Trace Norm Regularization and Application to Tensor Based Feature Extraction

摘要

The trace norm regularization has an interesting property that is rank of a matrix is reduced according to its continuous regularization parameter. We propose a new efficient algorithm for a kind of trace norm regularization problems. Since the algorithm is not gradient-based approach, its computational complexity does not depend on initial states or learning rate. We also apply the proposed algorithm to a tensor based feature extraction method, that is an extension of the trace norm regularized feature extraction. Computational simulations show that the proposed algorithm provides an accurate solution in less time than conventional methods. The proposed trace based feature extraction method show almost that same performance as Multilinear PCA.