Positive semidefinite spectral clustering method based on Lagrange dual

Abstract

The invention provides a positive semidefinite spectral clustering method based on a Lagrange dual, and relates to a spectral clustering method. A, principal component analysis in given sample data is adopted to conduct dimensionality reduction. B, similarity matrix forms sample data based on an omnibearing connection diagram, and similarity between the sample data is used based on weighted sum and a method of a Gaussian kernel function and a polynomial kernel function. C, positive semidefinite of similarity matrix is conducted based on Lagrange dual property. D, singular value decomposition of normalization matrix is conducted, and then the matrix which is formed by feature vector corresponding to the front K eigenvalue of maximum is obtained. E, a traditional K mean value cluster or other cluster methods is adopted to conduct clustering analysis on the feature vector matrix and obtain a final clustering result. All data can be effectively clustered, people know by algorithm analysis that compared with a common positive semidefinite spectral clustering method, not only be precision of spectral clustering can improved, but also required time for the spectral clustering can be greatly reduced .

Description

technical field [0001] The invention relates to a spectral clustering method, in particular to a Lagrangian dual-based semi-positive definite spectral clustering method. Background technique [0002] Cluster analysis is one of the most popular techniques in the field of statistical data analysis and processing. It has been widely used in image analysis, pattern recognition, machine learning and information retrieval. The goal of cluster analysis is to effectively distinguish different data categories (called "clusters") in the data set, so that the similarity of data in the same cluster is large, while the similarity of data between different clusters is small. In recent years, spectral clustering methods have rapidly developed into a class of effective clustering techniques. The spectral clustering method is based on the spectral graph theory, and mainly uses the eigenvectors of the similarity matrix of the data set for effective clustering. Compared with traditional clu...

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Problems solved by technology

[0006] The purpose of the present invention is to provide that the existing eigenvalue decomposition and gradient descent method can be used very conveniently to solve the semi-positive definite programming problem, and the global optimal solution can be found in polynomial time, and its time complexity is only (O(t · no 3 ), where t is the number of iterations, usually about 250), based on the Lagrangian dual semi-positive definite spectrum clustering method

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