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Multiway Spectral Clustering with Out-of-Sample Extensions through Weighted Kernel PCA

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2 Author(s)
Alzate, C. ; Dept. of Electr. Eng., Katholieke Univ. Leuven, Leuven, Belgium ; Suykens, J.A.K.

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.

Published in:

Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:32 ,  Issue: 2 )