Fast Spectral Clustering Via Deep Learning And Graph Filtering

Spectral clustering is a widely used unsupervised learning method that is effective in dealing with many real-world problems.However,in the context of big data,spectral clustering may involve thousands of pieces of data in the actual application process.The complexity of traditional spectral clustering algorithms in processing these data will increase with the increase of the problem scale,which makes many applications cannot be realized when dealing with large-scale data.Traditional spectral clustering has three disadvantages: it cannot learn effective representation in non-European data,and the clustering accuracy will be affected;The existing algorithms based on spectral clustering all require eigendecomposition of the Laplacian matrix,which is very time-consuming in the process of processing large-scale data.When the data scale is large,the application of 6)-means algorithm will lead to a large time complexity.Inspired by graph convolutional networks,Chebyshev polynomial approximation and sampling techniques,the following work is proposed to solve the above problems:Firstly,the graph convolutional network is used to express and analyze the data,which not only learns the features of each node itself,but also considers the structural information between nodes.The new representation of nodes is generated by the aggregation of side information and node information,so as to effectively learn the features of the original data.The main advantages of graph convolutional network are as follows: Graph convolutional network can process non-European data.Even though the number of neighboring vertices of each vertex may be different,graph convolutional network can still effectively extract data features for learning,which is conducive to capturing global information and better expressing node features.Second,traditional spectral clustering depends on characteristics of Laplacian characteristic vectors of the decomposed matrix,in order to solve the problem of Laplace characteristics of the matrix decomposition,this paper adopts the way totally different from traditional spectral clustering,namely through chebyshev multinomial approximation design spectrum filter,will do parameterized spectrum domain convolution kernels,the convolution operation in the process of using its development to accelerate the filtering,Thus,the eigendecomposition of the Laplace matrix is avoided.Chebyshev polynomial approximation has the following three advantages:(1)It reduces the number of original free parameters and speeds up the filtering speed;(2)no longer rely on the eigenvector matrix after the Laplace matrix decomposition,that is,no longer need to do time-consuming eigendecomposition of the Laplace matrix;(3)The time complexity of the algorithm can be reduced by using the sparsity of Laplacian matrix.Finally,in order to reduce the time complexity of the 6)-means algorithm,this paper adopts the adaptive random sampling technique for reference to the idea of graph signal sampling.Under the premise of retaining all the information of the original data,by optimizing the constraints,the randomly sampled samples are extended to large-scale data,and the 6)-means algorithm can be implemented under the small scale of data,so as to reduce the time complexity.At the same time,the least square method is used to reconstruct the data iteratively,obtain the interpolation signal,and get the clustering result of the original data.Adaptive random sampling can reduce the size of data and achieve rapid convergence at the same time,and ensure that the information is not lost,can realize the reconstruction of the original data.To sum up,according to the research contents of the above three parts,this paper puts forward a kind of deep learning fast spectral clustering method and filter,effective study the representation of the data,avoid the characteristics of spectral clustering algorithm decomposition,implementation of sampling data clustering,solve the traditional spectral clustering in the process of clustering,Thus,the complex and large amount of data in real applications are processed accurately and effectively,and the clustering accuracy is ensured,and the clustering speed is improved.