Out-of-sample eigenvectors in kernel spectral clustering

A method to estimate eigenvectors for out-of-sample data in the context of kernel spectral clustering is presented. The proposed method is within a constrained optimization framework with primal and dual model representations. This formulation allows the clustering model to be extended naturally to out-of-sample points together with the possibility to perform model selection in a learning setting. A model selection methodology based on the Fisher criterion is also presented. The proposed criterion can be used to select clustering parameters such that the out-of-sample eigenvector space show a desirable structure. This special structure appears when the clusters are well-formed and the clustering parameters have been chosen properly. Simulation results with toy examples and images show the applicability of the proposed method and model selection criterion.