Jointly local statistics and topological proximity consideration in spectral clustering

Efficient deals of mathematical techniques have been devoted to cluster data with complicated manifold structures. Although local geometrical properties of data are considered in these techniques, some essential local statistics behaviours are ignored. In this paper, a method is proposed in which local topological and local statistics structures are jointly considered. More precisely, local correlations, local distributions and high-order proximity of data points are simultaneously considered to construct more efficient affinity matrix. Local correlations and high-order proximity are considered to modify the connectivity of the graph representation of data, and local distributions are utilized to obtain a free parameter similarity function between data points. After obtaining the new similarity matrix, spectral clustering is employed to evaluate the efficiency of it. The experimental results on various benchmark data sets demonstrate that the new method can significantly improve the clustering performance compared with state-of-the-art techniques.