JP7282052B2 - Graph variable estimation model, apparatus and method for convolution with edge feature dependent intra-graph relations - Google Patents

Description

The present invention relates to technology for estimating information related to a graph from the structure of the graph.

2. Description of the Related Art In an organization as a group of multiple members, there are not a few needs to predict various events that may occur in relation to the organization and its members, and to make use of it for the management and operation of the organization.

As a technical example that meets such needs, for example, Patent Document 1 discloses a leave of absence prediction system capable of predicting whether or not an employee of a company or the like will take a leave of absence at a predetermined time. Specifically, this system learns the relationship between data that includes employee working hours and data that indicates whether employees are on leave or not, and builds a prediction model that predicts the risk of employees taking leave at a given time. predictive model construction means for predicting the risk of an employee subject to prediction taking a leave of absence at a predetermined time based on data including the working hours of the employee subject to prediction and the prediction model; there is

On the other hand, GNN (Graph Neural Networks) technology that applies deep learning, which has achieved remarkable results in recent years in fields such as image recognition and natural language analysis, to the graph structure and estimates information related to the graph. is making great progress.

By using this GNN, for example, an organization can be regarded as a graph, each member can be a node in it, and the relationship between nodes (members) can be represented by edges. Events can be predicted as a matter of estimating information related to the graph.

Among these GNNs, R-GCNs (Relational Graph Convolutional Networks) proposed in Non-Patent Document 1 are currently attracting a great deal of attention. This R-GCN is an algorithm that improves the accuracy of estimating information related to the graph by convolving the feature amount of the graph for each relationship in a situation where there are multiple relationships between nodes in the graph. .

JP 2019-135662 A

Michael Schlichtkrull, Thomas N. Kipf, Peter Bloem, Rianne van den Berg, Ivan Titov, Max Welling, “Modeling Relational Data with Graph Convolutional Networks”, European Semantic Web Conference (ESWC 2018): The Semantic Web, pp.593-607 , 2018

The technology described in the above-mentioned Patent Document 1 calculates the leave of absence risk of the employee from the attendance data of the individual employee. However, the mental health situation in the workplace is also an indirect cause of employees taking leave of absence. It is also known to be greatly influenced by Therefore, with the technique described in Patent Document 1, it is difficult to obtain a sufficiently high-precision predicted value of the risk of absence from work.

On the other hand, if the above-mentioned R-GCN is used to address such a problem, the relationships (edges) between the members (nodes) in the organization (graph) can also be incorporated into the estimation process, which matches the actual situation of the organization. There is a possibility that more accurate estimation processing can be performed.

However, even if R-GCN is applied to the problem of employees taking leave of absence, it is not trivial to aggregate/extract the feature values of the organization (graph). , etc. are usually considered to be dynamic things that change over time rather than fixed things, and how to take in such dynamic relationships is completely unsolved.

Therefore, the present invention provides a graph variable estimation model, a graph variable estimation device, and a graph variable estimation method that can more reliably capture the intra-graph relationships inherent in a graph and estimate information related to the graph. With the goal.

According to the present invention, a graph variable estimation model that receives graph information related to a graph as an input, convolves the graph information in a plurality of intermediate layers having virtual nodes corresponding to nodes of the graph, and estimates objective variables for the graph. and
at least one intra-graph relationship is set corresponding to each of at least one value range of values taken by edge feature quantities representing edge features in the graph;
Each virtual node in the intermediate layer is a node representing the characteristics of the virtual node corresponding to the intra-graph relationship in the preceding intermediate layer for each intra-graph relationship included in a set of intra-graph relationships including at least one intra-graph relationship. Convoluting the feature amount and the edge feature amount representing the feature of the virtual edge connecting the virtual nodes corresponding to the intra-graph relation in the intermediate layer in the previous stage to generate the node feature amount representing the feature of itself. A graph variable estimation model is provided.
Moreover, according to the present invention,
A graph variable estimation model that receives graph information related to a graph as an input, convolves the graph information in a plurality of intermediate layers having virtual nodes corresponding to the nodes of the graph, and estimates an objective variable for the graph,
at least one intra-graph relation is set corresponding to each of at least one value range of values taken by edge feature quantities representing edge features in the graph,
Each virtual node in the intermediate layer represents, for each intra-graph relation included in a set of intra-graph relations including the at least one intra-graph relation, a feature of a virtual node corresponding to the intra-graph relation in the preceding intermediate layer. Convolve the node features to generate node features that represent their own features,
The graph expresses a group including a plurality of communication subjects as nodes that can communicate with each other. A group is formed, and the target variable is a variable that takes a value related to an event that can be affected by whether or not the communication subject belongs to the subgroup.
Provided is a graph variable estimation model characterized by:

Further, in the graph variable estimation model according to the present invention, each virtual node in the intermediate layer is determined for each in-graph relation for each in-graph relation included in the set, with respect to the convolution result for the in-graph relation Alternatively, it is also preferable to generate a node feature amount representing its own feature by adding learned weights.

Furthermore, the graph variable estimation model according to the present invention preferably further includes an objective variable estimation layer that receives outputs from the last stages of the plurality of intermediate layers and outputs values related to the objective variables estimated for the graph.

In addition, in the graph variable estimation model according to the present invention, the objective variables to be estimated are the objective variables related to the nodes of the graph, the objective variables related to the edges of the graph, and the objective variables related to the whole or part of the graph. It is also preferred that at least one of

According to the present invention, graph information related to a graph is input, the graph information is convoluted in a plurality of intermediate layers having virtual nodes corresponding to the nodes of the graph, and an objective variable for the graph is estimated. A variable estimation model,
at least one intra-graph relationship is set corresponding to each of at least one value range of values taken by edge feature quantities representing edge features in the graph;
Each virtual node in the intermediate layer has, for each intra-graph relation included in a set of intra-graph relations including at least one intra-graph relation, a virtual edge connecting the virtual nodes corresponding to the intra-graph relation in the preceding intermediate layer. Provided is a graph variable estimation model characterized by convolving an edge feature quantity representing a feature to generate a node feature quantity representing its own feature.

According to the present invention, further, using the graph variable estimation model as described above, the input graph information is used to output information about the objective variable estimated for the graph associated with the graph information. A graph variable estimator is provided.

According to the present invention, there is further provided a graph that receives graph information related to a graph as an input, convolves the graph information in a plurality of intermediate layers having virtual nodes corresponding to the nodes of the graph, and estimates an objective variable for the graph. A computer -implemented method of graph variable estimation using a variable estimation model, comprising:
setting at least one intra-graph relation corresponding to each of at least one value range of values taken by edge feature quantities representing features of edges in the graph;
In each virtual node of the intermediate layer, for each intra-graph relation included in a set of intra-graph relations including the at least one intra-graph relation, characteristics of the virtual node corresponding to the intra-graph relation in the previous intermediate layer are determined. A step of convolving the node feature value representing the node feature value and the edge feature value representing the feature of the virtual edge connecting the virtual nodes corresponding to the intra-graph relation in the intermediate layer in the previous stage to generate the node feature value representing the feature of each of the virtual nodes. There is provided a graph variable estimation method comprising:
Further, according to the present invention, graph information relating to a graph is input, the graph information is convoluted in a plurality of intermediate layers having virtual nodes corresponding to the nodes of the graph, and an objective variable for the graph is estimated. A computer-implemented method of graph variable estimation using an estimation model, comprising:
setting at least one intra-graph relation corresponding to each of at least one value range of values taken by edge feature quantities representing features of edges in the graph;
In each virtual node of the intermediate layer, for each in-graph relation included in a set of in-graph relations including the at least one in-graph relation, for a virtual node corresponding to the in-graph relation in the preceding intermediate layer, the virtual a step of convolving a node feature representing a feature of a node to generate a node feature representing a feature of each virtual node;
has
The graph expresses a group including a plurality of communication subjects as nodes that can communicate with each other. A group is formed, and the target variable is a variable that takes a value related to an event that can be affected by whether or not the communication subject belongs to the subgroup.
There is provided a graph variable estimation method characterized by:

According to the graph variable estimation model, the graph variable estimation device, and the graph variable estimation method of the present invention, it is possible to more reliably capture the intra-graph relationships inherent in a graph and estimate information related to the graph.

1 is a schematic diagram showing an embodiment of a graph variable estimation device that performs graph variable estimation processing using a graph variable estimation model according to the present invention; FIG. FIG. 10 is a schematic diagram for explaining a specific example of setting the "dynamic graph relations" according to the present invention;

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

[Graph variable estimation device, graph variable estimation model]
FIG. 1 is a schematic diagram showing an embodiment of a graph variable estimation device that performs graph variable estimation processing using a graph variable estimation model according to the present invention.

The graph variable estimation device 2 of this embodiment shown in FIG.
(a) Information on individual components (employees) (e.g., employee attribute information, attendance data, and statistics such as the average and variance of these values),
(b) Information related to communication or action/connection between components (employees) (e.g., amount related to e-mails and chats exchanged between employees)
Based on
(c) Objective variables that are information about constituents (employees) or groups (company A) (e.g., absence risk, which is the probability that a particular employee will be absent from work at some point or period in the future).
is a device for estimating

More specifically, in this graph variable estimating device 2, the group (company A) is regarded as a graph, the constituent elements (employees) are nodes, and the communication or action/connection between the constituent elements (employees) is After expressing the information at the edge,
Let the information in (a) above be a feature amount related to a node (node feature amount),
Using the above information (b) as a feature amount related to the edge (edge feature amount),
Using the graph variable estimation model 1, the graph variable (risk of absence from work), which is the objective variable of (c) above, is estimated.

Here, the graph variable estimation model 1, which is the core of such graph variable estimation processing, is a model constructed using the GCN (Graph Convolutional Networks) algorithm in this embodiment, and in the graph (group, company) A dynamic graph relationship that exists and changes dynamically depending on the communication between nodes (components, employees) or the state of action/connection (edge state). The above feature amount is convoluted for each “relationship in the graph” including , and the model outputs graph variables (objective variable, risk of absence from work) as estimated values.

By the way, the "dynamic intra-graph relation" that dynamically changes depending on the edge state, as described above, means that the nodes (components, employees) that belong to it in the graph (group, company) change dynamically. It is also understood to define a dynamic subgraph (dynamic subgroup) that Then, the graph variables (objective variable, risk of absence from work) as estimated values are whether or not the node (component, employee), which is the subject of communication or action/connection, belongs to the dynamic subgraph (dynamic subgroup). It can also be regarded as a variable that is influenced by something.

Also in FIG. 1, graph variable estimation model 1 is more specifically:
(A) Graph information (for example, node features and edge features) related to a graph is input, and the graph information (node features and It is a graph variable estimation model that convolves the edge feature value) and estimates the objective variable for the graph,
(B) Each “virtual node” in each of a plurality of “intermediate layers” is set for each in-graph relation included in a set of in-graph relations including at least one set “dynamic in-graph relation”, It is characterized by convoluting the node feature amount representing the feature of the "virtual node" corresponding to the intra-graph relation in the "middle layer" to generate the node feature amount representing its own feature.

In addition, the above (B) "relationship within dynamic graph" will be described later in detail with reference to FIG.
(C) At least one is set corresponding to each of at least one value range of the value taken by the edge feature amount in the graph. In this way, the "dynamic intra-graph relation" is a relation that changes "dynamically" as the value of the edge feature quantity changes and the value range to which this value belongs also changes.

For example, in the case of estimating the future risk of absence from work for each employee of company A, the edge feature value is, for example, "the number of e-mails in a predetermined unit period between employees (as nodes connected by the edge)" is defined, as a "dynamic graph relation", for example,
(a) "Relationship r_1 in dynamic graph": a relation whose number is less than 10;
(b) "Intra-dynamic graph relation r_2": a relation whose number is 10 or more and less than 20;
(c) "Intra-dynamic graph relation r_3": A relation whose number is 20 or more can be set. Such a relationship is automatically calculated based on the edge feature amount (the number of e-mails), and is dynamic in that it changes, for example, daily according to changes in the edge feature amount. .

Here, each "virtual node" corresponding to each employee in the "middle layer" included in the graph variable estimation model 1 has each The node features of the "virtual nodes" (in the intermediate layer in the previous stage) corresponding to the employee and other employees who have a relationship within the dynamic graph are convoluted to generate a node feature representing the feature of the employee.

In this way, the graph variable estimation model 1 more reliably captures the relationships within the graph including the "dynamic relationships within the graph" as described above, thereby estimating the graph variables (objective variable, risk of absence from work) with higher accuracy. It also makes it possible to

In this regard, it is true that in the case of estimating the risk of absence from work described above, not only the attendance data (node feature amount) of each employee is taken into consideration, but also the dynamic graph shown in (a) to (c) above. By taking into account dynamic employee subgroups that are formed by the degree and frequency of communication between employees, it is possible to obtain more accurate results for estimating the risk of absence from work. Conventionally, however, it has been difficult to appropriately set such "dynamic graph relationships" and incorporate them into an estimation model.

On the other hand, the graph variable estimation model 1, as defined in (C) above, can automatically set the "dynamic graph relations" based on the value of the edge feature value of each edge. Graph variables (objective variable, risk of absence from work) estimation processing that takes into account dynamic relationships within graphs has also been realized. This makes it possible to obtain more accurate estimates of graph variables (objective variable, risk of absence from work) that also reflect the dynamic relationships inherent in the graph.

By the way, the "dynamic intra-graph relation" in (C) above can be said to be a convolution process enabled by discretizing and quantizing the edge feature quantity expressing the relation between nodes. With this kind of ingenuity, for example, in the case of estimating the above-mentioned risk of absence from work, in addition to labor and personnel knowledge such as superiors, colleagues and subordinates at company A, the degree and frequency of communication in each of these work relationships It is possible to incorporate variable information related to the degree of activation of workers and ease of work into the estimation of the risk of absence from work.

Furthermore, in the graph variable estimation model 1 shown in FIG. 1, as a preferred embodiment,
(D) Each “virtual node” in each of a plurality of “intermediate layers” is set for each in-graph relation included in a set of in-graph relations including at least one set “dynamic in-graph relation”, It is also preferable to convolve the edge feature quantity representing the feature of the "virtual edge" connecting the "virtual nodes" corresponding to the intra-graph relation in the "intermediate layer" to generate the node feature quantity representing its own feature.

In this case, not only the "virtual nodes (features)" of the "intermediate layer" in the previous stage, but also the "virtual edges (features)" are convoluted based on the "dynamic intra-graph relations". It is also possible to directly incorporate changing communication or action/connection situations as appropriate, thereby enabling execution of more accurate estimation processing of graph variables (objective variable, risk of absence from work).

As described above, the above configuration of the graph variable estimation model 1 expresses the structure of a program that embodies a machine learning algorithm that realizes the model, in this embodiment, the GCN algorithm. It preferably relates to the R-GCN (Relational Graph Convolutional Networks) algorithm, which is advanced in the field.

[Model configuration, device configuration, graph variable estimation program]
The configurations and functions of the graph variable estimation model 1 and the graph variable estimation device 2 will be described in detail below. Of these, the graph variable estimation model 1, as shown in FIG. 1, is a model that is incorporated into the graph variable estimation program according to the present invention installed in the graph variable estimation device 2 and that makes it possible to execute the main steps of the graph variable estimation process. and, as its constituent elements,
It has (a) a graph feature quantity extraction unit 10 and (b) an objective variable estimation unit 11 .

First, the "node feature amount" and the "edge feature amount", which are the graph information input to the graph feature amount extraction unit 10 in (a) above, will be described.

"Node feature amount" is a vector amount calculated for each node and having node information related to the node as a feature amount component. For example, when an employee is set as a node, the node information is:
(a) Employee demographic information such as gender, age, place of residence, and length of service;
(b) Attendance data including at least one of the employee's working hours (in a predetermined period), overtime hours, days of paid leave taken, job organization, leave history, etc.;
(c) Statistical quantities such as averages and variances (calculated for each department or company A as a whole) in the above values (a) and (b) can be employed. Of course, when the objective variable is the risk of absence from work for each employee (node), other information related to employees that may be related to the event of absence from work can also be adopted as the node feature amount. .

Next, the "edge feature amount" is calculated for each edge connecting nodes, and is a vector amount whose feature amount component is the edge information related to the edge. For example, when an employee is set as a node, the edge information is ,
(d) Information related to communication between employees by e-mails, chats, etc. exchanged between employees (for example, the number of e-mails and chats (exchanged during a predetermined period), predetermined words included in e-mails and chats number of appearances or frequency of appearance, vectors embedded representation of sentences contained in emails and chats (generated by known feature quantification methods using neural networks, etc.), presence or absence or number of pictogram reactions to emails and chats, etc.) or,
(e) Organizational relationships between employees (e.g., superior-subordinate relationships, co-worker relationships, relationships belonging to the same department, etc.)
may be adopted. In addition, of course, when the objective variable is the risk of absence from work for each employee (node), other information related to the state/event between employees that may be related to the event of absence from work is also adopted as the edge feature value. Is possible.

Next, the "intra-graph relation" (including the dynamic intra-graph relation) utilized in the convolution process in the graph feature quantity extraction unit 10 of (a) above will be described.

The intra-graph relations are divided into the already explained "dynamic intra-graph relations" and other "static intra-graph relations". Of these, the "dynamic graph relation" is a relation set at least one corresponding to each of at least one value range for the value taken by the predetermined edge feature value, and the value of the edge feature value changes. Then, as the value range to which the value belongs also changes, it dynamically changes.

For example, as already explained, in the case of estimating the future risk of absence from work for each employee of company A, the edge feature value is, for example, "a predetermined unit period between employees (as a node connected by the edge) If the number of e-mails in "is defined, as the "dynamic graph relationship", for example,
(a) "Relationship r_1 in dynamic graph": a relation whose number is less than 10;
(b) "Intra-dynamic graph relation r_2": a relation whose number is 10 or more and less than 20;
(c) "Relationship r_3 in dynamic graph": A relation whose number is 20 or more can be set.

Here, the edge feature quantity (the number of e-mails) that determines the “dynamic relations in the graph” of (a) to (c) above is usually a quantity that changes day by day or moment by moment. The "relationship in the graph" also changes, for example, day by day or moment by moment, according to the temporal change in the edge feature amount.

As another example, if the edge feature value is "relationships between employees in terms of organizational structure (e.g., relationships between superiors and subordinates, relationships between colleagues, etc.)", "relationships within a dynamic graph" may be, for example,
(d) “Relationship r_4 in dynamic graph”: A relation in which the numerical value (the value of the edge feature value) representing the relationship on the organizational structure is a numerical value (for example, “2”) indicating the “relationship between superior and subordinate”;
(e) "Relationship r_5 in dynamic graph": Setting a relationship in which the numerical value (edge feature value) representing the relation in the job organization is a numerical value (for example, "1") indicating the "relationship between colleagues". can also

Here, the edge features (relationships in the organizational structure) that determine the "dynamic graph relationships" in (d) and (e) above are also variables that can change over a relatively long period of time. , the "relationship in the dynamic graph" also changes according to the temporal change of the edge feature amount.

In addition, the "dynamic graph relationship" is defined by directed edges (or including the directed edges) that express the direction of influence in the relationship and the degree of influence by the direction of the edge and its feature value, respectively. It may be specified. For example, in the case of the "relationship between a boss and a subordinate" as in (d) above, a directed edge having a direction from the "supervisor" node to the "subordinate" node and a certain edge feature quantity can be used to generate "( It is also possible to define a "dynamic intra-graph relation" such as "I am a subordinate to the other node". Here, by prescribing such a "dynamic graph relationship", (as will be explained in detail later), when calculating the node feature values of virtual nodes, for example, By convoluting the feature quantity, it is possible to reliably capture the influence of the boss on the subordinate. Incidentally, a plurality of such directed edges may be set as having different orientations and edge feature amounts for one pair of nodes.

On the other hand, the "static relations in the graph" are relations in the graph other than the "dynamic relations in the graph" that are not linked to edge features. It can be a relationship that is set depending on the value. For example, if the node feature value is "employee's gender", the "static graph relation" is, for example,
(f) “Relationship r_6 in static graph”: A relation in which the sex of the employee (the value of the node feature value) is “female” (for example, “2”);
(g) "Relationship r_7 in static graph": A relation can be set in which the sex of the employee (the value of the node feature value) is "male" (for example, "1").

Furthermore, it is also possible to set, for example, a "relationship between co-creators (co-authors) of a specific report or paper among employees" as the "relationship within the static graph". In this case, it can be understood that a static relationship is set that connects different concepts such as "employee (creator, author)" and "report, paper".

FIG. 2 is a schematic diagram for explaining a specific example of the setting of the "dynamic graph relations" according to the present invention.

According to the relationship setting example shown in FIG. 2, the dynamic graph relationships r_p _, r_q, r_r, . is set. in particular,
(a) intra-graph relation r_p: a relation in which the value of the edge feature quantity e _i,j is within a value range equal to or greater than a and less than b;
(b) intra-graph relation r_q: a relation in which the value of the edge feature quantity e _i,j is c;
(c) intra-graph relation r_r: a relation in which the value of the edge feature quantity e _i,j is within a value range equal to or greater than d and less than e;
・・・
is set. Of course, the number line range including the values a to e shown in FIG. 2 is the value range that the edge feature quantity e _i,j can take.

Here, if the value of the edge feature quantity e _i,j changes for each edge, the relationships r_p, r_q, r_r, . . . The setting range and distribution of

By the way, even if the value of the edge feature quantity e _i,j at each edge changes over time, the setting range and distribution state of the relations r_p, r_q, r_r, ... in the dynamic graph do not change. However, even in such a situation, the relationships r_p _, r_q, r_r, . . . It can be said to be "dynamic" in the sense that it can change depending on it.

As described above, in the present embodiment, the "dynamic intra-graph relation" expresses a dynamic relation automatically defined by a threshold value as a hyperparameter related to the edge feature amount. That is, for example, if the threshold value is set based on a predetermined knowledge, the "dynamic graph intra-relationship" itself can be automatically generated and incorporated into the graph variable estimation process.

Returning to FIG. 1, the (above (a)) graph feature amount extraction unit 10 receives graph information ("node feature amount" and "edge feature amount") as described above, and extracts "dynamic graph The virtual graph feature amount is generated by convolving the graph information with the graph intra-relationship including the "internal relation", and the virtual graph feature amount is output to the objective variable estimating unit 11 connected to its subsequent stage.

More specifically, in the present embodiment, the graph feature amount extraction unit 10 extracts a plurality of intermediate layers each having a plurality of virtual nodes respectively corresponding to a plurality of nodes in a graph related to a graph variable to be estimated (objective variable). configuration.

Let l be the index indicating the intermediate layer, i be the index indicating the virtual node in the intermediate layer, and h _i (l) be the node feature amount at the virtual node i in the intermediate layer ( ^l) . When node features are expressed in this way, l takes an integer value from 0 to L (L is (the number of intermediate layers - 1)), and i takes an integer value from 1 to N (N is the number of virtual nodes in one intermediate layer. ). However, the virtual node in the first hidden layer (0) is the node of the graph related to the graph variable (objective variable) to be estimated, and the node feature quantity h _i ⁽⁰⁾ is the node feature of the node of the graph. amount. Note that the hidden layer (0) may directly receive such node features h _i ⁽⁰⁾ (or edge features) from the input layer (not shown), or may be the input layer itself. may

In addition, let R be the set of set intra-graph relations including "dynamic intra-graph relations", let r be the intra-graph relation belonging to the set R (r∈R), and be adjacent to the virtual node i in the relation r Let N _i ^r be a set of virtual nodes (having relationship r with virtual node i), and let j (j∈N _i ^r ) be an index indicating a virtual node belonging to set N _i ^r . The node feature value h _i ^{(l+1) at the virtual node i in l+1) is expressed} by the following equation (1) h _i ^(l+1) = σ(Σ _r Σ _j c _i,r ⁻¹・A _r ^(l)・_hj ^(l) ＋C ^(l)・h _i ^(l) )
is calculated as

Here, in the above formula (1), l takes an integer value from 0 to (L-1). Also, σ is an activation function such as a ramp function ₍ ReLU), Σ _r is the summation of r (r∈R) in the set R, and Σ _j is the node ^j (j ∈N _i ^r ). Incidentally, the relationship r is fixed as given regardless of the intermediate layer. In addition, c _i,r is a normalization constant for virtual node i in relation r, and is a value that can be interpreted as the number of adjacent nodes of virtual node i in relation r. set. Furthermore, A _r ^(l) and C ^(l) are the learned internal parameters (matrices).

In this way, each virtual node i in the intermediate layer (l+1) is assigned to the intermediate layer (l) is convoluted with the node feature h _j ^(l) representing the feature of the virtual node j corresponding to the intra-graph relation r in , to generate the node feature h _i ^(l+1) representing its own feature. In other words, in generating the node feature amount of the virtual node, it is possible to appropriately capture the intra-graph relation r including the "dynamic intra-graph relation".

Further, as an embodiment different from the node feature amount generation processing according to the above equation (1), it is possible to perform node feature amount generation processing in which the edge feature amount is also convoluted.

In this case, the edge feature amount of the virtual edge (i,j) connecting the virtual node i and the virtual node j (j∈N _i ^r ) in the intermediate layer (l) is expressed as ei _,j . Here, in this embodiment, the edge feature quantity e _i,j takes the same value for all intermediate layers including the first intermediate layer (0). The input edge feature amount is handed over to each intermediate layer as this edge feature amount ei _,j .

In the embodiment in which such edge features e _i,j are also convoluted, the node feature h _i ^{(l+1) at the virtual node i in the intermediate layer (l+1} ) is expressed by the following equation (2) h _i ^(l+1) ＝σ(Σ _r Σ _j c _i,r ⁻¹・(A _r ^(l)・h _j ^(l) ＋B _r ^(l)・e _i,j )＋C ^(l)・h _i ^(l) )
is calculated as Here, l takes an integer value from 0 to (L-1). Also, B _r ^(l) is an internal parameter (matrix) to be learned like A _r ^(l) and C ^(l) .

In this way, in the node feature value generation processing using the above formula (2), the intermediate layer (l ), the edge feature value e of the virtual edge (i, j) that connects the virtual node i and the virtual node j corresponding to the relation r in the graph, or connects the two including the direction from the virtual node i to the virtual node j The node feature quantity _h i ^(l+1 ) is generated by also convolving _{i,j (} a constant edge feature quantity e i,j independent of the l value in this embodiment). That is, even in this case, it is possible to appropriately incorporate the intra-graph relation r including the "dynamic intra-graph relation" when generating the node feature amount of the virtual node.

Furthermore, the node feature value generation processing according to the above equation (2) is based on the graph variable (objective variable) to be estimated by adding the edge feature value e _i,j in the convolution with the relation r (r∈R). This is a process for more reliably extracting the characteristics of such graphs.

Further, as an embodiment different from the node feature amount generation processing by the above equations (1) and (2), it is also possible to perform node feature amount generation processing by convolving the edge feature amount without using the node feature amount. is. In this case, the node feature value h _i ^{(l+1) at the virtual node i in the intermediate layer (l+1)} is expressed by the following equation (3) h _i ^(l+1) = σ(Σ _r Σ _j c _{i, r} ^-1・B _r ^(l)・e _i,j ＋C ^(l)・h _i ^(l) )
is calculated as Here, l takes an integer value from 0 to (L-1).

In this way, in the node feature value generation processing using the above formula (3), for each in-graph relation r included in the set R of in-graph relations including the "dynamic in-graph relation", the intermediate layer (l ), the edge feature value e of the virtual edge (i, j) that connects the virtual node i and the virtual node j corresponding to the relation r in the graph, or connects the two including the direction from the virtual node i to the virtual node j The node feature quantity _h i ^(l+1 ) is generated by convolving _{i,j (a constant edge feature quantity e i,j independent} of the l value in this embodiment). That is, even in this case, it is possible to appropriately incorporate the intra-graph relation r including the "dynamic intra-graph relation" when generating the node feature amount of the virtual node.

Three embodiments relating to the node feature generation processing in each intermediate layer have been described above using equations (1) to (3), but in any case, the final typical node features:
h ₁ ^(L) , h ₂ ^(L) , . . . , h _N ^(L)
and, if necessary, the edge feature quantity e _i,j are output to the objective variable estimation unit 11 as the virtual graph feature quantity.

Here, the final node feature values h ₁ ^(L) _, h ₂ ^{(L) ,} . , with each subgraph group containing dynamic subgroups (corresponding to dynamic intragraph relations) (to each virtual node i in the hidden layer (l+l) It can be regarded as the result of accumulating the process of aggregating (towards) from the middle layer (1).

As another example, the node feature value h _i (l+1) of the intermediate layer ( ^l+1) is such that the number of dimensions (the number of feature vector components) becomes smaller as l increases from 0. may be set to For example, while the input node feature quantity h _i ⁽⁰⁾ has 100 dimensions, the final node feature quantity h _i ^(L) can be reduced to 10 dimensions, for example. Even in such a case, the graph feature quantity extraction unit 10 extracts the features of the graph related to the graph variable (objective variable) to be estimated while contracting to a lower dimension. , it is possible to skillfully incorporate "dynamic graph relations" as conditions for feature aggregation.

Furthermore, in any of the above three embodiments using equations (1)-(3), each virtual node i in the hidden layer (l+1) is for each intra-graph relation r contained in the set R , weighting the convolution result for the in-graph relation r by multiplying the determined or learned weight c _i,r ⁻¹ (c _i,r is a normalization constant) for the in-graph relation r, It generates its own node feature h _i ^(l+1) . Here, by setting this weight c _i,r ⁻¹ as a value to be learned, the contribution of the intra-graph relation r (including the dynamic intra-graph relation) to the node feature h _i ^{(l+1) to} be generated is It is also possible to adjust the degree appropriately.

For example, "the number of e-mails between employees in a predetermined unit period" is specified as an edge feature value, and "the number of e-mails is less than 10" is defined as the relationship r_1 in the dynamic graph and the relationship r_2 in the dynamic graph. a certain relation” and “a relation whose number is 10 or more and less than 20” are set, for example, the weight c _{i,r_1} ⁻¹ of the relation r_1 in the dynamic graph becomes Construct a more suitable model such that the weight c _{i,r_2} of the internal relation r_2 becomes greater than ^-1 , and as a result, the dynamic graph internal relation r_1 has a greater impact on the estimation of the risk of absence from work, which is the objective variable. It is also possible to

A comparison of the above three embodiments using equations (1)-(3) will now be made. First, in the embodiment according to Equation (1), in calculating the node feature quantity h _i ^(l+1) , the edge feature quantity e _i,j does not explicitly exist in Equation (1). , are captured as rough (quantized) features in the form of convolutions with “dynamic intra-graph relations”. As a result, the burden of feature quantity extraction processing is reduced, and overfitting of the constructed graph variable estimation model 1 can be suppressed or avoided.

On the other hand, in the embodiment according to the formula (2) and the embodiment according to the formula (3), in calculating the node feature amount h _i ^(l+1) , the edge feature amount e _i,j is calculated by the formula (2 ) and (3). As a result, the edge features e _i,j are captured as rough (quantized) features in the form of convolution with the "dynamic intra-graph relations", while their raw values are taken as the extracted features It can be understood that the adjustment of As a result, it is possible to extract more suitable feature amounts in the graph feature amount extracting unit 10, and it is expected that the accuracy of estimating the graph variables will eventually be improved.

Similarly, in FIG. 1, the objective variable estimator 11 (above (b)) receives the virtual graph feature quantity from the graph feature quantity extractor 10 and estimates a graph variable (objective variable). That is, the virtual graph feature amount generated by the graph feature amount extraction unit 10 is input, and a value related to the graph variable (objective variable) as an estimated value is output.

Specifically, in the case of estimating the future risk of absence from work for each employee of Company A, for example, the objective variable estimation unit 11 is composed of, for example, a fully connected layer of a neural network, and the output of each neuron constituting the output layer The value may be set to be the absence risk value for each employee (eg, a value between 0 and 1).

As a matter of course, the objective variables (graph variables) estimated by the objective variable estimation unit 11 are limited to variables related to indicators for each node, such as the risk value of leave of absence for each employee in the above case. not a thing In fact, the target variable that can be estimated in the graph variable estimation model 1 that inputs graph information (node feature amount and edge feature amount) is
(a) Node-related or node-based indicators: For example, employee leave risk, SNS (Social Networking Service) user click rate/conversion rate, etc.
(b) Edge-related or per-edge metrics: e.g., transition probability between web pages (in the case where each web page is a node) or road traffic as an edge (in the case where an intersection or base point is a node) quantity, etc.
(c) Indicators related to graphs or graph units: For example, the activity index of the entire company, the characteristics of the product compound (in the case where atoms, molecules, groups, etc. that are bonded to each other are nodes), etc.
(d) Indicators related to sub-graphs (as a part of the graph) formed in the graph or for each sub-graph The objective variable of the type can also be adopted as an estimation target.

In any case, the objective variable estimator 11 is a model part that can be configured with various known machine learning algorithms, for example, according to the task to be executed, that is, the aspect of the objective variable to be estimated.

Furthermore, in this case, for one graph feature amount extraction unit 10 constructed for a predetermined graph (for example, a graph expressing company A), according to the objective variable to be estimated for the graph, the objective variable for estimating the objective variable It is also possible to configure the graph variable estimation model 1 by connecting the variable estimation unit 11 . For example, if a general-purpose (common specification) graph feature quantity extraction unit 10 is prepared for the graph, the objective variable estimation unit 11 for the objective variable to be estimated can be selected from the lineup of objective variable estimation units 11. It is also possible to select and construct the graph variable estimation model 1 simply. In this case, the graph feature quantity extraction unit 10 functions as a highly versatile model module as a common part of the model configuration.

Next, similarly using FIG. 1, the graph variable estimation model 1 described above is installed, and from the input graph information, a predetermined target variable for the graph related to the graph information is estimated (as an estimated value ) will be described.

The graph variable estimating device 2 includes an input unit 21, a learning unit 22, a graph variable estimating unit 23, and an output unit 24. The learning unit 22 and the graph variable estimating unit 23 are configured to generate graphs according to the present invention. One can think of it as a function of a processor memory that stores an embodiment of a variable estimation program. Further, from this, the graph variable estimation device 2 may be a dedicated device for graph variable estimation, but it may be a cloud server, a non-cloud server device, a personal computer (for example, a cloud server, a non-cloud server device, a personal computer ( PC), a notebook or tablet computer, or a smart phone.

Similarly, in FIG. 1, the input unit 21 of the graph variable estimation device 2 has a communication function, for example, from a database of an externally installed server (for example, an in-house attendance management server), objective variable (for example, leave of absence risk) information Graph information (node feature amount and edge feature amount) with a correct label (for example, presence or absence of leave of absence) is received, converted into a predetermined data format, and stored in the learning unit 22 . The input unit 21 also receives, for example, the setting information of the intra-graph relations including the dynamic intra-graph relations input by the operator (for example, threshold information defining each dynamic intra-graph relation), and outputs it to the learning unit 22. do.

The learning unit 22
(a) setting an intra-graph relationship including a dynamic intra-graph relationship based on the received intra-graph relationship setting information and the edge feature;
(b) Based on the set intra-graph relations, the graph variable estimation model 1 is constructed by learning using the self-stored graph information group labeled with the correct answer, and output to the graph variable estimation unit 23 .

The graph variable estimation unit 23 receives from the input unit 21 the graph information (node feature amount and edge feature amount) of the graph (for example, company A) related to the objective variable to be estimated (for example, risk of absence from work), from the learning unit 22. It is input to the received learned graph variable estimation model 1, and as its output, an estimated value of a desired objective variable (for example, a value related to the risk of absence from work of each employee) is acquired and output to the output unit 24.

The output unit 24 can, for example, display information related to the received objective variable estimated value on a display, or transmit the information to an external information processing device (if it has a communication function). Here, the information related to the objective variable estimated value to be displayed/transmitted is, for example, information to the effect that "the risk of taking a leave of absence in the next fiscal year for employee α is as low as **%, which is significantly below the support required level".

As described in detail above, the graph variable estimation model according to the present invention can more accurately estimate graph variables as objective variables by more reliably capturing intra-graph relationships including dynamic intra-graph relationships. can.

Here, the relationship in the dynamic graph is, so to speak, the discretization and quantization of the edge feature value expressing the relationship between nodes to enable convolution processing. In the case of estimating the risk of absence from work for employees of a large company, in addition to labor and personnel knowledge such as superiors, colleagues, and subordinates in the company, the degree and frequency of communication in each of these work relationships, such as the activation of the workplace. It is possible to incorporate variable information related to the degree and ease of work into the risk estimation for absence from work.

In particular, the present invention presents a method of incorporating the above-described dynamic graph relations inherent in the graph into the estimation process in the GNN technology, which is currently being actively researched and developed. It is believed that this method not only improves the accuracy of estimating objective variables related to graphs, but also contributes to the expansion of its application fields.

For the various embodiments of the present invention described above, various changes, modifications and omissions within the spirit and scope of the present invention can be easily made by those skilled in the art. The foregoing description is exemplary only and is not intended to be limiting. The invention is to be limited only as limited by the claims and the equivalents thereof.

1 graph variable estimation model 10 graph feature amount extraction unit 11 objective variable estimation unit 2 graph variable estimation device 21 input unit 22 learning unit 23 graph variable estimation unit 24 output unit

Claims (9)

A graph variable estimation model that receives graph information related to a graph as an input, convolves the graph information in a plurality of intermediate layers having virtual nodes corresponding to the nodes of the graph, and estimates an objective variable for the graph,
at least one intra-graph relationship is set corresponding to each of at least one value range of values taken by edge feature quantities representing edge features in the graph;
Each virtual node in the intermediate layer represents a feature of a virtual node corresponding to the intra-graph relationship in the preceding intermediate layer for each intra-graph relationship included in a set of intra-graph relationships including the at least one intra-graph relationship. Convoluting the node feature amount and the edge feature amount representing the feature of the virtual edge connecting the virtual nodes corresponding to the intra-graph relation in the intermediate layer in the previous stage to generate the node feature amount representing the feature of itself Graph variable estimation model for . A graph variable estimation model that receives graph information related to a graph as an input, convolves the graph information in a plurality of intermediate layers having virtual nodes corresponding to the nodes of the graph, and estimates an objective variable for the graph,
at least one intra-graph relationship is set corresponding to each of at least one value range of values taken by edge feature quantities representing edge features in the graph;
Each virtual node in the intermediate layer represents a feature of a virtual node corresponding to the intra-graph relationship in the preceding intermediate layer for each intra-graph relationship included in a set of intra-graph relationships including the at least one intra-graph relationship. Convolve the node features to generate node features that represent their own features,
The graph expresses a group including a plurality of communication subjects as nodes that can communicate with each other. A group is formed, and the target variable is a variable that takes a value related to an event that can be affected by whether or not the communication subject belongs to the subgroup.
A graph variable estimation model characterized by: Each virtual node of the intermediate layer assigns a determined or learned weight to the convolution result of the in-graph relation for each in-graph relation included in the set, 3. The graph variable estimation model according to claim 1 or 2, wherein a node feature quantity representing the feature of is generated. 4. The method according to any one of claims 1 to 3, further comprising an objective variable estimation layer that receives an output from the last stage of the plurality of intermediate layers and outputs a value related to the objective variable estimated for the graph. Graph variable estimation model described in section. The objective variable is at least one of an objective variable associated with a node of the graph, an objective variable associated with an edge of the graph, and an objective variable associated with the whole or part of the graph. 5. The graph variable estimation model according to any one of 1 to 4. A graph variable estimation model that receives graph information related to a graph as an input, convolves the graph information in a plurality of intermediate layers having virtual nodes corresponding to the nodes of the graph, and estimates an objective variable for the graph,
at least one intra-graph relationship is set corresponding to each of at least one value range of values taken by edge feature quantities representing edge features in the graph;
Each virtual node in the intermediate layer is a virtual edge connecting virtual nodes corresponding to the intra-graph relationship in the preceding intermediate layer for each intra-graph relationship included in a set of intra-graph relationships including the at least one intra-graph relationship. A graph variable estimation model characterized by convolving an edge feature representing a feature of to generate a node feature representing its own feature. The graph variable estimation model according to any one of claims 1 to 6 is used to output, from input graph information, information on objective variables estimated for graphs related to the graph information. Graph variable estimator for . By a computer using a graph variable estimation model that inputs graph information related to a graph, convolves the graph information in a plurality of intermediate layers having virtual nodes corresponding to the nodes of the graph, and estimates objective variables for the graph A graph variable estimation method implemented comprising:
setting at least one intra-graph relation corresponding to each of at least one value range of values taken by edge feature quantities representing features of edges in the graph;
In each virtual node of the intermediate layer, for each intra-graph relation included in a set of intra-graph relations including the at least one intra-graph relation, characteristics of the virtual node corresponding to the intra-graph relation in the previous intermediate layer are determined. A step of convolving the node feature value representing the node feature value and the edge feature value representing the feature of the virtual edge connecting the virtual nodes corresponding to the intra-graph relation in the intermediate layer in the previous stage to generate the node feature value representing the feature of each of the virtual nodes. A graph variable estimation method characterized by comprising: By a computer using a graph variable estimation model that inputs graph information related to a graph, convolves the graph information in a plurality of intermediate layers having virtual nodes corresponding to the nodes of the graph, and estimates objective variables for the graph A graph variable estimation method implemented comprising:
setting at least one intra-graph relationship corresponding to each of at least one value range of values taken by edge feature quantities representing features of edges in the graph;
In each virtual node of the intermediate layer, for each in-graph relation included in a set of in-graph relations including the at least one in-graph relation, for a virtual node corresponding to the in-graph relation in the preceding intermediate layer, the virtual convolving the node feature representing the feature of the node to generate a node feature representing the feature of each virtual node ;
The graph expresses a group including a plurality of communication subjects as nodes that can communicate with each other. A group is formed, and the target variable is a variable that takes a value related to an event that can be affected by whether or not the communication subject belongs to the subgroup.
A graph variable estimation method characterized by :

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