A semi-supervised formulation to binary kernel spectral clustering

A semi-supervised formulation to binary kernel spectral clustering is presented. The formulation fits in a constrained optimization setting with primal and dual model representations. The clustering model can be applied naturally to out-of-sample points allowing model selection and achieving good generalization capabilities. The proposed method incorporates labeled information into the core binary kernel spectral clustering by adding an extra term into the objective function together with a regularization constant. The resulting dual problem is no longer an eigenvalue problem as in the case of the original core model but a linear system. A model selection criterion combining a cluster distortion measure on the unlabeled part and the classification accuracy on the labeled part is also presented. This criterion can be used to obtain clustering parameters such that the clustering model evaluated at validation points display a desirable structure. Simulation results with toy data and real benchmark datasets show the applicability of the proposed method.