A multi-kernel method of measuring adaptive similarity for spectral clustering

Abstract

Accurate representation of similarities between data points is an important determinant in the success of many clustering approaches. Previous studies have shown that kernel methods are effective in this representation. However, using multi-kernels to merge probabilistic neighborhoods in data still needs further research. In this paper, a multi-kernel method of measuring adaptive similarity for spectral clustering is proposed. Kernels with more accurate adaptive similarity measure on the data are assigned bigger weights and an optimum combined kernel that truly reflects the internal structure of the data points is obtained. The proposed method ascribes adaptive and optimal neighbors to each data point based on the local structure using the combined kernels. The combined similarity measure and data clustering are learnt simultaneously to obtain optimal clustering results. We rank constraint the Laplacian matrix of the data similarity matrix to ensure that the connected components in the similarity matrix are exactly equal to the cluster number. The presented technique is significant in the sense that it is able to search the underlying similarity relationships amongst data points and is robust to complex data. Compared with other state-of-the-art spectral clustering methods, our proposed method achieves better performance in terms of NMI and accuracy in experiments performed on both synthetic and real datasets.