Multi-scale data which contains structures at different scales of size and density is a big challenge for spectral clustering. Even given a suitable locally scaled affinity matrix, the first k eigenvectors of such a matrix still cannot separate clusters well. Thus, in this paper, we exploit the fusion of the cluster-separation information from all eigenvectors to achieve a better clustering result. Our method FUll Spectral ClustEring (FUSE) is based on Power Iteration (PI) and Independent Component Analysis (ICA). PI is used to fuse all eigenvectors to one pseudo-eigenvector which inherits all the cluster-separation information. To conquer the cluster-collision problem, we utilize PI to generate p (p > k) pseudo-eigenvectors. Since these pseudo-eigenvectors are redundant and the cluster-separation information is contaminated with noise, ICA is adopted to rotate the pseudo-eigenvectors to make them pair-wise statistically independent. To let ICA overcome local optima and speed up the search process, we develop a self-adaptive and self-learning greedy search method. Finally, we select k rotated pseudoeigenvectors (independent components) which have more cluster-separation information measured by kurtosis for clustering. Various synthetic and real-world data verifies the effectiveness and efficiency of our FUSE method.

Filed under: Dimensionality Reduction