetermined number or period of performance data from the performance data storage unit 210, which stores performance data in a network as shown in Figure 5, for example, and outputs it to the graph acquisition unit 120.

[0116] (S203: Graph structure data acquisition) Next, the graph acquisition unit 120 acquires graph structure data representing the graph structure of the graph model to be evaluated (S203). Step S203 can be performed in the same way as step S110 in Figure 4. That is, the graph acquisition unit 120 may, for example, acquire pre-created graph structure data from the graph structure data storage unit 220. Alternatively, the graph acquisition unit 120 may acquire graph structure data by creating the graph structure of the graph model by aggregating or deleting nodes and edges based on the graph structure of the original graph obtained from the actual data acquisition unit 110. The actual data acquisition unit 110 may also acquire graph structure data of the original graph that represents the elements and connections as they are. The graph acquisition unit 120 outputs the acquired graph structure data to the evaluation index calculation processing unit 130.

[0117] (S205-S213: Calculation of the first evaluation index) The evaluation index calculation processing unit 130 then calculates a first evaluation index for evaluating the reproducibility of the graph model. Steps S205 to S213, which are the calculation processes for the first evaluation index, can be performed in the same way as steps S120 to S160 in Figure 4.

[0118] First, the actual passage pattern generation unit 131 generates the node passage pattern (actual passage pattern) of the original graph from the actual data acquired by the actual data acquisition unit 110 (S205). Next, the node passage pattern generation unit 133 generates the node passage pattern of the graph model based on the graph structure data acquired by the graph acquisition unit 120 in step S203 (S207).

[0119] Then, the probability parameter setting unit 135 sets the probability parameters for each node traversal pattern of the graph model (S209). The probability parameters of the graph model θ = {θ1,···,θ K}∈R K The value of can be set arbitrarily; for example, it may be set to the probability of occurrence for each node passage pattern of the actual passage pattern. For example, the probability parameter θ can be a value (i.e., the maximum likelihood estimate) θ that is set to maximize the likelihood of the actual passage pattern based on the maximum likelihood estimation method, which can be calculated using the above equation (1) or equation (2). ML This may also be used. After the probability parameter setting unit 135 sets the probability parameters for each node passage pattern in this manner, the likelihood calculation unit 137 calculates the likelihood of the actual passage pattern in the graph model based on the set probability parameters (S211). The likelihood may also be the log-likelihood.

[0120] Subsequently, the evaluation index calculation unit 139 calculates a first evaluation index for the graph model based on the likelihood of the actual passing patterns calculated in step S209 (S213). The first evaluation index may be, for example, the maximum likelihood ML represented by the above formula (3-1), or the maximum log-likelihood MLL represented by the above formula (3-2). If smoothing is performed on the number of occurrences of the node passing patterns in step S209, the evaluation index calculation unit 139 calculates the maximum likelihood ML or the maximum log-likelihood MLL based on the number of occurrences of each node passing pattern after smoothing.

[0121] (S215: Calculation of the second evaluation indicator) Furthermore, the evaluation index calculation unit 139 calculates a second evaluation index based on the number of node traversal patterns included in the graph model and the weight coefficients (S215). Specifically, the evaluation index calculation unit 139 calculates the second evaluation index by multiplying the number of free parameters F (=K-1), which is the number of node traversal patterns K included in the graph model minus 1, by the weight coefficient w. The weight coefficients can be set as appropriate by the user, for example, and may be set based on a balance with the first evaluation index. The second evaluation index represents the complexity of the graph. The larger the value of the weight coefficient w of the second evaluation index, the more strongly the simplicity of the graph model is evaluated in the evaluation index described later.

[0122] (S217: Calculation of evaluation indicators) Then, the evaluation index calculation unit 139 adds the first evaluation index calculated in step S213 and the second evaluation index calculated in step S215 to calculate the evaluation index (S217). The evaluation index Z can be expressed as shown in the following equation (4) when the first evaluation index is represented by the maximum log-likelihood MLL shown in the above equation (3-2).

[0123]

number

[0124] For example, when calculating the evaluation index for the graph model of graph B in Figure 6, the first evaluation index is MLL = -92.646 as described above, and the second evaluation index is w × F = 40, assuming the number of free parameters is F = 4 (number of node traversal patterns K = 5) and the weight coefficient w = 10. Substituting these values ​​into equation (4) above, the evaluation index Z is 132.65. Similarly, when calculating the evaluation index for the graph model of graph A in Figure 6, the evaluation index Z is 137.43. The closer the value of the evaluation index for the graph model of graph B is to the value of the evaluation index for the original graph (graph A), the more the graph model of graph B can be evaluated as a graph model that balances reproducibility and simplicity.

[0125] (S219-S223: Graph Model Search) Once the evaluation index is calculated in step S217, the search unit 140 searches for the optimal graph model that best matches the objective based on the evaluation index, considering the reproducibility and complexity of the graph model. First, the search unit 140 determines whether the graph model evaluated this time satisfies predetermined termination conditions (S219). The termination conditions are set in advance; for example, the search may be terminated when the evaluation index is improved compared to the evaluation index of the original graph model, or the search may be terminated when the fluctuation of the evaluation index converges after repeatedly performing the search while changing the graph structure of the graph model. Based on the evaluation index calculated in step S217, the search unit 140 determines whether or not to terminate the search for graph models.

[0126] For example, suppose a search termination condition is set so that the search is terminated if the evaluation metric does not improve after repeating the search 100 times. If the evaluation metric of the graph model evaluated this time improves from the previous evaluation metric, or if the evaluation metric of the graph model evaluated this time does not improve from the previous evaluation metric for 100 consecutive times, the search unit 140 determines that the search termination condition has not been met (S219:NO), and instructs the graph acquisition unit 120 to recreate a new graph model in order to search for a graph structure with a better evaluation metric (S221).

[0127] The creation of a new graph model is performed by changing the nodes to be aggregated and the edges to be deleted. For example, a group of graph models created by manipulating the graph structure of the graph model G* (evaluation index f*) with the smallest evaluation index value among the graph models explored so far, by aggregating nodes or deleting edges, are calculated as neighboring solutions to the graph model evaluated this time. The group of graph models may also be created, for example, by creating new graph structure data in the graph structure data G of the graph model evaluated this time, keeping the parent and child nodes the same, and changing the aggregation of nodes between them. As a concrete example, Figure 14 shows an example of a group of graph models of a simplified graph (graphs C to I) created from graph B in Figure 6, without changing the parent nodes A and B and the child nodes C, D and E, but by changing the aggregation of nodes AGV1 to AGV5 between them or deleting edges.

[0128] When the graph acquisition unit 120 receives an instruction from the search unit 140 to recreate the graph model, it creates a group of new simplified graph models with different graph structures, as shown in graphs C to I in Figure 14. Note that the method of recreating the graph model is not limited to this example; for example, if the graph evaluation device 100 has high computing power, it may sequentially create a group of simplified graph models for all possible graph structures from the original graph.

[0129] When the graph acquisition unit 120 recreates the group of graph models for the simplified graphs, the calculation of the first evaluation indicator (S207-S213), the calculation of the second evaluation indicator (S215), and the calculation of the evaluation indicator (S217) are performed for each graph model of the simplified graph. Note that for the calculation of the first evaluation indicator from the second time onward, it is not necessary to create the actual passing pattern (S205), and the actual passing pattern created the first time may be used.

[0130] Then, if the evaluation index of the graph model evaluated this time does not improve from the previous evaluation index even after repeating the search 100 times, and the search termination condition is met (S219: YES), the search unit 140 outputs the graph model with the smallest evaluation index up to that point as the optimal graph model to the display device 300 (S223). This makes it possible for the user to more accurately understand the network status using the optimal graph model that best matches their purpose based on the reproducibility and complexity of the graph model.

[0131] For example, Figure 15 shows the values ​​of the evaluation index Z of the graph models calculated based on the above formula (4) for graphs A and B in Figure 6 and graphs C to I in Figure 14. From Figure 15, the graph model of graph E, which has the smallest evaluation index, is the optimal graph model. Graph E aggregates nodes AGV3 and AGV5, and referring to graph A, both nodes AGV3 and AGV5 are adjacent to nodes B and D. By simplifying the graph as in graph E, which aggregates nodes that share common adjacent nodes, node passage patterns that do not exist in the actual passage patterns do not occur, the reproducibility of the graph model is increased, and the value of the evaluation index is also reduced.

[0132] For comparison, as shown in Figure 11, Graph B contains a node passage pattern "A-AGV1-E" that is not present in the actual passage patterns. Therefore, the evaluation index for the graph model is higher in Graph B than in Graph E. Thus, by using the evaluation index shown in equation (4) above, it is possible to evaluate the graph model while taking into account that passage patterns not present in the actual data may be reproduced.

[0133] [4. Hardware Configuration] Based on Figure 16, the hardware configuration of the graph evaluation device 100 according to this embodiment will be described. Figure 16 is a block diagram showing an example of the hardware configuration of the information processing device 900 that functions as the graph evaluation device 100 according to this embodiment.

[0134] The information processing device 900 includes a processor (CPU 901 in Figure 16), a ROM 903, and a RAM 905. The information processing device 900 also includes a bus 907, an input I / F 909, an output I / F 911, a storage device 913, a drive 915, a connection port 917, and a communication device 919.

[0135] The CPU 901 functions as both an arithmetic processing unit and a control unit. The CPU 901 controls the overall operation or a part of it within the information processing unit 900 according to various programs recorded in the ROM 903, RAM 905, storage device 913, or removable recording medium 925. The ROM 903 stores programs or arithmetic parameters used by the CPU 901. The RAM 905 temporarily stores programs used by the CPU 901, or parameters that change as appropriate during program execution. These are interconnected by a bus 907, which is composed of an internal bus such as the CPU bus.

[0136] Bus 907 is connected to an external bus, such as the PCI (Peripheral Component Interconnect / Interface) bus, via a bridge.

[0137] The input interface 909 is an interface that receives input from an input device 921, which is a means of operation operated by the user, such as a mouse, keyboard, touch panel, button, switch, and lever. The input interface 909 is configured, for example, as an input control circuit that generates an input signal based on information entered by the user using the input device 921 and outputs it to the CPU 901. The input device 921 may be, for example, a remote control device using infrared or other radio waves, or an external device 927 such as a PDA (Personal Digital Assistant) that is compatible with the operation of the information processing device 900. The user of the information processing device 900 can operate the input device 921 to input various data to the information processing device 900 or instruct it to perform processing operations.

[0138] The output I / F 911 is an interface that outputs the input information to an output device 923 that can visually or audibly notify the user. The output device 923 may be, for example, a display device such as a CRT display, liquid crystal display, plasma display, EL display, or lamp. Alternatively, the output device 923 may be an audio output device such as a speaker or headphones, or a printer, mobile communication terminal, or facsimile. The output I / F 911 instructs the output device 923 to output, for example, the processing results obtained from various processes performed by the information processing device 900. Specifically, the output I / F 911 instructs the display device to display the processing results from the information processing device 900 as text or an image. The output I / F 911 also instructs the audio output device to convert an audio signal, such as audio data that has been instructed to be played, into an analog signal and output it.

[0139] The storage device 913 is one of the storage units of the information processing device 900 and is a device for storing data. The storage device 913 is composed of, for example, a magnetic storage device such as an HDD (Hard Disk Drive), a semiconductor storage device such as an SSD (Solid State Drive), an optical storage device, or a magneto-optical storage device. The storage device 913 stores programs executed by the CPU 901, various data generated by the execution of programs, and various data acquired from external sources.

[0140] The drive 915 is a reader / writer for recording media and is either built into or external to the information processing device 900. The drive 915 reads information recorded on the installed removable recording media 925 and outputs it to the RAM 905. The drive 915 can also write information to the installed removable recording media 925. The removable recording media 925 is, for example, a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory. Specifically, the removable recording media 925 may be CD media, DVD media, Blu-ray® media, CompactFlash® (CF), flash memory, SD memory card (Secure Digital memory card), etc. Alternatively, the removable recording media 925 may be, for example, an IC card (Integrated Circuit card) equipped with a contactless IC chip or an electronic device.

[0141] Connection port 917 is a port for directly connecting devices to the information processing device 900. Connection port 917 can be, for example, a USB (Universal Serial Bus) port, an IEEE1394 port, a SCSI (Small Computer System Interface) port, or an RS-232C port. The information processing device 900 can directly acquire various data from or provide various data to external devices 927 connected to connection port 917.

[0142] The communication device 919 is a communication interface composed of, for example, communication devices for connecting to the communication network 929. The communication device 919 may be, for example, a wireless LAN (Local Area Network), Bluetooth (registered trademark), or an antenna for mobile communication. Alternatively, the communication device 919 may be a wired LAN, a router for optical communication, a router for ADSL (Asymmetric Digital Subscriber Line), or a modem for various types of communication. The communication device 919 can, for example, send and receive signals to and from the Internet or other communication devices in accordance with a predetermined protocol such as TCP / IP. The communication network 929 connected to the communication device 919 is composed of a network connected by wire or wireless means. For example, the communication network 929 may be a wide area network (WAN) such as the Internet, a LAN, a mobile communication network, infrared communication, radio wave communication, or satellite communication.

[0143] As shown in Figure 16, an external information processing device 931 is connected to the communication network 929. The information processing device 931 may be a device having the same hardware configuration as the information processing device 900. In this embodiment, the information processing device 931 is, for example, a processing device that processes information received from the graph evaluation device 100, and is an analysis device that analyzes logistics networks or a simulation device that simulates logistics.

[0144] The above describes an example of the hardware configuration of the information processing device 900. Each of the above-mentioned components may be made using general-purpose materials, or each component may be made using hardware specialized for its function. The hardware configuration of the information processing device 900 can be appropriately changed depending on the level of technology at the time of implementing this embodiment.

[0145] Although preferred embodiments of the present invention have been described in detail above with reference to the attached drawings, the present invention is not limited to these examples. It is clear to any person with ordinary skill in the art to which the present invention belongs that various modifications or alterations can be conceived within the scope of the technical idea described in the claims, and these are also understood to fall within the technical scope of the present invention.

[0146] For example, the above embodiment described an example of evaluating a graph representing a logistics network, but the present invention is not limited to such examples. For example, the graph evaluation method of the present invention can evaluate graphs representing networks with a sequence and flow of movement, such as logistics networks. Specifically, it can evaluate graphs representing networks such as roads, trains, and airplanes, or business networks representing administrative processes in companies, hospitals, etc.

[0147] Furthermore, in the above embodiment, the graph evaluation device also created and acquired original graphs and simplified graphs that directly represent the actual data, but the present invention is not limited to such examples. For example, the graph evaluation device may calculate a first evaluation index for a graph model that has been acquired in advance, or calculate an evaluation index based on the first evaluation index and the second evaluation index. [Explanation of symbols]

[0148] 100 Graph Evaluation Device 110 Performance Data Acquisition Department 120 Graph acquisition section 130 Evaluation Index Calculation Processing Unit 131 Performance Pass Pattern Generation Unit 133 Node Passage Pattern Generation Unit 135 Probability parameter setting section 137 Likelihood Calculation Unit 139 Evaluation Index Calculation Unit 140 Search Department 210 Performance data storage unit 220 Graph structure data storage unit 300 display device 900 Information Processing Equipment 907 Bus 913 Storage device 915 Drive 917 Connection Ports 919 Communication equipment 921 Input device 923 Output device 925 Removable recording media 927 External equipment 929 Communications Network 931 (External) Information Processing Device Go to the original graph Gs Simplified Graph

Claims

1. The system includes an evaluation index calculation processing unit that calculates an index for evaluating a graph model represented by a graph structure using nodes and edges, and probability parameters representing the probability of occurrence for each node traversal pattern of the graph structure. The aforementioned evaluation index calculation processing unit is: A likelihood calculation unit calculates the likelihood of the actual passing pattern, which is the actual passing pattern of nodes in the graph model, based on the probability parameters for each of the aforementioned node passing patterns. An evaluation index calculation unit calculates a first evaluation index for evaluating the reproducibility of the aforementioned performance pattern based on the likelihood of the aforementioned performance pattern, A graph evaluation device having the following features.

2. The aforementioned probability parameter is a value set to maximize the likelihood of the aforementioned actual passage pattern. The graph evaluation device according to claim 1, wherein the evaluation index calculation unit calculates the maximum likelihood or maximum log-likelihood of the actual performance pattern as the first evaluation index.

3. The probability parameter is a value set to maximize the likelihood of the actual passing pattern, based on the number of occurrences of the actual passing pattern included in the smoothed node passing pattern. The graph evaluation device according to claim 2, wherein the evaluation index calculation unit calculates the maximum likelihood or the maximum log-likelihood of the actual passing pattern based on the number of occurrences of each of the node passing patterns after smoothing.

4. The aforementioned evaluation index calculation processing unit is: A performance pass pattern generation unit that generates the performance pass pattern from performance data, A node passage pattern generation unit generates the node passage pattern based on the graph structure of the graph model, A probability parameter setting unit sets the probability parameters for each node passage pattern of the graph model, A graph evaluation device according to claim 1, having the following features.

5. The graph evaluation device according to claim 1, wherein the evaluation index calculation unit calculates a second evaluation index representing the complexity of the graph model based on the number of node traversal patterns included in the graph model and a weight coefficient.

6. The graph evaluation device according to claim 5, wherein the evaluation index calculation unit calculates the sum of the first evaluation index and the second evaluation index as the evaluation index of the graph model.

7. Based on the aforementioned evaluation indicators, the system includes a search unit that searches for the optimal graph model that best matches the objective based on the reproducibility and complexity of the graph model. The evaluation index calculation processing unit calculates the evaluation index for each of the multiple different graph models, The graph evaluation device according to claim 6, wherein the search unit selects the graph model with the smallest evaluation index from among the plurality of graph models as the optimal graph model.

8. The graph evaluation apparatus according to any one of claims 1 to 7, wherein the evaluation index calculation processing unit outputs to the processing unit at least one of the graph structure of the graph model for which the first evaluation index has been calculated, the probability parameters, or an index for evaluating the graph model.

9. The graph evaluation device according to claim 8 receives at least one of the graph structure of the graph model, the probability parameters of the graph model, or an index for evaluating the graph model. A processing unit that processes received information.

10. A graph evaluation method using a graph evaluation device, A graph model represented by a graph structure using nodes and edges and probability parameters representing the probability of occurrence for each node passage pattern of the graph structure, a likelihood calculation step of calculating the likelihood of the actual passage pattern, which is the actual node passage pattern, based on the probability parameters for each node passage pattern, As an indicator for evaluating the graph model, a first evaluation indicator calculation step is performed to calculate a first evaluation indicator for evaluating the reproducibility of the actual passing pattern based on the likelihood of the actual passing pattern, A graph evaluation method that includes this.

11. The aforementioned probability parameter is a value set to maximize the likelihood of the aforementioned actual passage pattern. The graph evaluation method according to claim 10, wherein the first evaluation indicator calculation step calculates the maximum likelihood or maximum log-likelihood of the performance pattern as the first evaluation indicator.

12. The probability parameter is a value set to maximize the likelihood of the actual passing pattern, based on the number of occurrences of the actual passing pattern included in the smoothed node passing pattern. The graph evaluation method according to claim 11, wherein in the first evaluation index calculation step, the maximum likelihood or maximum log-likelihood of the actual passing pattern is calculated based on the number of occurrences of each of the node passing patterns after smoothing.

13. A performance pass pattern generation step that generates the performance pass pattern from performance data, A node passage pattern generation step that generates the node passage pattern based on the graph structure of the graph model, A probability parameter setting step of setting the probability parameters for each node passage pattern of the graph model, The graph evaluation method according to claim 10, including the method described in claim 10.

14. The graph evaluation method according to claim 10, further comprising a second evaluation index calculation step of calculating a second evaluation index that represents the complexity of the graph model based on the number of node traversal patterns included in the graph model and a weight coefficient.

15. The graph evaluation method according to claim 14, further comprising an evaluation index calculation step of calculating the sum of the first evaluation index and the second evaluation index as an evaluation index for the graph model.

16. The search step includes searching for the optimal graph model that best suits the objective based on the reproducibility and complexity of the graph model, based on the evaluation indicators. In the evaluation index calculation step, the evaluation index is calculated for each of the multiple different graph models. The graph evaluation method according to claim 15, wherein in the search step, the graph model with the smallest evaluation index among the plurality of graph models is defined as the optimal graph model.

17. A graph evaluation method according to any one of claims 10 to 16, comprising an output step of outputting to a processing device at least one of the graph structure of the graph model from which the first evaluation index was calculated, the probability parameters, or an index for evaluating the graph model.

18. The graph structure of the graph model calculated by the graph evaluation method described in claim 17, the probability parameters of the graph model, or an index for evaluating the graph model is received, A method of processing received information.

19. On the computer, For a graph model represented by a graph structure using nodes and edges, and probability parameters representing the probability of occurrence for each node passage pattern of the graph structure, the likelihood of the actual passage pattern, which is the actual node passage pattern, is calculated based on the probability parameters for each node passage pattern. As an indicator for evaluating the graph model, a first evaluation indicator is calculated based on the likelihood of the actual passing pattern, to evaluate the reproducibility of the actual passing pattern by the graph model. A program to execute.

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