CN115983341A - Node classification method based on relation aggregation hypergraph - Google Patents
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Abstract
The invention discloses a node classification method based on a relational aggregation hypergraph, belongs to the technical field of complex networks, and solves the problems that the existing hypergraph construction method is single, partial high-order information loss is easily caused, and the node classification accuracy is influenced; the method comprises the following steps: constructing explicit and implicit super edges respectively based on explicit relations and implicit relations between nodes; calculating the importance between the node and the neighbor node sharing the implicit super edge by adopting a global attention mechanism, and defining the importance as an implicit characteristic correlation coefficient; the implicit relation is used as supplementary information and aggregated with the explicit relation to generate a hypergraph structure of relational aggregation; and performing weighted calculation on the generated incidence matrix of the hypergraph structure, transmitting the aggregation characteristics along a path of vertex-hyperedge-vertex through a hypergraph neural network to obtain embedded representation of the nodes, and classifying the nodes by using a softmax classifier.
Description
Technical Field
The invention relates to the technical field of complex networks, in particular to a hypergraph node classification method based on relationship aggregation.
Background
The graph is a high-level abstraction of the associated data that may be used to represent interrelationships between multiple entities of the internet, social networks, biological networks, and the like. In the traditional graph modeling, one edge can only connect two nodes, and often only can model the two-dimensional pairwise relationship between the nodes, so that the multivariate and high-order relationship in the real world is difficult to describe. The super edge in the super graph can comprise any plurality of nodes and can represent that a plurality of authors collaborate together to form a paper in a scientific research collaboration network; in the internet, a plurality of users buy the same kind of articles and other higher-order relationships together. Compared with a general graph structure, the hypergraph has stronger capacity of depicting and mining nonlinear high-order association among data samples, and can more accurately model the multivariate relation. Therefore, the hypergraph is widely applied to node classification tasks in multiple fields such as image segmentation, high-dimensional spatial clustering, multi-modal data modeling, recommendation systems, social networks and the like. Meanwhile, with the excellent performance of the graph neural network in each task, the graph neural network is applied to the hypergraph, and the representation learning of the hypergraph has become a research hotspot in recent years.
However, in the face of increasingly complex network structures and increasingly rich node characteristics, the traditional hypergraph construction method only considers a single relation, cannot completely reflect high-order information between graph data nodes with high-dimensional characteristics, and has great limitation on high-order relational data modeling. For example, in a hypergraph based on scientific research cooperation, only the relationship of a plurality of authors cooperating with one paper is modeled, and the high-order relationship generated by the association among the plurality of papers or the plurality of authors is ignored; in the social recommendation based on the hypergraph, only the interactive relation between the user and the item is modeled, and the high-order relation generated by self-association between the user, the user and the commodity is ignored. This will inevitably result in the effect that the sub-optimal representation of the nodes will affect the task of node classification.
Disclosure of Invention
The invention provides a node classification method based on a relation aggregation hypergraph, which can solve the problems of incomplete extraction of single feature information and the like in the traditional node classification method based on the hypergraph. Constructing a hypergraph structure of relationship aggregation by aggregating explicit and implicit relationships and calculating embedded representation of nodes through a neural network on the hypergraph, thereby improving the precision of node classification; sparsity based on single information representation is effectively supplemented, and the global structure of the network is better maintained.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a node classification method based on a relation aggregation hypergraph comprises the following steps:
s1, defining explicit and implicit relations according to the structure of high-order relation graph data and node characteristics;
s2, constructing an explicit super edge according to the explicit relation;
s3, constructing an implicit over edge according to the implicit relation;
s4, defining an implicit characteristic correlation coefficient, calculating the importance between a target node and a neighbor node in implicit super-edges by adopting a global attention mechanism, and generating a hypergraph structure aggregated with the explicit super-edge aggregation;
s5, embedding and representing the generated relation aggregation hypergraph structure by adopting a hypergraph neural network;
and S6, embedding the trained nodes into a representation and sending the representation into a softmax classifier, and classifying the nodes according to the inherent labels.
The technical scheme of the invention is further improved as follows: in S1, definitions of explicit relations and implicit relations are given according to the structure of high-order relation graph data and node characteristics, and all relations among nodes can be expressed as the sum of the explicit relations and the implicit relations.
The technical scheme of the invention is further improved as follows: in S2, the explicit super-edge is constructed according to explicit relations in network data, such as friend relations and enemy relations in social networks, reference relations in thesis cooperative networks, co-author relations, protein interaction relations in biological networks and the like.
The technical scheme of the invention is further improved as follows: in S3, the implicit super-edge construction adopts two methods of KNN and K-means, the implicit relation between nodes is expressed from two angles of local and global, and for a given target node v, K neighbors of the target node v and a cluster where a centroid vertex closest to the target node v is located are selected to form the implicit super-edge.
The technical scheme of the invention is further improved as follows: in S4, the method for generating the relational aggregation hypergraph structure specifically comprises the following steps:
s4.1, setting a group of input node characteristics
Where n is the number of nodes and F is the characteristic dimension of a single node. Setting a weight vector W with the introduction of a self-attention mechanism a ∈R 2×F And a learnable parameter a.
e ij The similarity coefficient between the node j and the node i in the feature space is represented, and the larger the value of the similarity coefficient, the closer the two nodes are in the feature space.
S4.2, injecting the implicit super edge incidence matrix constructed based on the implicit relation into an attention mechanism as a mask to obtain an implicit characteristic correlation coefficient alpha of the node i and the node j ij ：
Wherein Z i Representing the set of all nodes of the target node in the super-edge constructed based on the implicit relationship.
S4.3, setting a threshold value beta and a threshold value alpha ij Beta or more, namely the existence of the high similarity coefficient of the implicit characteristic with the target nodeAt a threshold value beta, v is j Supplementing E to generate new super edge E A Form a relational aggregate hypergraph structure G A ＝(V,E A W), where W is a weight matrix representing vertices belonging to different super-edges.
The technical scheme of the invention is further improved as follows: the node embedding method based on the hypergraph neural network in the S5 specifically comprises the following steps:
s5.1, expressing the point edge connection relation in the relation aggregation hypergraph by using a weighted incidence matrix, namely expressing the link condition of the node and the explicit hyperedge by using an incidence matrix H and expressing the link condition of the node and the implicit hyperedge by using an H l Means that both are polymerized with alpha ij Filling correspondingly to obtain a weighted incidence matrix H A ；
S5.2, inputting the hypergraph neural network into a correlation matrix H A And node characteristics X, wherein the embedded expression updating formula of the node is as follows:
wherein X (l) ∈R F Is the characteristic of the node at the l-th layer, sigma is a nonlinear activation function, D v A diagonal matrix representing degrees of vertices, i.e. the number of super-edges associated with a vertex, D e A diagonal matrix representing excess edges, i.e. the number of vertices in the excess edge, E A(l) Is characterized by the super edge at the layer I.
The technical scheme of the invention is further improved as follows: s6, the trained nodes are embedded and expressed to be sent to a softmax classifier, and finally, an NxM matrix is output, namely the probability of the class to which each node belongs. The loss function of the model selects the NLLLoss (negative log likelihood loss) function:
where N is the number of samples, M is the sample class, p mn Summary of nth sample output for model belonging to mth categoryAnd (4) rate.
Wherein
Y when the label of the m-th sample is n n =1 otherwise y n ＝0。
Due to the adoption of the technical scheme, the invention has the technical progress that:
1. a new node classification modeling method based on a hypergraph is provided, which not only represents the explicit relation in the network structure information, but also considers the implicit relation of the nodes, and supplements the high-order information in the hypergraph structure;
2. the global attention mechanism is combined to perform weighted calculation on the incidence matrix of the hypergraph, and the hypergraph neural network is adopted to realize the aggregate representation of implicit information and explicit information in graph data, so that the node embedding effectiveness is improved;
3. a large number of comparison experiments are carried out on the public network data set, and the results show that the method provided by the invention has a certain effect on improving the node classification result.
Drawings
FIG. 1 is a schematic diagram of a model matching process according to the present invention;
FIG. 2 is a diagram of an overall model of the present invention;
FIG. 3 is a super-edge construction case of the thesis collaboration network in the present invention;
FIG. 4 is a schematic diagram of the generation of a relational aggregation hypergraph in the present invention;
Detailed Description
The invention is described in further detail below with reference to the following figures and examples:
as shown in fig. 1 and 2, a node classification method based on a relational aggregation hypergraph includes the following steps:
s1, defining explicit and implicit relations according to the structure of high-order relation graph data and node characteristics;
in the conventional hypergraph G, a node set V = { V } is set 1 ，v 2 ,…,v n With A (V) = { A } 1 ,A 2 ,…,A m Denotes the attribute set of the node, then A i (v j ) It represents the node v j The value of the ith attribute of (1). If A is i (v j )＝{v k |v k ∈A j (v j ) V is arbitrarily taken j ∈V,v k ∈A i (v j ). Then node v j And v k The relationship (c) is called a display relationship and is denoted as R e . Arbitrarily get v j ∈V,v k epsilon.V, define f (A) i (v j ),A i (v k ) Represents node v) j And v k Is called implicit relation and is denoted as R i . Therefore, all relationships between nodes can be represented as R = { R = { R i }∪{R e }。
S2, constructing an explicit hypergraph according to the explicit relationship;
a conventional hypergraph is typically represented by G = (V, E) wherein V = { V = 1 ,…,v n Denotes a set of n nodes, E = { E = } 1 ,…,e m The representation of the set of m super edges in the super graph, wherein each super edge is an unordered node set
The nodes in the traditional hypergraph G are in an explicit relationship R e Connected together to form a super-side set>
j is more than or equal to 2, and for convenience of description, the traditional hypergraph is defined as an explicit hypergraph, and E is called an explicit hyperedge. As shown in fig. 3, taking a thesis collaboration network as an example, authors with cooperative relationships are connected by a supergraph, at this time, the cooperative relationship shown in the supergraph is an explicit relationship, and a supergraph structure established based on the relationship is an explicit supergraph.
S3, constructing an implicit hypergraph according to the implicit relationship, wherein the implicit hypergraph comprises the following two steps;
a1, mining the implicit relation of the nodes in the feature space by using the basic rule that samples of the same category in the KNN algorithm should be gathered together in the feature space. For each target node, K neighbors closest to the target node are found, and the target node and the K nearest neighbors form a super edge.
And A2, correcting the excess edge generated by the KNN by adopting a K-MEANS method. First, all vertices are grouped directly into k clusters, and then all vertices in the same cluster are linked by a hyper-edge. And (4) calculating the distance between the target vertex and each cluster center particle, and selecting the edge where the centroid vertex closest to the target vertex is positioned as the excess edge of the vertex. Super edge set based on implicit relation
Wherein p super edges are generated by KNN and q super edges are generated by k-means.
S4, defining an implicit characteristic correlation coefficient, calculating the importance between a target node and a neighbor node in implicit super-edges by adopting a global attention mechanism, and generating a hypergraph structure aggregated with the explicit super-edge aggregation;
b1, setting a group of node characteristics of input
Where n is the number of nodes and F is the characteristic dimension of a single node. Setting a weight vector W with the introduction of a self-attention mechanism a ∈R 2×F And a learnable parameter a.
e ij The similarity coefficient between the node j and the node i in the feature space is represented, and the larger the value of the similarity coefficient is, the closer the two nodes are in the feature space is represented.
B2, injecting the implicit super edge incidence matrix constructed based on the implicit relation into an attention mechanism as a mask to obtain an implicit characteristic correlation coefficient alpha of the node i and the node j ij ：
Wherein Z i Representing the set of all nodes of the target node in the super-edge constructed based on the implicit relationship.
B3, setting a threshold value beta, if alpha ij Beta is larger than or equal to beta, namely the similarity coefficient of the implicit characteristic with the target node is larger than the threshold value beta, v is calculated j Supplementing to E, and generating new super edge E A Form a relational aggregate hypergraph structure G A ＝(V,E A W), where W is a weight matrix representing vertices belonging to different hyper-edges. When E is l Where { Φ }, RAH degenerates to a traditional hypergraph.
FIG. 4 is a schematic diagram of the generation of the relational aggregation hypergraph.
S5, embedding and representing the generated relation aggregation hypergraph structure by adopting a hypergraph neural network;
s5.1, expressing the point edge connection relation in the relation aggregation hypergraph by using a weighted incidence matrix, namely expressing the link condition of the node and the explicit hyperedge by using an incidence matrix H and expressing the link condition of the node and the implicit hyperedge by using an H l Means that both are polymerized with alpha ij Filling correspondingly to obtain a weighted incidence matrix H A 。
S5.2, inputting the hypergraph neural network into a correlation matrix H A And node characteristics X, wherein the embedded expression update formula of the node is as follows:
wherein X (l) ∈R F Is the characteristic of the node at the l-th layer, and sigma is a nonlinear activation function. D v A diagonal matrix representing the degrees of vertices, i.e., the number of hyper-edges associated with a vertex. D e A diagonal matrix representing excess edges, i.e. the number of vertices in the excess edge, E A(l) Is characterized by the super edge at the layer I.
And S6, embedding the trained nodes into a representation and sending the representation into a softmax classifier, and classifying the nodes according to the inherent labels.
The final output of the model is an N x M matrix, i.e., the probability corresponding to the class to which each node belongs. The loss function of the model selects the NLLLoss (negative log likelihood loss) function:
where N is the number of samples, M is the sample class, p mn The probability that the nth sample output for the model belongs to the mth class.
Wherein
Y when the label of the m-th sample is n n =1 else y n ＝0。
Experiments were performed using the Cora and 20newsgroups datasets in the more widely used graph dataset. The data set statistics are shown in table 1.
Table 1 data set statistics table
The results of comparing the method of the invention with other models are shown in table 2: the relation aggregated hypergraph neural network model (RAHGNN) is superior to the comparison model in performance. The hypergraph constructed by aggregating the explicit and implicit relations is shown, and higher-order information can be better captured on data sets with different node characteristic dimensions than a common graph and a homogeneous hypergraph, so that more accurate node representation is obtained, and the effectiveness of the method is verified.
TABLE 2 comparison of results
In order to better reflect the performance of a hypergraph neural network model (RAHGNN) with relation aggregation in node classification, different proportion data sets are respectively selected to carry out experiments on different models. Taking the example of the Cora data set, except training with the fixed 5.2% data set, a proportion of the data was randomly re-extracted and compared with other models on the Cora data set, and the experimental results are shown in Table 3. With the increase of the number of training samples, the classification precision steadily rises. When random samples are selected and samples are selected in sequence to carry out experiments respectively, classification results are relatively stable, which shows that the model can better capture high-order relations in a network and improve the accuracy of node classification.
Table 3: contrast experiment for different divisions of Cora data set
To illustrate the role of the implicit and explicit hyperedge construction modules in the present invention, ablation experiments were performed on the Cora dataset and the 20news dataset. Namely, the model is divided into four modules, namely, a KNN (K-nearest neighbor) constructed implicit over edge, a K-means constructed implicit over edge, an explicit over edge based on an explicit relation, and a global attention mechanism based relation is aggregated, and the four modules are removed one by one in an experiment to obtain experiment results shown in a table 4. Experiments have shown that removing any module from the model will degrade the model accuracy. But the different super-edge construction methods do not perform the same result on different data sets. The construction method of the relation aggregation hypergraph has better expandability on different data sets, and the proposed method can obtain better results for different data distribution forms.
TABLE 4 influence of different super-edge construction methods on node classification accuracy
In conclusion, the method and the device can solve the problems that the extraction of single feature information is incomplete in the traditional hypergraph modeling method and the like. The hypergraph structure of relationship aggregation is constructed by aggregating explicit and implicit relationships, and the embedded representation of the nodes is calculated through a neural network on the hypergraph, so that the precision of node classification is improved. Sparsity based on single information representation is effectively supplemented, and the global structure of the network is better maintained.
Claims (7)
1. A node classification method based on a relation aggregation hypergraph is characterized by comprising the following steps: the method comprises the following steps:
s1, defining explicit and implicit relations according to the structure and node characteristics of high-order relational graph data;
s2, constructing an explicit super edge according to the explicit relation;
s3, constructing an implicit over edge according to the implicit relation;
s4, defining an implicit characteristic correlation coefficient, calculating the importance between a target node and a neighbor node in implicit super-edges by adopting a global attention mechanism, and generating a hypergraph structure aggregated with the explicit super-edge aggregation;
s5, embedding and representing the generated relation aggregation hypergraph structure by adopting a hypergraph neural network;
and S6, embedding the trained nodes into a representation and sending the representation into a softmax classifier, and classifying the nodes according to the inherent labels.
2. The node classification method based on the relational aggregation hypergraph as claimed in claim 1, wherein: the specific operation of S1 is as follows:
explicit relationship definition: in the conventional hypergraph G, a node set V = { V } is set 1 ，v 2 ,…,v n }, using A (V) = { A = 1 ,A 2 ,…,A m Denotes the set of attributes of the node, then A i (v j ) It means node v j If A is the value of the ith attribute of i (v j )＝{v k |v k ∈A j (v j ) V is arbitrarily taken j ∈V,v k ∈A i (v j ) Then node v j And v k The relationship (c) is called a display relationship and is denoted as R e ；
Implicit relationship definition: in the conventional hypergraph G, a node set V = { V } is set 1 ，v 2 ,…,v n }, using A (V)＝{A 1 ,A 2 ,…,A m Denotes the attribute set of the node, then A i (v j ) It represents the node v j Of the ith attribute of (1), optionally, v j ∈V,v k epsilon.V, define f (A) i (v j ),A i (v k ) Represents node v) j And v k Is called implicit relation and is denoted as R i Therefore, all relationships between nodes can be expressed as R = { R = i }∪{R e }。
3. The node classification method based on the relational aggregation hypergraph as claimed in claim 1, wherein: the specific operation of S2 is as follows:
traditional hypergraph: a conventional hypergraph is typically represented by G = (V, E) represents, wherein V = { V = 1 ,…,v n Denotes a set of n nodes, E = { E = } 1 ,…,e m The representation of the set of m super edges in the super graph, wherein each super edge is an unordered node set
When the number of the super-edge connecting nodes is 2, the hypergraph is degenerated into a common graph;
unlike traditional graphs, where one edge can only connect two vertices, the degree of vertices is not limited in the hypergraph structure, i.e., each hypergraph can connect any number of vertices, and thus is commonly referred to as a high-order representation of the graph, a traditional hypergraph constructed from explicit relationships is defined as an explicit hypergraph, referred to as E as an explicit hyperedge.
4. The node classification method based on the relational aggregation hypergraph as claimed in claim 1, wherein: in the S3, two methods of KNN and K-MEANS are adopted, the high-order relation between nodes is extracted from two angles of local and global, an implicit super edge is constructed, in order to capture global information in a feature space and avoid the influence caused by poor noise data, outliers and parameter selection, the K-MEANS method is adopted to correct the super edge generated by the KNN, and a super edge set based on the implicit relation is
Wherein p super edges are generated by KNN and q super edges are generated by k-means.
5. The node classification method based on the relational aggregation hypergraph as claimed in claim 1, wherein: the specific operation of S4 is as follows:
implicit characteristic correlation coefficient alpha ij : importance coefficient between node and its neighbor node sharing implicit super edge in implicit super edge set
e ij Is a coefficient of similarity between node nodes, Z i The method comprises the following steps of (1) taking a neighbor node set of a node, wherein exp is an exponential function with e as a base;
relational aggregated hypergraph RAH: provided with a node set V = { V = { (vi) 1 ，v 2 ,…,v n At explicit excess edge E and implicit excess edge E l In (b), there is a node v i ∈E,v j ∈E l And is
If α is ij Beta is larger than or equal to beta, namely the similarity coefficient of the implicit characteristic with the target node is larger than the threshold value beta, v is calculated j Supplementing to E, and generating new super edge E A Form a relational aggregate hypergraph structure G A ＝(V,E A W), where W is a weight matrix representing vertices belonging to different super-edges, when E l Where = { Φ }, RAH degenerates to the traditional hypergraph.
6. The node classification method based on the relational aggregation hypergraph as claimed in claim 1, wherein: the specific steps of S5 are as follows: weighted incidence matrix H for hypergraph structure of relational aggregation A Representing the inputs to the neural network as a correlation matrix H A And the embedded representation update formula of the node feature X node is as follows:
the training process of the model can be divided into two steps of vertex convolution and super-edge convolution:
vertex convolution, node relation aggregation to the hyper-edge,
super edge convolution, obtaining the embedded representation of the node by the characteristics of the super edge,
wherein X (l) ∈R F Is the characteristic of the node at the l-th layer, sigma is a nonlinear activation function, D v A diagonal matrix representing degrees of vertices, i.e. the number of super-edges associated with a vertex, D e A diagonal matrix representing excess edges, i.e. the number of vertices in the excess edge, E A(l) The characteristic of the super edge in the layer I.
7. The node classification method based on the relational aggregation hypergraph as claimed in claim 1, wherein: the S6 specifically comprises the following steps:
sending the embedded representation of the nodes into a softmax classifier, wherein the final output of the model is an NxM matrix, namely the probability of the class to which each node belongs is corresponded, and the loss function of the model selects a negative log-likelihood loss NLLLoss function:
where N is the number of samples, M is the sample class, p mn The probability that the nth sample output for the model belongs to the mth class;
wherein
Y when the label of the m-th sample is n n =1 else y n ＝0。
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| CN116845889A (en) * | 2023-09-01 | 2023-10-03 | 东海实验室 | Hierarchical hypergraph neural network-based power load prediction method |
| CN117392386A (en) * | 2023-10-13 | 2024-01-12 | 浙江省测绘科学技术研究院 | Classification training method and device for superside mask generation network based on instance segmentation |
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| CN116845889A (en) * | 2023-09-01 | 2023-10-03 | 东海实验室 | Hierarchical hypergraph neural network-based power load prediction method |
| CN116845889B (en) * | 2023-09-01 | 2023-12-22 | 东海实验室 | Hierarchical hypergraph neural network-based power load prediction method |
| CN117392386A (en) * | 2023-10-13 | 2024-01-12 | 浙江省测绘科学技术研究院 | Classification training method and device for superside mask generation network based on instance segmentation |
| CN117392386B (en) * | 2023-10-13 | 2024-05-10 | 浙江省测绘科学技术研究院 | Classification training method and device for superside mask generation network based on instance segmentation |
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