Information processing device, information processing method, and program

Abstract

This invention provides an information processing device, information processing method, and program that allow for adjustment of the PageRank correlation when analyzing a hypergraph using PageRank. [Solution] One aspect of the information processing device of the present disclosure comprises: a definition unit that defines a hypergraph represented including nodes and hyperedges; a random walk unit that repeatedly performs a process of determining a destination hyperedge according to the edge transition probability to each hyperedge connected to the transition start node, and transitioning to the destination node determined according to the node transition probability to each node included in the destination hyperedge; and an output unit that outputs the processing result, wherein the random walk unit adjusts the magnitude of a first weight according to the edge size of each hyperedge using a first weighting parameter, and adjusts the magnitude of a second weight according to the order of each node using a second weighting parameter.

Description

[Technical Field]

[0001] This disclosure relates to an information processing device, an information processing method, and a program. [Background technology]

[0002] In recent years, methods have been proposed that aim to create new value from the data sets being analyzed that could not be found in the past. These methods involve representing the data sets as hypergraphs and performing analysis using PageRank (PR).

[0003] A hypergraph is a generalized (extended) form of a graph, represented using edges called hyperedges that can hold (connect) two or more nodes. PageRank is an index that evaluates nodes and edges that are likely to be transitioned to in a random walk (RW), where transitions are made randomly to adjacent nodes connected by edges.

[0004] When analyzing a hypergraph using PageRank (random walk), examples include methods that directly apply the random walk to the hypergraph (see, for example, Non-Patent Document 1) and methods that apply the random walk to a general graph obtained by clique expansion of the hypergraph (see, for example, Non-Patent Documents 2 and 3). [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] U. Chitra and B. Raphael, “Random walks on hypergraphs with edge-dependent vertex weights”, International conference on machine learning PMLR, 2019, pp.1172-1181. [Non-Patent Document 2] K. Xirogiannopoulos, U. Khurana, and A. Deshpande, “Graphgen : Exploring interesting graphs in relational data”, Proceedings of the VLDB Endowment, 2015, vol.8, no.12, pp.2032-2035. [Non-Patent Document 3] K. Xirogiannopoulos and A. Deshpande, “Extracting and analyzing hidden graphs from relational databases”, Proceedings of the 2017 ACM International Conference on Management of Data, 2017, pp.897-912. [Overview of the Initiative] [Problems that the invention aims to solve]

[0006] However, in a method that directly applies random walks to a hypergraph, transitions to connected hyperedges occur with equal probability regardless of the edge size (number of nodes held) of the hyperedges. This means that transitions to nodes included in hyperedges with small edge sizes occur with a high probability. In other words, this method results in low correlations between PageRank and elements with a large number of data points in the analyzed dataset (hereinafter referred to as "PageRank correlation"), such as the correlation between the PageRank of a hyperedge and the edge size of the hyperedge, or the correlation between the PageRank of a node and the degree of the node (number of hyperedges connected to the node). Consequently, the influence of elements with a large number of data points in the analyzed dataset is ignored, reducing the usefulness of the data obtained using PageRank.

[0007] On the other hand, in the method of applying a random walk by clique expansion of the hypergraph, transitions to nodes connected by edges occur with equal probability, resulting in a high probability of transitioning to nodes included in hyperedges with large edge sizes. In other words, this method results in a high PageRank correlation, where the influence of elements with a large number of data points in the analyzed dataset is overemphasized, while the influence of elements with a small number of data points is ignored, thus limiting the amount of information obtained from PageRank.

[0008] Thus, conventional methods all have a fixed PageRank correlation, forcing analysis under conditions where the influence of some element in the data set being analyzed is ignored, and there is room for improvement.

[0009] This disclosure is made in view of the above circumstances and aims to provide an information processing device, information processing method, and program that can adjust the PageRank correlation when analyzing a hypergraph using PageRank. [Means for solving the problem]

[0010] One embodiment of the information processing device of the present disclosure comprises: a definition unit that defines a hypergraph represented by nodes and hyperedges to which any number of nodes can be connected; a random walk unit that repeatedly performs a process of determining a destination hyperedge according to the edge transition probability to each hyperedge connected to the transition start node, and transitioning to the destination node determined according to the node transition probability to each node included in the destination hyperedge; and an output unit that outputs the processing result, wherein the random walk unit performs a process of calculating the edge transition probability by adjusting the magnitude of a first weight according to the edge size of each hyperedge using a first weighting parameter whose value can be adjusted within a first range, and a process of calculating the node transition probability by adjusting the magnitude of a second weight according to the order of each node using a second weighting parameter whose value can be adjusted within a second range.

[0011] One aspect of the information processing method of the present disclosure includes a definition step in which a definition unit defines a hypergraph that includes nodes and hyperedges to which any number of nodes can be connected; a random walk step in which a random walk unit repeatedly determines a destination hyperedge according to the edge transition probability to each hyperedge connected to the transition start node, and transitions to the destination node determined according to the node transition probability to each node included in the destination hyperedge; and an output step in which an output unit outputs the processing result, wherein the random walk step includes a process of calculating the edge transition probability by adjusting the magnitude of a first weight according to the edge size of each hyperedge using a first weighting parameter whose value can be adjusted within a first range, and a process of calculating the node transition probability by adjusting the magnitude of a second weight according to the order of each node using a second weighting parameter whose value can be adjusted within a second range.

[0012] One aspect of the program of this disclosure involves causing a computer to execute a definition step that defines a hypergraph which includes nodes and hyperedges to which any number of nodes can be connected; a random walk step that repeatedly determines a destination hyperedge according to the edge transition probability to each hyperedge connected to the transition start node, and transitions to the destination node determined according to the node transition probability to each node included in the destination hyperedge; and an output step that outputs the processing result. The random walk step includes a process of calculating the edge transition probability by adjusting the magnitude of a first weight according to the edge size of each hyperedge using a first weighting parameter whose value can be adjusted within a first range, and a process of calculating the node transition probability by adjusting the magnitude of a second weight according to the order of each node using a second weighting parameter whose value can be adjusted within a second range. [Effects of the Invention]

[0013] According to this disclosure, it is possible to provide an information processing device, an information processing method, and a program that can adjust the PageRank correlation when analyzing a hypergraph using PageRank. [Brief explanation of the drawing]

[0014] [Figure 1] Figure 1 is a block diagram showing an example of the hardware configuration of the information processing device according to this embodiment. [Figure 2] Figure 2 is a block diagram showing an example of the functional configuration of the information processing device according to this embodiment. [Figure 3] Figure 3 shows an example of the data structure of the RDB (Relational Database) in this embodiment. [Figure 4] Figure 4 shows the RDB shown in Figure 3 defined as a hypergraph. [Figure 5] Figure 5 is an explanatory diagram of an example of a conventional method that directly applies random walks to a hypergraph. [Figure 6] Figure 6 is a graph showing an example of NPR correlation (correlation between the page rank of a node and the degree of the node (number of hyperedges connected to the node)) in a conventional method that directly applies random walks to a hypergraph. [Figure 7] Figure 7 is an explanatory diagram illustrating an example of a conventional method that applies a random walk by performing a clique expansion on a hypergraph. [Figure 8] Figure 8 is a graph showing an example of NPR correlation in a conventional method that applies a random walk after clique expansion of a hypergraph. [Figure 9] Figure 9 is an explanatory diagram illustrating an example of the edge size and node order of the hyperedge in this embodiment. [Figure 10] Figure 10 is an explanatory diagram illustrating an example of edge transition probabilities in a random walk according to this embodiment. [Figure 11] Figure 11 is an explanatory diagram illustrating an example of node transition probabilities in a random walk according to this embodiment. [Figure 12]Figure 12 is a flowchart showing an example of the PageRank generation process performed in the information processing device of this embodiment. [Figure 13] Figure 13 is a flowchart showing an example of the random walk processing in this embodiment. [Figure 14] Figure 14 is an explanatory diagram showing an example of PageRank in this embodiment. [Figure 15] Figure 15 shows an example of PageRank correlation when the value of the first weighting parameter (α) is adjusted. [Figure 16] Figure 16 is a graph showing an example of the relationship between the first weighting parameter (α) and the PageRank correlation. [Figure 17] Figure 17 shows an example of PageRank correlation when the value of the second weighting parameter (β) is adjusted. [Figure 18] Figure 18 is a graph showing an example of the relationship between the second weighting parameter (β) and the PageRank correlation. [Figure 19] Figure 19 is a graph showing an example of the relationship between the first weighting parameter (α) and the second weighting parameter (β) when the PageRank correlation is fixed. [Figure 20] Figure 20 is a graph showing an example of the relationship between weighting parameters (α, β) when the NPR correlation is fixed, and the EPR correlation (the correlation between the PageRank of hyperedges and the edge size (number of nodes held) of hyperedges). [Figure 21] Figure 21 is a graph showing an example of the relationship between weighting parameters (α, β) and NPR correlation when the EPR correlation is fixed. [Modes for carrying out the invention]

[0015] Hereinafter, embodiments of the present disclosure (hereinafter simply referred to as "these embodiments") will be described in detail with reference to the drawings. However, this disclosure is not limited to the following embodiments.

[0016] In the following, the method of this disclosure will be explained using the example of a data set to be analyzed in a relational database (hereinafter referred to as RDB), where the RDB is converted to a hypergraph and analysis is performed using PageRank (PR). However, the data set to be analyzed is not limited to RDBs.

[0017] A hypergraph is a generalized (extended) form of a graph, represented using edges called hyperedges that can hold (connect) two or more nodes. PageRank is an index that evaluates nodes and edges that are likely to be transitioned to in a random walk (RW), where transitions are made randomly to adjacent nodes connected by edges.

[0018] Specifically, in this embodiment, the information processing device converts the RDB into a hypergraph, adjusts the weights of each hyperedge and each node based on user input, calculates the edge transition probability to each hyperedge and the node transition probability to each node using the adjusted weights, and performs a random walk according to the calculated transition probabilities. The information processing device ranks the number of transitions to each hyperedge and node after the random walk as a PageRank and presents it to the user. Subsequently, the user repeatedly adjusts the weights to change the transition probabilities and regenerates and checks the PageRank in order to discover new value from the RDB that could not be found before.

[0019] As will be explained in detail later, in this embodiment, by adjusting the weights, the correlation between the PageRank of a hyperedge and the edge size of the hyperedge (number of nodes held) (hereinafter referred to as "EPR correlation"), and the correlation between the PageRank of a node and the node's order (number of hyperedges connected to the node) (hereinafter referred to as "NPR correlation") can be adjusted to various high and low values. In other words, in this embodiment, by adjusting the weights, it is possible to adjust the correlation between PageRank and elements with a large number of records in the RDB (hereinafter referred to as "PageRank correlation").

[0020] Therefore, as described above, by repeatedly regenerating the PageRank while adjusting the weights, even if the influence of some element in the RDB is ignored in the PageRank with one weight, the influence of that element can be taken into account in the PageRank with another weight. Thus, in this embodiment, by adjusting the weights, the PageRank can be generated while adjusting the elements of the RDB that are affected by the PageRank. Therefore, according to this embodiment, it is possible to support users in creating new value from the RDB that they could not previously find.

[0021] First, the configuration of the information processing device of this embodiment will be described.

[0022] Figure 1 is a block diagram showing an example of the hardware configuration of the information processing device 10 of this embodiment. As shown in Figure 1, the information processing device 10 comprises a control device 11, a main memory 12, an auxiliary storage device 13, a communication device 14, an input device 15, a display device 16, and various buses 19. The control device 11, main memory 12, auxiliary storage device 13, communication device 14, input device 15, and display device 16 are connected via various buses 19. Thus, the information processing device 10 of this embodiment has a general hardware configuration using a normal computer.

[0023] The control device 11 controls the overall operation of the information processing device 10. The control device 11 may be, for example, at least one of a CPU (Central Processing Unit) and a GPU (Graphics Processing Unit), but is not limited to these. There may be one or more CPUs or GPUs, and they may be single-core or multi-core.

[0024] Examples of main memory 12 include, but are not limited to, ROM (Read Only Memory) and RAM (Random Access Memory). ROM stores various programs, such as programs for controlling the information processing device 10 and programs for generating page rank. RAM is used as a workspace when the control device 11 performs various controls based on the programs stored in ROM.

[0025] The auxiliary storage device 13 stores the various programs and data described above. The various programs described above only need to be stored in at least one of the main storage device 12 and the auxiliary storage device 13. Examples of the auxiliary storage device 13 include, but are not limited to, at least one of existing storage devices capable of magnetic, electrical, or optical storage, such as an HDD (Hard Disk Drive), SSD (Solid State Drive), and DVD (Digital Versatile Disc). The auxiliary storage device 13 may be built into the information processing device 10 or externally connected to the information processing device 10 via an interface such as USB (Universal Serial Bus). Furthermore, the auxiliary storage device 13 may be a NAS (Network Attached Storage) connected via a network such as a LAN or WAN (Wide Area Network).

[0026] The communication device 14 is used to communicate with external devices, etc., via a network (not shown). Examples of the communication device 14 include, but are not limited to, a communication device for a wired LAN or a wireless communication device for a wireless LAN.

[0027] The input device 15 is used by the user for various inputs, selections, and specifications, and serves as a user interface between the user and the system. Examples of input devices 15 include, but are not limited to, keyboards, mice, and touch panels. The input device 15 may be built into the information processing device 10 or connected externally to the information processing device 10 via an interface such as USB.

[0028] The display device 16 displays various screens and serves as a user interface between the user and the device. Examples of the display device 16 include, but are not limited to, liquid crystal displays, organic electro-luminescence (OLED) displays, and touch panel displays. The display device 16 may be an internal display built into the information processing device 10, or an external display connected to the information processing device 10 via a display interface such as HDMI®.

[0029] In addition to the above configuration, the information processing device 10 may also be equipped with hardwired circuits such as ICs (Integrated Circuits), ASICs (Application Specific Integrated Circuits), and FPGAs (Field-Programmable Gate Arrays) that are specific to the information processing device 10.

[0030] Figure 2 is a block diagram showing an example of the functional configuration of the information processing device 10 in this embodiment. As shown in Figure 2, the information processing device 10 includes a definition unit 101, an adjustment unit 103, a random walk unit 105, and an output unit 107. The definition unit 101, adjustment unit 103, random walk unit 105, and output unit 107 can be realized, for example, by the control device 11, main memory 12, and communication device 14 described in Figure 2. The control device 11 reads the program for generating page rank stored in the main memory 12 (ROM) or auxiliary memory 13 and expands it into the main memory 12 (RAM). The control device 11 realizes each of the above-mentioned functional units by executing various processes according to the expanded program. Here, the case in which each of the above-mentioned functional units is realized as software has been explained as an example, but at least a part of each of the above-mentioned functional units may be realized as hardware. In this case, the functional unit to be realized as hardware may be realized, for example, by the hardwired circuit described above. Alternatively, any of the above-mentioned functional units may be realized through the cooperation of software and hardware.

[0031] Furthermore, the information processing device 10 of this embodiment does not necessarily require all of the above-described functional units to be part of its essential configuration; at least some of the functional units can be omitted.

[0032] The method of this embodiment will be explained below, using cooking recipes as examples, but this embodiment is not limited to these.

[0033] The definition unit 101 defines a hypergraph that includes nodes and hyperedges to which any number of nodes can be connected. In this embodiment, the definition unit 101 defines the hypergraph by converting the records and fields that constitute the RDB into nodes and hyperedges, respectively.

[0034] Figure 3 shows an example of the data structure of the RDB in this embodiment. The RDB shown in Figure 3 is a database of cooking recipes, where each record represents a recipe (recipe name and ingredients), each column represents the classification of ingredients (meat, vegetables, etc.), and each field represents specific ingredients (pork, soy sauce, etc.).

[0035] Figure 4 is a diagram that defines the RDB shown in Figure 3 as a hypergraph. In the hypergraph shown in Figure 4, the records of the RDB shown in Figure 3 are represented as nodes, and the fields of the RDB shown in Figure 3 are represented as hyperedges.

[0036] For example, node 201, which represents the record for recipe A, has hyperedges 251 representing pork, an ingredient in recipe A, and 253 representing soy sauce, an ingredient in recipe A, connected to it. Similarly, node 211, which represents the record for recipe B, has hyperedges 261 representing bacon, an ingredient in recipe B, 263 representing komatsuna (Japanese mustard spinach), an ingredient in recipe B, and 265 representing dashi (Japanese soup stock), an ingredient in recipe B. Furthermore, node 221, which represents the record for recipe C, has hyperedges 251 representing pork, an ingredient in recipe C, 263 representing komatsuna, an ingredient in recipe C, and 275 representing oyster sauce, an ingredient in recipe C, connected to it.

[0037] As mentioned above, a hyperedge can hold (connect) two or more nodes. Therefore, hyperedge 251, which represents pork, holds (connects) node 201, which represents the record for recipe A, and node 221, which represents the record for recipe C. Similarly, hyperedge 263, which represents komatsuna (Japanese mustard spinach), holds (connects) node 211, which represents the record for recipe B, and node 221, which represents the record for recipe C. Thus, in the hypergraph shown in Figure 4, records (nodes) with identical elements in each column of the RDB shown in Figure 3 are connected by hyperedges.

[0038] The adjustment unit 103 performs at least one of the following: adjusting the value of the first weighting parameter (hereinafter sometimes referred to as "α") within a first range, and adjusting the value of the second weighting parameter (hereinafter sometimes referred to as "β") within a second range. Specifically, the adjustment unit 103 performs at least one of the following in response to user operation: adjusting the value of the first weighting parameter and adjusting the value of the second weighting parameter.

[0039] The first weighting parameter is a parameter for adjusting the magnitude of the first weight according to the edge size of each hyperedge included in the hypergraph defined by the definition unit 101, and its value can be adjusted within a first range. The first weight will be described later. In this embodiment, the first range is 0 to 1 (0 ≤ α ≤ 1), and the adjustment unit 103 adjusts the first weighting parameter (α) within the range of 0 to 1 according to user operation.

[0040] The second weighting parameter is a parameter for adjusting the magnitude of the second weight according to the order of each node included in the hypergraph defined by the definition unit 101, and its value can be adjusted within the second range. The second weight will be described later. In this embodiment, the second range is 0 to 1 (0 ≤ β ≤ 1), and the adjustment unit 103 adjusts the second weighting parameter (β) within the range of 0 to 1 according to user operation.

[0041] The user operation for adjusting the first and second weighting parameters may be of any kind. For example, the user may directly input the values ​​of the first and second weighting parameters using the input device 15. Alternatively, a user interface (UI) such as a dial or slider for adjusting the values ​​of the first and second weighting parameters may be displayed on the display device 16, and the user may operate the UI using the input device 15.

[0042] Before explaining the random walk method of this embodiment using the random walk unit 105, we will first describe the conventional random walk method.

[0043] First, we will explain the conventional method of directly applying random walks to a hypergraph. Figure 5 is an explanatory diagram of an example of the conventional method of directly applying random walks to a hypergraph. In the hypergraph shown in Figure 5, hyperedges 351 and 353 are connected to node 301, and in addition to node 301, nodes 302, 303, and 304 are connected (held) to hyperedge 351, and in addition to node 301, node 305 is connected (held) to hyperedge 353.

[0044] As mentioned earlier, a random walk repeatedly transitions randomly to adjacent nodes connected by edges. If node 301 is the starting node, the probability of transitioning to hyperedges 351 and 353 is 1 / 2 each. If the transition is to hyperedge 351, since hyperedge 351 contains three nodes other than node 301 (nodes 302, 303, and 304), the probability of transitioning to each node is 1 / 3 each. Therefore, the probability of transitioning from node 301 to nodes 302, 303, and 304 is 1 / 6 ((1 / 2)*(1 / 3)), each. Also, if the transition is to hyperedge 353, since hyperedge 353 contains node 305 in addition to node 301, the probability of transitioning to node 305 is 1. Therefore, the probability of transitioning from node 301 to node 305 is 1 / 2 ((1 / 2)*(1)).

[0045] Thus, in conventional methods that directly apply random walks to hypergraphs, transitions occur with equal probability to connected hyperedges regardless of the edge size of the hyperedges. As a result, transitions to nodes included in hyperedges with small edge sizes occur with high probability. Consequently, this method results in low PageRank correlations such as EPR correlation and NPR correlation.

[0046] Figure 6 is a graph showing an example of NPR correlation in a conventional method that directly applies random walks to a hypergraph. In the graph shown in Figure 6, the vertical axis represents the Page Rank (NPR) of the node, and the horizontal axis represents the degree of the node. It can be seen that the two are not correlated (the correlation is low).

[0047] Therefore, in conventional methods, the influence of hyperedges and nodes originating from elements with a large number of records (hyperedges with large edge sizes and nodes with high degrees) is ignored in PageRank, reducing the usefulness of the data obtained by PageRank.

[0048] Next, we will describe a conventional method of applying a random walk by clique-expanding a hypergraph. Figure 7 is an explanatory diagram of an example of a conventional method of applying a random walk by clique-expanding a hypergraph. The hypergraph shown in Figure 7 is the same as the hypergraph shown in Figure 5, but because it has been clique-expanded, nodes 301, 302, 303, and 304 included in hyperedge 351 are connected to each other by normal edges, and nodes 301 and 305 included in hyperedge 353 are connected by normal edges.

[0049] Here, as in Figure 5, if we assume that node 301 is the transition initiation node, then since node 301 is connected to four nodes, 302, 303, 304, and 305, by normal edges, the probability of transitioning to each node is 1 / 4.

[0050] Thus, in the method of applying a random walk by clique expansion of the hypergraph, transitions to nodes connected by edges occur with equal probability. Therefore, it can be seen that transitions to nodes included in hyperedges with large edge sizes occur with high probability. Consequently, this method results in high PageRank correlations such as EPR correlation and NPR correlation.

[0051] Figure 8 is a graph showing an example of NPR correlation in a conventional method that applies a random walk after clique expansion of a hypergraph. In the graph shown in Figure 8, the vertical axis represents the Page Rank (NPR) of the node, and the horizontal axis represents the degree of the node, and it can be seen that the two are correlated (high correlation).

[0052] Therefore, in conventional methods, the influence of hyperedges and nodes originating from elements with a large number of records is given too much weight in PageRank, while the influence of hyperedges and nodes originating from elements with a large number of records is ignored, resulting in a limited amount of information obtained from PageRank.

[0053] In this embodiment, a first weight is assigned to each hyperedge in the hypergraph according to its edge size, and the value of the first weight can be adjusted by adjusting the value of the first weighting parameter. The edge transition probability is then calculated using the adjusted first weight. Similarly, a second weight is assigned to each node in the hypergraph according to its degree, and the value of the second weight can be adjusted by adjusting the value of the second weighting parameter. The node transition probability is then calculated using the adjusted second weight. Finally, a random walk is performed according to the calculated edge transition probability and node transition probability.

[0054] In this embodiment, the edge transition probability and node transition probability can be adjusted by adjusting the first and second weighting parameters, making it possible to perform a random walk by adjusting the PageRank correlation, such as the EPR correlation and NPR correlation.

[0055] Based on the above, the random walk method of this embodiment using the random walk unit 105 will be described in detail.

[0056] The random walk unit 105 performs the following processes: using the first weighting parameter adjusted by the adjustment unit 103, adjust the magnitude of the first weight according to the edge size of each hyperedge included in the hypergraph defined by the definition unit 101 to calculate the edge transition probability; and using the second weighting parameter adjusted by the adjustment unit 103, adjust the magnitude of the second weight according to the order of each node included in the hypergraph to calculate the node transition probability.

[0057] The first weight is used to calculate the edge transition probability to each hyperedge in the hypergraph, and its value is determined by the edge size. The second weight is used to calculate the node transition probability to each node in the hypergraph, and its value is determined by the degree of the node.

[0058] Figure 9 is an explanatory diagram illustrating an example of the edge size and node order of the hyperedge in this embodiment, and shows a part of the hypergraph shown in Figure 4. In the following, hyperedge 251 representing pork will be referred to as e P , Hyper Edge 253 which indicates soy sauce S It is sometimes referred to as such. Similarly, node 201, which represents the record of recipe A, is v A Node 221, which shows the record for recipe C, C Node 205, which shows the record for recipe X, X Node 206, which shows the record for recipe Y, Y Node 207, which shows the record for recipe Z, Z This may be referred to as such. In this embodiment, the node order is not the number of hyperedges connected to the node, but rather the number of normal edges that are considered to be connected to the node from the hyperedges connected to the node.

[0059] Hyperedge 251 contains four nodes: node 201 indicating the record of Recipe A, node 221 indicating the record of Recipe C, node 205 indicating the record of Recipe X, and node 206 indicating the record of Recipe Y. Therefore, the edge size of hyperedge 251 is S_e P = 4. Similarly, hyperedge 253 contains two nodes: node 201 indicating the record of Recipe A and node 207 indicating the record of Recipe Z. Therefore, the edge size of hyperedge 253 is S_e S = 2.

[0060] Node 201 indicating the record of Recipe A is considered to have four edges connected to nodes 221, 205, 206, and 207 respectively. Therefore, the degree of node 201 is d_v A = 4. Similarly, node 221 indicating the record of Recipe C is considered to have three edges connected to nodes 201, 205, and 206 respectively. Although the illustration is omitted, it is assumed that there are three more edges connected to node 221 in addition to nodes 201, 205, and 206. Therefore, the degree of node 221 is d_v C = 6. Similarly, node 205 indicating the record of Recipe X is considered to have three edges connected to nodes 201, 206, and 221 respectively. Therefore, the degree of node 205 is d_v X = 3. Similarly, node 206 indicating the record of Recipe Y is considered to have three edges connected to nodes 201, 205, and 221 respectively. Although the illustration is omitted, it is assumed that there is one more edge connected to node 206 in addition to nodes 201, 205, and 221. Therefore, the degree of node 206 is d_v Y = 4. Similarly, node 207 indicating the record of Recipe Z is considered to have one edge connected to node 201. Therefore, the degree of node 207 is d_v Z = 1.

[0061] The random walk unit 105 assigns a first weight to each hyperedge included in the hypergraph defined by the definition unit 101. Here, the first weight is expressed by formula (1).

[0062]

number

[0063] w_e k HyperEdge e k This shows the weight (first weight) assigned to S_e. k HyperEdge e k This indicates the edge size. α is the first weighting parameter used to adjust the magnitude of the first weight, as mentioned above. The possible values ​​of α are 0 ≤ α ≤ 1, as mentioned above. k is a variable.

[0064] Furthermore, the random walk unit 105 assigns a second weight to each node included in the hypergraph defined by the definition unit 101. Here, the second weight is expressed by formula (2).

[0065]

number

[0066] w_v k , node v k This indicates the weight (second weight) assigned to d_v. k , node v k This indicates the degree of the function. β, as mentioned above, represents the second weighting parameter used to adjust the magnitude of the second weight. As mentioned above, the possible values ​​of β are 0 ≤ β ≤ 1. k represents the variable.

[0067] The random walk unit 105 calculates the edge transition probability of each hyperedge using the first weight assigned to each hyperedge, and calculates the node transition probability of each node using the second weight assigned to each node.

[0068] Figure 10 is an explanatory diagram illustrating an example of edge transition probabilities in a random walk according to this embodiment. In the example shown in Figure 10, in the hypergraph shown in Figure 9, node 201 is v A The edge transition probabilities when the transition start node are shown, categorized by the value of α. Note that code 401 shows the edge transition probability when α=0, code 411 shows the edge transition probability when 0<α<1, and code 421 shows the edge transition probability when α=1.

[0069] First, let's explain the edge transition probability when α=0, indicated by symbol 401. When α=0, from equation (1), the hyperedge e P weight w_e P 3. HyperEdge e S weight w_e S This becomes 1. HyperEdge e P Edge transition probability P_e P ((w_e P ) / (w_e P )+(w_e S Since it is expressed as )), it becomes 3 / 4. Similarly, hyperedge e S Edge transition probability P_e S ((w_e S ) / (w_e P )+(w_e S Since it is expressed as )), it becomes 1 / 4. Thus, the edge transition probability when α=0 is the same as the transition probability of the conventional method that applies a random walk by clique expanding the hypergraph as explained in Figure 7.

[0070] Next, we will explain the edge transition probability for the case 0 < α < 1, indicated by symbol 411. In the case of 0 < α < 1, from equation (1), the hyperedge e P weight w_e P is, 3 1-α HyperEdge e S weight w_e S is, 1 1-α This is the result. HyperEdge e P Edge transition probability P_e P ((w_e P ) / (w_e P)+(w_e S )) is expressed as, 3 1-α / (3 1-α +1 1-α ) Similarly, HyperEdge e S Edge transition probability P_e S ((w_e S ) / (w_e P )+(w_e S )) is represented as, 1 1-α / (3 1-α +1 1-α )

[0071] Finally, we will explain the edge transition probability when α=1, indicated by symbol 421. When α=1, from equation (1), the hyperedge e P weight w_e P 1. HyperEdge e S weight w_e S This becomes 1. HyperEdge e P Edge transition probability P_e P ((w_e P ) / (w_e P )+(w_e S Since it is expressed as )), it becomes 1 / 2. Similarly, hyperedge e S Edge transition probability P_e S ((w_e S ) / (w_e P )+(w_e S Since it is expressed as )), it becomes 1 / 2. Thus, the edge transition probability when α=1 is the same as the transition probability of the conventional method that applies a random walk directly to the hypergraph as explained in Figure 5.

[0072] Furthermore, PageRank correlations, such as EPR correlation and NPR correlation, are highest when α=0, and decrease as the value of α approaches 1 from 0, with the lowest value being when α=1. Thus, in this embodiment, by adjusting the value of α within the range of 0 to 1, it is possible to represent PageRank using PageRank correlations that could not be represented conventionally.

[0073] FIG. 11 is an explanatory diagram of an example of node transition probability in the random walk of the present embodiment. In the example shown in FIG. 11, in the hypergraph shown in FIG. 9, v which is node 201 A is the transition start node, and the node transition probability when transitioning to hyperedge e P is shown by classifying according to the value of β. Note that reference numeral 501 indicates the node transition probability when β = 0, reference numeral 511 indicates the node transition probability when 0 < β < 1, and reference numeral 521 indicates the node transition probability when β = 1.

[0074] First, the node transition probability when β = 0 indicated by reference numeral 501 will be described. When β = 0, from Equation (2), the weight w_v C of node v C is 1, the weight w_v X of node v X is 1, the weight w_v Y of node v Y is 1, and so on. The node transition probability P_v C to node v C is represented by ((d_v C ) / (d_v C ) + (d_v X ) + (d_v Y )), so it is 1 / 3. Similarly, the node transition probability P_v X to node v X is represented by ((d_v X ) / (d_v C ) + (d_v X ) + (d_v Y )), so it is 1 / 3. Similarly, the node transition probability P_v Y to node v Y is represented by ((d_v Y ) / (d_v C ) + (d_v X ) + (d_v Y )), so it is 1 / 3. Thus, the edge transition probability when β = 0 is the same as the transition probability of the conventional method that applies random walk by performing a clique expansion on the hypergraph described in FIG. 7.

[0075] Next, we will explain the node transition probability when 0 < β < 1, as indicated by symbol 511. When 0 < β < 1, from equation (2), node v C Weight w_v C is 6 -β , node v X Weight w_v X is, 3 -β , node v Y Weight w_v Y is 4 -β This is the result. Node v C Node transition probability P_v C ((d_v C ) / (d_v C )+(d_v X )+(d_v Y )) is represented as, 6 -β / 6 -β +3 -β +4 -β Similarly, node v X Node transition probability P_v X ((d_v X ) / (d_v C )+(d_v X )+(d_v Y )) is expressed as, 3 -β / 6 -β +3 -β +4 -β Similarly, node v Y Node transition probability P_v Y ((d_v Y ) / (d_v C )+(d_v X )+(d_v Y )) is represented as, 4 -β / 6 -β +3 -β +4 -β This is the result.

[0076] Finally, we will explain the edge transition probability when β=1, indicated by symbol 521. When β=1, from equation (2), node v C Weight w_v C 1 / 6, node v X Weight w_v X 1 / 3, node v Y Weight w_vY This becomes 1 / 4. Node v C Node transition probability P_v C ((d_v C ) / (d_v C )+(d_v X )+(d_v Y Since it is expressed as )), it becomes 2 / 9. Similarly, node v X Node transition probability P_v X ((d_v X ) / (d_v C )+(d_v X )+(d_v Y Since it is represented as )), it becomes 4 / 9. Similarly, node v Y Node transition probability P_v Y ((d_v Y ) / (d_v C )+(d_v X )+(d_v Y Since it is expressed as )), it becomes 1 / 3.

[0077] Furthermore, PageRank correlations, such as EPR correlation and NPR correlation, are highest when β=0, and decrease as the value of β approaches 1 from 0, with the lowest value being when β=1. Thus, in this embodiment, by adjusting the value of β within the range of 0 to 1, it is possible to represent PageRank using PageRank correlations that could not be represented conventionally.

[0078] The random walk unit 105 determines the destination hyperedge according to the edge transition probability to each hyperedge connected to the transition start node, and repeats the process of transitioning to the destination node determined according to the node transition probability to each node included in the destination hyperedge.

[0079] Specifically, the random walk unit 105 calculates the edge transition probability to each hyperedge connected to the transition start node, and determines the destination hyperedge according to the calculated edge transition probability. The random walk unit 105 calculates the node transition probability to each node included in the destination hyperedge, and transitions to the destination node determined according to the calculated node transition probability. The random walk unit 105 uses the transitioned node as the transition start node and repeats the above process until the termination condition is met. The termination condition may include, but is not limited to, reaching the upper limit of the number of transitions or the expiration of the transition time.

[0080] The output unit 107 outputs the processing results of the random walk processing performed by the random walk unit 105. Specifically, the output unit 107 ranks the number of transitions to each hyperedge and each node after the random walk processing by the random walk unit 105 as a PageRank and displays it on the display device 16.

[0081] Next, the operation of the information processing device of this embodiment will be described.

[0082] Figure 12 is a flowchart showing an example of the PageRank generation process performed in the information processing device 10 of this embodiment.

[0083] First, the definition unit 101 converts the records and fields that make up the RDB into nodes and hyperedges, respectively, to define the hypergraph (step S101).

[0084] Next, the adjustment unit 103 adjusts the value of at least one of the first weighting parameter and the second weighting parameter in response to user operation (step S103).

[0085] Next, the random walk unit 105 performs a random walk process (step S105).

[0086] Figure 13 is a flowchart showing an example of the random walk processing in this embodiment.

[0087] First, the random walk unit 105 assigns a first weight, adjusted by the first weighting parameter, to each hyperedge connected to the transition start node in the defined hypergraph (step S201).

[0088] Next, the random walk unit 105 calculates the edge transition probability to each hyperedge connected to the transition start node using the assigned first weight (step S203).

[0089] Next, the random walk unit 105 determines the destination hyperedge according to the calculated edge transition probability (step S205).

[0090] Next, the random walk unit 105 assigns a second weight, adjusted by the second weighting parameter, to each node included in the hyperedge of the transition destination (step S207).

[0091] Next, the random walk unit 105 calculates the node transition probability to each node included in the hyperedge of the transition destination using the assigned second weight (step S209).

[0092] Next, the random walk unit 105 determines the destination node according to the calculated node transition probability (step S211).

[0093] Next, the random walk unit 105 transitions to the determined node and designates that node as the transition start node (step S213).

[0094] Next, the random walk unit 105 repeats the processes from steps S201 to S213 if the termination condition is not met (No in step S215), and terminates the process when the termination condition is met (Yes in step S215).

[0095] Returning to Figure 12, the output unit 107 ranks the number of transitions to each hyperedge and each node after the random walk processing by the random walk unit 105 as a page rank and displays it on the display device 16 (step S107).

[0096] Next, if the information processing device 10 receives a user input to adjust the value of at least one of the first weighting parameter and the second weighting parameter (Yes in step S109), it repeats the process in steps S101 to S109. If no user input is received (No in step S109), it terminates the process.

[0097] Figure 14 is an explanatory diagram showing an example of PageRank in this embodiment, specifically illustrating the transition of HyperEdge's PageRank (EPR) by adjusting the first weighting parameter.

[0098] In the example shown in Figure 14, the first EPR is generated and displayed on the display device 16 with the value of the first weighting parameter (α) set to 0 in UI601. As mentioned above, when α=0, the EPR places emphasis on the influence of hyperedges originating from elements with a large number of records (hyperedges with large edge sizes), so general-purpose seasonings that are often used in any recipe, such as sugar and salt, occupy the top ranks.

[0099] Furthermore, the second EPR is generated in UI601 displayed on the display device 16 with the first weighting parameter (α) set to 0.5, and is displayed on the display device 16. In the case of α=0.5, the influence of hyperedges originating from elements with a large number of records is mitigated, and the influence of hyperedges originating from elements with a small number of records (hyperedges with small edge sizes) is taken into account. As a result, the rank of general-purpose seasonings decreases, and the rank of less versatile ingredients such as cooking sake begins to increase.

[0100] Furthermore, the third EPR is generated in UI601 displayed on the display device 16 with the value of the first weighting parameter (α) set to 1, and is displayed on the display device 16. In the case of α=1, as mentioned above, the influence of hyperedges originating from elements with a large number of records is ignored, so the rank of general-purpose seasonings is further lowered, and the rank of less general-purpose ingredients is further raised.

[0101] By allowing users to view the PageRank generated while adjusting these RDB elements, users can create new value from RDBs that they could not previously find. For example, by having users view the EPR as shown in Figure 14, it is possible to remind them that ingredients that rank highly for a certain value of α are still available in their refrigerator, making it easier for them to decide on the day's menu.

[0102] Here, we have described an example of using PageRank to remind users of ingredients remaining in their refrigerators, but the scope of application of this disclosure is not limited to this. For example, it could also apply to the expiration dates of individual ingredients, or to things determined by the user's individual preferences. Furthermore, it is not limited to cooking recipes, but can be similarly applied to other content such as movies, books, and hotel reviews. For example, in the case of movies, it can be expected to remind users of movies involving minor actors or directors that they were interested in in the past but have now forgotten, thereby rekindling their interest. Thus, the scope of application of this disclosure largely depends on the individual preferences of the user, but the framework of this disclosure, namely the method of generating PageRank by adjusting the PageRank correlation, is expected to allow users to discover new value in any application.

[0103] Next, we will describe the evaluation results of the PageRank correlation in this embodiment.

[0104] Figure 15 shows an example of PageRank correlation when the value of the first weighting parameter (α) is adjusted. Specifically, it shows the NPR correlation and EPR correlation when α=0, and the NPR correlation and EPR correlation when α=0.7, in matrix format. Figure 16 is a graph showing an example of the relationship between the first weighting parameter (α) and PageRank correlation. Specifically, it shows a graph showing the relationship between α and NPR correlation, and a graph showing the relationship between α and EPR correlation. In both Figure 15 and Figure 16, the value of β is fixed at 0.

[0105] As is clear from Figures 15 and 16, decreasing the value of α reduces the correlation of both NPR and EPR, indicating that the NPR and EPR correlations can be adjusted by adjusting the value of α.

[0106] Figure 17 shows an example of PageRank correlation when the value of the second weighting parameter (β) is adjusted. Specifically, it shows the NPR correlation and EPR correlation when β=0, and the NPR correlation and EPR correlation when β=0.5, in matrix format. Figure 18 is a graph showing an example of the relationship between the second weighting parameter (β) and PageRank correlation. Specifically, it shows a graph showing the relationship between β and NPR correlation, and a graph showing the relationship between β and EPR correlation. In both Figure 17 and Figure 18, the value of α is fixed at 0.

[0107] As is clear from Figures 17 and 18, decreasing the value of β reduces the correlation of both NPR and EPR, indicating that the NPR and EPR correlations can be adjusted by adjusting the value of β.

[0108] Figure 19 is a graph showing an example of the relationship between the first weighting parameter (α) and the second weighting parameter (β) when the PageRank correlation is fixed. Specifically, it shows the relationship between α and β when the NPR correlation is fixed to the value shown in the upper right of the graph, and the relationship between α and β when the EPR correlation is fixed to the value shown in the upper right of the graph. As is clear from Figure 19, multiplying α and β together further reduces the correlation of both the NPR correlation and the EPR correlation.

[0109] Figure 20 is a graph showing an example of the relationship between weighting parameters (α, β) and EPR correlation when the NPR correlation is fixed. Specifically, it shows a graph showing the relationship between α and EPR correlation when the NPR correlation is fixed to the value shown in the upper right of the graph, and a graph showing the relationship between β and EPR correlation when the NPR correlation is fixed to the value shown in the upper right of the graph. Figure 21 is a graph showing an example of the relationship between weighting parameters (α, β) and NPR correlation when the EPR correlation is fixed. Specifically, it shows a graph showing the relationship between α and NPR correlation when the EPR correlation is fixed to the value shown in the upper right of the graph, and a graph showing the relationship between β and NPR correlation when the EPR correlation is fixed to the value shown in the upper right of the graph.

[0110] As is clear from Figures 20 and 21, α contributes particularly to the decrease in EPR correlation, and β contributes to the decrease in NPR correlation. When viewed at the same NPR correlation, a larger value of α leads to a decrease in EPR correlation, and when viewed at the same EPR correlation, a larger value of β leads to a decrease in NPR correlation. Therefore, the first weighting parameter (α) functions as a parameter to adjust the correlation between hyperedge page rank and edge size (EPR correlation), and the second weighting parameter (β) functions as a parameter to adjust the correlation between node page rank and node order (NPR correlation).

[0111] As described above, in this embodiment, the PageRank correlation can be adjusted when analyzing a hypergraph using PageRank. Therefore, according to this embodiment, by converting an RDB into a hypergraph and analyzing it using PageRank, it is possible to help users create new value from an RDB that they could not previously find. Furthermore, according to this embodiment, since the RDB is converted into a hypergraph for analysis, it is possible to analyze the contents of the RDB (field values) while keeping them confidential, enabling secure data analysis.

[0112] (program) The program executed by the information processing device of the above embodiment is provided in an installable or executable file format stored on a computer-readable storage medium such as a CD-ROM, CD-R, memory card, DVD, or flexible disk (FD).

[0113] Furthermore, the program executed by the information processing device of the above embodiment may be stored on a computer connected to a network such as the Internet and provided by downloading it via the network. Alternatively, the program executed by the information processing device of the above embodiment may be provided or distributed via a network such as the Internet. Alternatively, the program executed by the information processing device of the above embodiment may be pre-installed in ROM or the like and provided.

[0114] The program executed by the above-described embodiment and information processing device is configured as a module for realizing the above-described parts on a computer. In actual hardware, for example, the CPU reads the program from the HDD into RAM and executes it, thereby realizing the above-described parts on the computer.

[0115] The embodiments described above are merely examples of how this disclosure may be implemented, and they do not restrict the technical scope of this disclosure. Therefore, this disclosure can be implemented in various ways without departing from its essence or its main features. For example, in the embodiments described above, some components may be removed from the entire set of components.

[0116] This disclosure also includes the following aspects:

[0117] (1) A definition section that defines a hypergraph that includes nodes and hyperedges that can connect any number of nodes, A random walk unit that repeatedly determines the destination hyperedge based on the edge transition probability to each hyperedge connected to the transition start node, and transitions to the destination node determined based on the node transition probability to each node included in the destination hyperedge, It comprises an output unit that outputs the processing result, The random walk unit performs the following processes: adjusting the magnitude of the first weight according to the edge size of each hyperedge using a first weighting parameter whose value can be adjusted within a first range, and calculating the edge transition probability; and adjusting the magnitude of the second weight according to the degree of each node using a second weighting parameter whose value can be adjusted within a second range, and calculating the node transition probability. Information processing device.

[0118] (2) The device further comprises an adjustment unit that performs at least one of the following: adjusting the value of the first weighting parameter within the first range and adjusting the value of the second weighting parameter within the second range. The information processing device described in (1) above.

[0119] (3) The adjustment unit performs at least one of the following in response to user operation: adjusting the value of the first weighting parameter and adjusting the value of the second weighting parameter. The information processing device described in (2) above.

[0120] (4) The definition unit converts the records and fields constituting the relational database into the nodes and hyperedges, respectively, to define the hypergraph. The information processing device described in (1) above.

[0121] (5) The first weighting parameter is a parameter for adjusting the correlation between the PageRank and edge size of the hyperedge that transitions as a result of the above process. The information processing device described in (1) above.

[0122] (6) The second weighting parameter is a parameter for adjusting the correlation between the PageRank of the node transitioning through the above process and the degree of the node. The information processing device described in (1) above.

[0123] (7) Definition step, which defines a hypergraph that includes nodes and hyperedges that can connect any number of nodes, The random walk section repeats a random walk step in which it determines the destination hyperedge according to the edge transition probability to each hyperedge connected to the transition start node, and transitions to the destination node determined according to the node transition probability to each node included in the destination hyperedge, The output unit includes an output step that outputs the processing result, The random walk step includes a process of calculating the edge transition probability by adjusting the magnitude of the first weight according to the edge size of each hyperedge using a first weighting parameter whose value can be adjusted within a first range, and a process of calculating the node transition probability by adjusting the magnitude of the second weight according to the degree of each node using a second weighting parameter whose value can be adjusted within a second range. Information processing methods.

[0124] (8) A definition step that defines a hypergraph which is represented by nodes and hyperedges which can connect any number of nodes, A random walk step that repeatedly determines the destination hyperedge based on the edge transition probability to each hyperedge connected to the transition start node, and transitions to the destination node determined based on the node transition probability to each node included in the destination hyperedge, The computer is instructed to perform an output step that outputs the processing result, The random walk step includes a process of calculating the edge transition probability by adjusting the magnitude of the first weight according to the edge size of each hyperedge using a first weighting parameter whose value can be adjusted within a first range, and a process of calculating the node transition probability by adjusting the magnitude of the second weight according to the degree of each node using a second weighting parameter whose value can be adjusted within a second range. program. [Explanation of Symbols]

[0125] 10 Information Processing Devices 101 Definition part 103 Adjustment section 105 Random Walk Section 107 Output section

Claims

1. A definition section that defines a hypergraph that includes nodes and hyperedges to which any number of nodes can be connected, A random walk unit that repeatedly determines the destination hyperedge based on the edge transition probability to each hyperedge connected to the transition start node, and transitions to the destination node determined based on the node transition probability to each node included in the destination hyperedge, It comprises an output unit that outputs the processing result, The random walk unit performs the following processes: adjusting the magnitude of the first weight according to the edge size of each hyperedge using a first weighting parameter whose value can be adjusted within a first range, and calculating the edge transition probability; and adjusting the magnitude of the second weight according to the degree of each node using a second weighting parameter whose value can be adjusted within a second range, and calculating the node transition probability. Information processing device.

2. The system further includes an adjustment unit that performs at least one of the following: adjusting the value of the first weighting parameter within the first range, and adjusting the value of the second weighting parameter within the second range. The information processing apparatus according to claim 1.

3. The adjustment unit performs at least one of the following processes in response to user operation: adjusting the value of the first weighting parameter and adjusting the value of the second weighting parameter. The information processing apparatus according to claim 2.

4. The definition unit converts the records and fields constituting the relational database into the nodes and hyperedges, respectively, to define the hypergraph. The information processing apparatus according to claim 1.

5. The first weighting parameter is a parameter for adjusting the correlation between the PageRank and edge size of the hyperedge that transitions as a result of the above process. The information processing apparatus according to claim 1.

6. The second weighting parameter is a parameter for adjusting the correlation between the PageRank of the node transitioning through the process and the degree of the node. The information processing apparatus according to claim 1.

7. The definition part includes a definition step that defines a hypergraph which is represented by nodes and hyperedges that can connect any number of nodes, The random walk section repeats a random walk step in which it determines the destination hyperedge according to the edge transition probability to each hyperedge connected to the transition start node, and transitions to the destination node determined according to the node transition probability to each node included in the destination hyperedge, The output unit includes an output step that outputs the processing result, In the random walk step, the process involves adjusting the magnitude of the first weight according to the edge size of each hyperedge using a first weighting parameter whose value can be adjusted within a first range, and calculating the edge transition probability, and adjusting the magnitude of the second weight according to the degree of each node using a second weighting parameter whose value can be adjusted within a second range, and calculating the node transition probability. Information processing methods.

8. A definition step that defines a hypergraph that includes nodes and hyperedges that can connect any number of nodes, A random walk step that repeatedly determines the destination hyperedge based on the edge transition probability to each hyperedge connected to the transition start node, and transitions to the destination node determined based on the node transition probability to each node included in the destination hyperedge, The computer is instructed to perform an output step that outputs the processing result, In the random walk step, the process involves adjusting the magnitude of the first weight according to the edge size of each hyperedge using a first weighting parameter whose value can be adjusted within a first range, and calculating the edge transition probability, and adjusting the magnitude of the second weight according to the degree of each node using a second weighting parameter whose value can be adjusted within a second range, and calculating the node transition probability. program.

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