Issue No. 02 - February (2010 vol. 32)
Carlos Alzate , Katholieke Universiteit Leuven, Leuven
Johan A.K. Suykens , Katholieke Universiteit Leuven, Leuven
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.
Spectral clustering, kernel principal component analysis, out-of-sample extensions, model selection.
Carlos Alzate, Johan A.K. Suykens, "Multiway Spectral Clustering with Out-of-Sample Extensions through Weighted Kernel PCA", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 32, no. , pp. 335-347, February 2010, doi:10.1109/TPAMI.2008.292