Abstract—A new formulation for multiway spectral clustering is proposed. This method corresponds to a weighted kernel principal component analysis (PCA) approach based on primal-dual least-squares support vector machine (LS-SVM) formulations.

The formulation allows the extension to out-of-sample points. In this way, the proposed clustering model can be trained, validated, and tested. The clustering information is contained on the eigendecomposition of a modified similarity matrix derived from the data. This eigenvalue problem corresponds to the dual solution of a primal optimization problem formulated in a high-dimensional feature space. A model selection criterion called the Balanced Line Fit (BLF) is also proposed.

This criterion is based on the out-of-sample extension and exploits the structure of the eigenvectors and the corresponding projections when the clusters are well formed. The BLF criterion can be used to obtain clustering parameters in a learning framework. Experimental results with difficult toy problems and image segmentation show improved performance in terms of generalization to new samples and computation times.

Multiway Spectral Clustering with Out-of-Sample Extensions

through Weighted Kernel PCA

Published in: IEEE Transactions On Pattern Analysis And Machine Intelligence

Date of Publication: Feb, 2010

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