Locality preserving difference component analysis based on the Lq norm

This paper develops locality preserving difference component analysis in which the intrinsic and global structure of data is exploited, and the model we propose also provides the flexibility to adapt some characteristics of data by applying the Lq norm. In order to solve the proposed model that is non-convex or non-smooth, we resort to the proximal alternating linearized optimization approach where each subproblem has good optimization properties. It is observed that the objective function in the proposed model is a semi-algebraic function. This allows us to give the convergence analysis of algorithms in terms of the Kurdyka-Lojasiewicz property. To be specific, the sequence of iterations generated by the proposed approach converges to a critical point of the objective function. The experiments on several data sets have been conducted to demonstrate the effectiveness of the proposed approach.