A-Optimal Non-negative Projection with Hessian regularization

Abstract

With the demand of high dimensional data analysis, data representation (or feature learning) has attracted more and more attention and becomes a central problem in pattern recognition and data mining. Non-negative Matrix Factorization (NMF) which is a useful data representation method makes great contribution in finding the latent structure of the data and leading to a parts-based representation by decomposing the data matrix into a few bases and encodings with the non-negative constraint. Considering the learned encodings from a statistical view by modeling the data points via ridge regression and minimizing the variance of the parameter, A-Optimal Non-negative Projection (ANP) improves the performance of NMF. However, it neglects the intrinsic geometric structure of the data. We introduce Hessian regularization and propose a novel method called A-Optimal Non-negative Projection with Hessian regularization (AHNP) to address this problem. Therefore, AHNP not only leads to parts-based and precise representations but preserves the intrinsic geometrical structure of the obtained subspace. We demonstrate the effectiveness of this novel algorithm through a set of evaluations on real world applications.