Kernel Method For Node Classification

Graph structure data,such as transportation networks,subway networks,and social networks,exist in large numbers in the real world.Therefore,learning and understanding graphs are the key to machine learning.The current research on graphs is mainly divided into graph classification and node classification.Node classification is a very important task in network mining,given a network with labels on some nodes,it will predict the labels of other nodes on the network.Node classification is actually a machine learning problem,which applies the classification model in machine learning to the network.The essence of node classification is to improve the existing classification model so that it can obtain a better classification effect.The graph shows that the graph convolutional network in learning,as an extension of the convolutional neural network in graph data processing,has been satisfactorily evaluated in the node classification task,and has been successfully applied to the node classification task in network analysis.The existing graph convolutional network has some problems in node classification.First of all,the graph convolutional network uses network data with a graph structure and is not suitable for data without a graph structure.Secondly,the original data attributes usually contain non-linear relationships,which are difficult to capture in low-dimensional space,and the current graph convolutional network does not consider the non-linear relationship between data attributes.Third,the original data usually contains noise and redundant features,which will have a bad influence on the constructed graph representation,thereby affecting the result of node classification.In addition,most graph convolutional networks currently use a single Euclidean distance to calculate the distance between two samples.It treats the differences between the different attributes of the samples(that is,various indicators or variables)as the same.This is sometimes Can not meet the actual requirements and single-distance metric learning may have over-fitting problems.This paper proposes two improved convolutional network algorithms for node classification tasks based on the above-mentioned problems of graph convolutional network in node classification combined with graph representation learning,kernel method,feature selection,sparse learning,and other theories.Its core content and original points are as follows:1.At present,most graph convolutional networks are only applicable to graph structure data.The original Euclidean data usually contains noise and redundant information,and there is a nonlinear relationship between data attributes.This paper proposes a new nonlinear graph learning convolutional network algorithm.The algorithm first uses a kernel function such as a Gaussian kernel function to map the original Euclidean data to the kernel space,making the original Euclidean data linearly separable,to capture the nonlinear relationship between data attributes,and then use structure-based information feature selection method removes noise and redundant features to construct a high-quality graph representation,and finally uses a commonly used graph convolutional network to perform node classification tasks.2.Since most graph convolutional networks use a single Euclidean distance to calculate the distance between two samples and are prone to overfitting,this paper proposes a new multi-graph kernel convolutional network algorithm.The algorithm first uses a multi-distance measurement method such as M-distance to obtain multiple trainable distance metrics.These multiple trainable distance metrics correspond to multiple graphs,and each graph has a distance matrix.The algorithm uses a feature mapping function for the input nodes to fully learn the local vertex feature information and graph topology information,thereby obtaining a new node representation.Then,the mixed kernel function of each graph is represented by the distance matrix and the new node.The mixed kernel function is composed of a basic kernel function and the effective kernel function constructed by each graph.By solving the mixed kernel function of each graph,the node representation of each graph is obtained.Finally,this paper uses a pooling to batch and normalize all node representations,and use the results of pooling to evaluate the performance of node classification.In short,these methods proposed in this paper effectively solve some of the current problems of graph convolutional network.For example,most graph convolutional networks are only applicable to graph structure data.The original data usually contains noise and redundant information,the nonlinear relationship between the data,and the single distance measurement.There may be problems such as overfitting in learning.The method proposed in this paper obtains better node classification performance on different evaluation indicators.In future work,I will consider the problems existing in other graph convolutional networks,such as high nonlinearity,structure preservation,attribute preservation,sparsity,etc.,and propose new solutions.