A Research On Improvement Of Spectral Clustering Algorithms

Spectral clustering is a new branch of cluster analysis based onspectral graph theory. Unlike the traditional clustering algorithms, thespectral clustering algorithms are applied to solve the clustering ofnon-convex sphere of sample spaces, so that they can be converged toglobal optimal solution. It constructs a simplified data space making useof Laplacian matrix that not only reduce the dimension of data but alsogives clearer distribution of data in the subspaceFirstly, an overview of the basic principle of spectral clustering,spectral clustering algorithm and its classification are outlined. In thesummary of domestic and overseas literature, problems and challengesexisting in the research of spectral clustering algorithms are discussed. Asan entry point that creating the similarity matrix, the traditional spectralclustering algorithms have been improved and the main problems to besolved and results are as follows:1. Introduce a fuzzy similarity matrix into spectral clustering, andavoid setting parameter according to previous experience in thetraditional spectral clustering algorithm. Considering the differentimportance of attributes, construct the weighted distance matrix and theweighted similarity matrix; In order to describe the data structure fully,consider both spatial proximity and feature information of data sets, andconstruct mixed weighted fuzzy similar matrix. The performance of the mixed weighted fuzzy similar matrix is enhanced by matrix transitiveclosure method furtherly. Introduce the mixed weighted fuzzy similarmatrix into the traditional spectral clustering algorithms, and propose aspectral clustering algorithm based on mixed weighted fuzzy similarmatrix. Considering the spectral clustering algorithm improved above issensitive to the order of input data, the spectral clustering algorithm basedon PSO is constructed.2. Considering defects of expert scoring method, AHP, factoranalysis and so on as the commonly used methods in the calculation ofattribute weights, propose the MDIV method inspired by the MIV methodof neural network.3. The samples analysis show that the MDIV method a wide range ofcalculating attribute weights, and the calculation results are more realistic;Compared with the traditional spectral clustering algorithms,the spectralclustering algorithm based on mixed weighted fuzzy similar matrix ismore precise. The spectral clustering algorithm based on PSO overcomethe sensitive to input data, then its result is more precise and scientific.4. Write MATLAB programs according to the above algorithm.