A method of classification employing a convolutional network with a sparse motif graph
By employing the sparse basalt graph convolutional network approach, sparse basalt matrices are used to eliminate spurious connections. Combined with global and local feature aggregation, the excessive smoothing problem of GCN as depth increases is solved, thus improving the classification accuracy of graph convolutional networks.
Patent Information
- Application Number
- CN202210636574.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-06-07
- Publication Date
- 2026-01-02
- Estimated Expiration
- 2042-06-07
AI Technical Summary
Graph Convolutional Networks (GCNs) are prone to oversmoothing as their depth increases, causing the differences between node embeddings to disappear and making them unable to perform effective classification.
A sparse basilo graph convolutional network is adopted to obtain global and local features by passing information through the original adjacency matrix and the basilo adjacency matrix. The sparse basilo matrix is used to eliminate spurious connections and aggregate information from multiple basilos to alleviate the oversmoothing problem.
It significantly improves classification accuracy, especially in datasets with complex graph structures, enabling more accurate capture of local topological structures, reducing over-smoothing, and improving classification accuracy.
Smart Images
Figure CN116258887B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application relates to a method for classification by using a sparse motif graph convolution network, and belongs to the technical field of artificial intelligence. BACKGROUND
[0002] Graph structure has become one of the main means for expressing real-world data such as knowledge base, molecule, social network, paper citation, etc., in which a large number of nodes are organized in an irregular and complex manner. Through the graph structure, deep learning can be performed on unknown targets by using a neural network, and classification of the unknown targets can be achieved, thus generating a kind of neural network called graph convolution network, among which the most typical one is GCN network.
[0003] A key challenge faced by GCN is that it cannot perform well when its depth is getting larger. Such an observation is contrary to the experimental results of a well-known convolutional neural network (CNN), in which increasing the depth of the network usually leads to significant performance improvement. This is because the expression ability of the GCN is often hindered by the problem of over-smoothing, which is caused by the fact that the graph convolution defined in the GCN is essentially a Laplacian smoothing operator. After the Laplacian smoothing is repeatedly applied in the GCN, the features of all nodes in the graph will converge to similar values.
[0004] The problem of over-smoothing is a well-known challenge faced by graph convolution networks, especially GCN. Specifically, as the depth of the GCN increases, the difference between the embeddings of nodes belonging to the same cluster tends to disappear, and eventually falls into a trivial embedding subspace.
[0005] Therefore, it is necessary to conduct in-depth research on the graph convolution network to solve the above problems. SUMMARY
[0006] In order to overcome the above problems, the present inventors have conducted in-depth research and proposed a method for classification by using a sparse motif graph convolution network, which comprises the following steps:
[0007] The target to be classified and the known target are made into a topological graph, in which the target is a node and the connection between the targets is an edge of the topological graph;
[0008] The topological graph is identified by using the graph convolution network to obtain the classification of the target to be classified in the topological graph.
[0009] The target to be classified and the known target can be individuals or nodes in a social network, authors in a paper citation, vehicles in traffic flow, words in a text, etc. Through the above steps, the classification of the occupation of the individual in the social network or the attribute classification of the node, the classification of the subject at which the author is good at, the attribute classification of the vehicle, the category of the word in the text, etc. are obtained.
[0010] Further, the graph convolution network is called a motif-based graph convolution network, which obtains a motif adjacency matrix from an original adjacency matrix of a topological graph when identifying the topological graph, and performs information transmission through the original adjacency matrix and the motif adjacency matrix.
[0011] The motif-based graph convolution network obtains global features through message passing of the original adjacency matrix, obtains local features through message passing of the motif adjacency matrix, aggregates the global features and the local features to obtain features of a target to be classified, and thus completes classification of the target to be classified.
[0012] In a preferred embodiment, the motif-based graph convolution network learns an input topological graph through information transmission of the original adjacency matrix according to a GCN method to obtain global features.
[0013] In a preferred embodiment, the motif-based graph convolution network learns an input topological graph through information transmission of the motif adjacency matrix according to a GCN method to obtain local features corresponding to motifs.
[0014] In a preferred embodiment, before the motif-based graph convolution network transmits information through the motif adjacency matrix, the motif adjacency matrix is preprocessed to convert the motif adjacency matrix into a sparse motif matrix, and the sparse motif matrix is used to replace the original motif adjacency matrix.
[0015] The sparse motif matrix is represented as:
[0016]
[0017] wherein, denotes a sparse motif matrix corresponding to the kth motif, A denotes an original adjacency matrix of a topological graph, and A k denotes an original motif adjacency matrix corresponding to the kth motif, and denotes element-wise multiplication.
[0018] In a preferred embodiment, the adjacency matrix A k of the kth motif is represented as:
[0019]
[0020] wherein, v i denotes an i th node in a topological graph, v j denotes a j th node in the topological graph, and i and j are different positive integers.
[0021] In a preferred embodiment, when the motif-based graph convolution network transmits information through the motif adjacency matrix, transmission between different layers of the convolution network is represented as:
[0022]
[0023] wherein, represents the output of the lth layer of the kth motif.
[0024] In a preferred embodiment, the initial feature of the 1st layer of the kth motif is obtained by:
[0025] obtaining an initial feature matrix of the topological graph;
[0026] The initial feature matrix is obtained by one or more linear layers and ReLU activation units, to obtain an early feature matrix H (0) ;
[0027] L0-layer message passing is performed on the early feature matrix to obtain an initial feature wherein the passing of each layer is represented as: H (l+1) = AH (l) , 1≤l
[0028] The initial feature is aggregated as
[0029] In a preferred embodiment, the aggregation of the global feature and the local feature includes aggregation of motif information, aggregation of global information,
[0030] The aggregation of motif information is represented as:
[0031]
[0032] The aggregation of global information is represented as:
[0033]
[0034] wherein, is a learnable parameter, is a learnable parameter, is the global feature output by the lth layer, and L1 is a hyperparameter.
[0035] In a preferred embodiment, the aggregation of the global feature and the local feature further includes aggregation of early features, represented as:
[0036]
[0037] wherein, w (l) is a learnable parameter,
[0038] The present application has the beneficial effects including:
[0039] (1) alleviate the problem of over-smoothing by integrating multiple motif-based message passing branches;
[0040] (2) greatly improve the accuracy of classification. BRIEF DESCRIPTION OF DRAWINGS
[0041] Figure 1 Fig. 1 shows a flowchart of a method for classification using a sparse motif graph convolution network according to a preferred embodiment of the present application;
[0042] Figure 2 Fig. 2 shows a motif graph;
[0043] Figure 3 Fig. 3 shows an example of spurious connections. DETAILED DESCRIPTION
[0044] The present application will be further described by the following drawings and examples. Through these descriptions, the features and advantages of the present application will become more apparent.
[0045] The word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any implementation described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other implementations. Unless specifically indicated otherwise, the drawings shown in the Figures are not necessarily to scale.
[0046] The present application provides a method for classification using a sparse motif graph convolution network, comprising the following steps:
[0047] A topology graph is made with the target to be classified and known targets, in which the targets are nodes and the connections between the targets are edges of the topology graph;
[0048] The topology graph is identified by a neural network to obtain the classification of the target to be classified in the topology graph.
[0049] The neural network is a graph convolution network, which is referred to as a motif-based graph convolution network in the present application.
[0050] Further, when the motif-based graph convolution network identifies the topology graph, a motif adjacency matrix is obtained from the original adjacency matrix of the topology graph, and information transmission is performed through the original adjacency matrix and the motif adjacency matrix, as shown in Figure 1
[0051] The original adjacency matrix refers to the adjacency matrix of the topology graph.
[0052] Wherein, the motif graph convolutional network is used to obtain global features by message passing based on the original adjacency matrix, and local features by message passing based on the adjacency matrix of the motif, and the global features and the local features are aggregated to obtain the features of the target to be classified, so as to complete the classification of the target to be classified.
[0053] Further, how to obtain the features of the target to be classified based on the graph convolutional network to complete the classification of the target to be classified is a common knowledge in the application of the graph convolutional network, and will not be repeated in the present application.
[0054] The motif is a graph pattern, defined as any induced subgraph, which is small and non-isomorphic, and is a method mentioned in the paper Austin RB Benson, David F Gleich, and Jure Leskovec. Higher-order organization of complex networks. Science, 2016, as shown in the formula (1) : Figure 2 As shown, v1-v2-v3 and v1-v2-v5 are both 3-node motifs of the topological graph.
[0055] Preferably, in the present application, the number of nodes in the motif is not more than 4, preferably 4, and more preferably 3, 4.
[0056] The inventors found that the target features obtained under 4 and less neighbor nodes are more accurate.
[0057] The inventors found that although many methods have been proposed to solve the problem of over-smoothing of graph convolutional networks, these methods mostly obtain graph spectrum information from the Laplacian matrix of the topological graph, and using only the Laplacian spectrum of the original graph cannot capture the diverse local structure of complex graphs. In the present application, the local topological structure of complex graphs is introduced into the graph convolutional network by using motifs, thereby improving the diversity of the graph spectrum.
[0058] Further, in the present application, the motif graph convolutional network learns the input topological graph by passing information through the original adjacency matrix according to the GCN method to obtain global features. Since the GCN method is one of the classical image recognition methods, the specific process will not be repeated in the present application.
[0059] In the process of obtaining global features, more preferably, unlike the GCN method, no activation function is used. The inventors found that the target classification accuracy obtained by aggregating the global features and the local features obtained by the traditional GCN method will be reduced, and instead, the target classification accuracy obtained by using the activation function will be greatly improved.
[0060] According to the application, the motif graph convolution network is used to pass information through the motif adjacency matrix according to the GCN method, and local features corresponding to the motif are obtained.
[0061] In the traditional GCN method, node information is passed through the original adjacency matrix, and only global features can be obtained, and then prediction and recognition are performed only on the basis of the global features. Since prediction and recognition are performed only on the basis of the global features, the problem of over-smoothing may occur. In the application, the message passing through the motif adjacency matrix according to the GCN method refers to replacing the original adjacency matrix with the motif adjacency matrix in the learning process of the topological graph according to the GCN method, and then obtaining local features corresponding to the motif. The inventor finds that, compared with the global information in the original graph, the motif can more effectively capture the topology of the local graph, so as to alleviate the problem of over-smoothing by introducing the diversity of the motif.
[0062] The inventor also finds that, although the introduction of the motif can increase a large number of local features, the connection of the motif adjacency matrix in the original definition is dense, and the blind use of the local features obtained by passing the message based on the motif adjacency matrix will lead to faster convergence to over-smoothing, that is, since the motif connection is much denser than the edge connection, it may converge to a full one matrix in a few times of passing the message in the neural network.
[0063] The inventor finds through in-depth research that this is because the motif corresponding adjacency matrix directly passes information, which may appear false connection, because two disconnected nodes v i 、v j may belong to a motif, even if v i and v j are not adjacent, the corresponding element in the motif corresponding adjacency matrix may also be positive. For false connection, when several times of feature transmission, the local feature will quickly evolve into a full one matrix, which is contrary to the goal of capturing local information.
[0064] To solve this problem, in the application, before passing information through the motif adjacency matrix according to the GCN method based on the motif graph convolution network, the motif adjacency matrix is pretreated, and the motif adjacency matrix is converted into a sparse motif matrix, and the original motif adjacency matrix is replaced with the sparse motif matrix.
[0065] The sparse motif matrix is represented as:
[0066]
[0067] Wherein, A k represents the sparse motif matrix corresponding to the kth motif, A represents the original adjacency matrix of the topological graph, and A k represents the original motif adjacency matrix corresponding to the kth motif, and represents element-wise multiplication.
[0068] The sparse motif matrix provided by the present application can eliminate false connections, thereby solving the problem of over-convergence of motif features, such as Figure 3 An example of false connection is shown. The local topological information of the blue node is expected to be captured to improve the accuracy of obtaining the target feature, and the connection of the gray node with low relevance is cut off. If the motif adjacency matrix is directly used, additional edges (shown by dashed lines) will be introduced, increasing the complexity between motif nodes. The sparse motif matrix provided by the present application is used to replace the original motif adjacency matrix, which can capture the local topological information of the blue node without introducing additional edges, i.e., eliminating false connections.
[0069] Further, the traditional motif adjacency matrix is generally defined as: the element A′ i，j of the matrix is the number of times that the nodes v i and v j co-occur in the same motif, as defined in the article Sam FL Windels et al. Graphlet laplacians for topology-function and topology-disease relationships. Bioinformatics, 2019. However, the inventors found that this traditional definition would make the elements of the obtained motif adjacency matrix present a highly skewed distribution. Only a few edges in the motif adjacency matrix have a high frequency, while the frequencies of other edges are still small. These edges with high frequencies will cover some important information in the edges with low frequencies.
[0070] In the present application, the element in the adjacency matrix A k corresponding to the kth motif is represented as:
[0071]
[0072] wherein v i represents the ith node in the topological graph, v j represents the jth node in the topological graph, and i and j are different positive integers. Through this definition, the above problems caused by the traditional definition are solved, so that the corresponding element in the adjacency matrix corresponding to the motif is positive only when the nodes v i and v j are adjacent and appear in at least one motif at the same time.
[0073] Further, when the motif adjacency matrix is used to transfer information based on the motif graph convolution network, the transfer between different layers of the convolution network is represented as:
[0074]
[0075] wherein, represents the output of the l-th layer of the k-th motif, so that the node features are passed to the relevant nodes through the local topology of the k-th motif.
[0076] According to the present application, through the sparse motif matrix, the spectral information for information transmission can be enriched to a great extent.
[0077] Further, in the present application, the initial features of the first layer of the k-th motif are obtained in the following way:
[0078] The initial feature matrix of the topological graph is obtained, and the way of obtaining the initial feature matrix is a common means for those skilled in the art, which is not described in detail in the present application;
[0079] The initial feature matrix is passed through one or more linear layers and ReLU activation units, preferably two linear layers, to obtain the early feature matrix H (0) ;
[0080] The early feature matrix is subjected to L0-layer message passing through the GCN method to obtain the initial feature where each layer of transmission is represented as: H (l+1) = AH (l) , 1≤l<L0, L0 is a hyperparameter;
[0081] The obtained initial feature is the initial feature of the first layer of the k-th motif, denoted as
[0082] According to the present application, after obtaining the local features and global features, these features need to be integrated. In order to improve the diversity of the graph, the integration is preferably performed in a hierarchical aggregation manner to integrate the spectral information from multiple sparse motifs.
[0083] For the k-th motif, the obtained by the above method contains multi-scale information; for different layers l in the motif graph convolutional network, the obtained contains multi-topological information, and in the present application, these information is aggregated in an adaptive manner, i.e. the aggregation of motif information.
[0084] In addition, since the motif only contains part of the edges of the topological graph, it may not be able to capture global information, and it is far from enough to use only the motif-based features for feature prediction. Therefore, the present application further aggregates global information using an adjacency matrix.
[0085] The aggregation of the global features and the local features includes the aggregation of the motif information and the aggregation of the global information,
[0086] The aggregation of the motif information is represented as:
[0087]
[0088] The aggregation of global information is represented as:
[0089]
[0090] where H loc represents the motif information aggregator, H glo represents the global information aggregator, is a learnable parameter, is a learnable parameter, is the global feature outputted by the l-th layer, and L1 is a hyperparameter representing the number of layers for extracting deep features.
[0091] Further, is obtained in the same way as , with the only difference being that it is performed on the initial feature using the original adjacency matrix A of the topology graph.
[0092] More preferably, and are normalized using Softmax, such that
[0093] In a preferred embodiment, in order to further consider low-level information, the global feature and local feature aggregation also includes the aggregation of early features, represented as:
[0094]
[0095] where H lou represents the early feature aggregator, w (l) is a learnable parameter,
[0096] Finally, the obtained feature H of the target to be classified is a linear combination of the motif information aggregator, the global information aggregator, and the early feature aggregator, represented as:
[0097] H = a(H loc + H glo ) + (1-a)H low Embodiments
[0098] Embodiment 1
[0099] Experiments were conducted on seven data sets with different sizes, densities, and homogeneity, which contained three categories:
[0100] The first type is the Coauthor CS dataset and the Coauthor Physics dataset used in the article Oleksandr Shchur, Maximilian Mumme, Aleksandar Bojchevski, and Stephan Gunnemann. Pitfalls of graph neural network evaluation. arXiv preprint arXiv:1811.05868, 2018. The dataset is a co-author network dataset, taking authors as nodes of a topological graph, and connecting nodes corresponding to two authors who are co-authors of a publication with edges, and the task is to map the target (author) to the respective research field (i.e., classification).
[0101] The second type is the Amazon Computers dataset and the Amazon Photo dataset used in the article Oleksandr Shchur, Maximilian Mumme, Aleksandar Bojchevski, and Stephan Gunnemann. Pitfalls of graph neural network evaluation. arXiv preprint arXiv:1811.05868, 2018. The dataset is an Amazon network dataset, taking goods as nodes of a topological graph, and connecting nodes corresponding to two goods that are often bought together with edges, and the task is to map the target (good) to the respective category (i.e., classification).
[0102] The third type is the Cornell dataset, the Texas dataset, and the Wisconsin dataset used in the article Hongbin Pei, Bingzhe Wei, Kevin Chen-Chuan Chang, Yu Lei, and Bo Yang. Geom-GCN: Geometric graph convolutional networks. In ICLR, 2020. The dataset is a web network dataset, taking web pages as nodes of a topological graph, and connecting nodes corresponding to two web pages that have a hyperlink relationship with edges, and the task is to map the target (web page) to the respective category (i.e., classification).
[0103] By identifying the topological graph based on the motif graph convolutional network, the classification of the target to be classified in the topological graph is obtained.
[0104] In the identification of the topology graph based on the motif graph convolution network, an original adjacency matrix and a motif adjacency matrix of the topology graph are obtained, and information is transmitted through the original adjacency matrix and the motif adjacency matrix.
[0105] In the identification of the topology graph based on the motif graph convolution network, an original adjacency matrix and a motif adjacency matrix of the topology graph are obtained, and information is transmitted through the original adjacency matrix and the motif adjacency matrix.
[0106] In the identification of the topology graph based on the motif graph convolution network, an original adjacency matrix and a motif adjacency matrix of the topology graph are obtained, and information is transmitted through the original adjacency matrix and the motif adjacency matrix.
[0107] Further, the motif graph convolution network learns the input topology graph through the original adjacency matrix according to the GCN method to obtain global features.
[0108] Further, the motif graph convolution network learns the input topology graph through the motif adjacency matrix according to the GCN method to obtain local features corresponding to the motifs.
[0109] Further, before the motif graph convolution network transmits information through the motif adjacency matrix according to the GCN, the motif adjacency matrix is preprocessed to convert the motif adjacency matrix into a sparse motif matrix, and the sparse motif matrix is used to replace the original motif adjacency matrix.
[0110] The sparse motif matrix is represented as:
[0111]
[0112] Further, the element of the adjacency matrix A k of the kth motif is represented as:
[0113]
[0114] Further, when the motif graph convolution network transmits information through the motif adjacency matrix, the transmission between different layers of the convolution network is represented as:
[0115]
[0116] wherein, represents the output of the lth layer of the kth motif.
[0117] Further, the initial feature of the 1st layer of the kth motif is obtained by the following method:
[0118] An initial feature matrix of the topology graph is obtained;
[0119] The initial feature matrix is transmitted through two linear layers and a ReLU activation unit to obtain an early feature matrix H (0) ;
[0120] L0-layer transfer is performed on the early feature matrix to obtain initial features where each layer transfer is represented as: H (l+1) = AH (l) , 1≤l<L0, L0 is a hyperparameter, set to 10;
[0121] The initial features are taken as
[0122] Further, the global feature and local feature aggregation include the aggregation of motif information, the aggregation of global information,
[0123] The aggregation of motif information is represented as:
[0124]
[0125] The aggregation of global information is represented as:
[0126]
[0127] Further, the global feature and local feature aggregation also include the aggregation of early features, represented as:
[0128]
[0129] Finally, the obtained features H of the target to be classified are represented as:
[0130] H = a (H loc + H glo ) + (1-a) H low
[0131] Comparative Example 1
[0132] The same experiment as Example 1 was performed using several currently more advanced methods, including: naive class method GCN, GAT; initial residual method APPNP and GCNII; skip connection method JKNet, GPRGNN and DAGNN.
[0133] Specifically, GCN refers to the paper Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In ICLR, 2017
[0134] GAT See the paper Petar Velickovic, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. Graph attention networks. In ICLR, 2018.
[0135] APPNP See the paper Johannes Klicpera, Aleksandar Bojchevski, and Stephan Gunnemann. Predict then propagate: Graph neural networks meet personalized pagerank. In ICLR, 2018.
[0136] GCNII See the paper Ming Chen, Zhewei Wei, Zengfeng Huang, Bolin Ding, and Yaliang Li. Simple and deep graph convolutional networks. In ICML, 2020.
[0137] JKNet See the paper Keyulu Xu, Chengtao Li, Yonglong Tian, Tomohiro Sonobe, Ken-ichi Kawarabayashi, and Stefanie Jegelka. Representation learning on graphs with jumping knowledge networks. In ICML, 2018.
[0138] GPRGNN See the paper Eli Chien, Jianhao Peng, Pan Li, and Olgica Milenkovic. Adaptive universal generalized pagerank graph neural network. In ICLR, 2020.
[0139] DAGNN See the paper Meng Liu et al. Towards deeper graph neural networks. In SIGKDD, 2020.
[0140] Experimental Example
[0141] The accuracy and standard deviation of different methods in Comparative Example 1 and Comparative Example 1 are shown in Table 1, where OOM represents that the result is unavailable due to an exception of insufficient memory.
[0142]
[0143] The accuracy refers to the classification accuracy, specifically, the percentage of the final classification of the obtained target to be classified and its true classification, and the standard deviation refers to the standard deviation of the accuracy, and in the present application, the results of the two are expressed in the form of "accuracy ± standard deviation".
[0144] From Table 1, it can be seen that 1) the method in Example 1 achieves the most advanced performance in all 7 data sets, verifying its effectiveness;
[0145] 2) The improvement of the method in Example 1 in the Cornell, Texas and Wisconsin web data sets is more significant, for two reasons: first, the web data set has higher heterogeneity, i.e., the difference between targets of the same classification is larger, so more fine-grained local information of motifs is needed to ensure distinguishability; second, these data sets are more dense, i.e., the difference between similar targets is smaller, and when using neural networks for process classification, over-smoothing is more likely to occur, and the proposed method can overcome over-smoothing, thereby improving the accuracy of classification;
[0146] 3) Example 1 performs well on different data sets, which shows that the method in Example 1 can adapt to different types of topological graphs due to the aggregation of multiple motifs.
[0147] In the description of the present application, it should be noted that the terms "upper", "lower", "inner", "outer", "front", "back" and the like indicate the orientation or positional relationship based on the working state of the present application, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore it cannot be understood as a limitation on the present application. In addition, the terms "first", "second", "third", "fourth" are only for descriptive purposes and cannot be understood as indicating or implying relative importance.
[0148] In the description of the present application, it should be noted that unless otherwise explicitly specified and limited, the terms "mounting", "connecting", "connecting" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the communication between the two elements inside. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.
[0149] The application has been described above with reference to preferred embodiments. However, these embodiments are merely exemplary and are intended to be illustrative only. Various substitutions and alterations are possible in view of the disclosure, without departing from the spirit and scope of the application.
Claims
1. A method for classification using a sparse motif graph convolutional network, characterized in that, Includes the following steps: The target to be classified is combined with the known targets to form a topology graph. In the topology graph, the target is a node and the connection between the targets is an edge of the topology graph. The topological graph is identified by a graph convolutional network to obtain the classification of the target in the topological graph. The graph convolutional network is called a radix-order graph convolutional network. When the topological graph is identified based on the radix-order graph convolutional network, the radix-order adjacency matrix is obtained through the original adjacency matrix of the topological graph, and information is transmitted through the original adjacency matrix and the radix-order adjacency matrix. Specifically, the basal sequence graph convolutional network obtains global features through message passing using the original adjacency matrix and local features through message passing using the basal sequence adjacency matrix. The global and local features are then aggregated to obtain the features of the target to be classified, thereby completing the classification of the target. Before transmitting information through the radix adjacency matrix in a radix graph convolutional network, the radix adjacency matrix is preprocessed to transform it into a sparse radix adjacency matrix, which is then used to replace the original radix adjacency matrix. The sparse basis sequence matrix is represented as follows: wherein, denotes the sparse motif matrix corresponding to the kth motif, A denotes the original adjacency matrix of the topological graph, A k denotes the original motif adjacency matrix corresponding to the kth motif, denotes element-wise multiplication; When a radix-based convolutional network transmits information through a radix-based adjacency matrix, the transmission between different layers of the convolutional network is represented as follows: in, This represents the output of the l-th layer of the k-th radix.
2. The method for classification using a sparse basation graph convolutional network according to claim 1, characterized in that, Based on the radix graph convolutional network, information is passed through the original adjacency matrix according to the GCN method to learn the input topological graph and obtain global features.
3. The method for classification using a sparse basation graph convolutional network according to claim 1, characterized in that, Based on the basilo graph convolutional network, the GCN method is used to learn the input topological graph by passing information through the basilo adjacency matrix, and obtain the local features corresponding to the basilo.
4. The method for classification using a sparse basation graph convolutional network according to claim 1, characterized in that, The element in the adjacency matrix A corresponding to the kth motif is denoted as: k The element in the adjacency matrix A corresponding to the kth motif is denoted as: wherein v i represents the ith node in the topological graph, v j represents the jth node in the topological graph, i, j are different positive integers.
5. The method for classification using a sparse basation graph convolutional network according to claim 1, characterized in that, The initial features of the first layer of the k-th motif are obtained in the following way: Obtain the initial feature matrix of the topological graph; The initial feature matrix passes through one or more linear layers and ReLU activation units to obtain an early feature matrix H (0) ; L0 layer message passing is performed on the early feature matrix to obtain the initial features. Each layer of transmission is represented as: H (l+1) =AH (l) 1≤l<L0, where L0 is a hyperparameter; Initial features As 6. The method for classification using a sparse basis sequence graph convolutional network according to claim 1, characterized in that, The aggregation of global and local features includes the aggregation of motif information and the aggregation of global information. The aggregate representation of sequence information is as follows: The aggregated representation of global information is as follows: in, These are learnable parameters. For learnable parameters, L1 represents the global features output by the l-th layer, and L1 is a hyperparameter.
7. The method for classification using a sparse basis sequence graph convolutional network according to claim 5, characterized in that, The aggregation of global and local features also includes the aggregation of earlier features, expressed as: Among them, w (l) These are learnable parameters.