A robust supervised subspace learning approach for output-relevant prediction and detection against outliers

Abstract This paper proposes a novel robust supervised subspace learning (RSSL) method for output-relevant prediction and detection against outliers. RSSL learns the robust subspaces by optimizing a joint problem over both the prediction of output and the reconstruction of input. To this end, the learned subspaces/data representations are informative, i.e., they are encapsulated with the critic information related to both the input and output, and thus can benefit the following tasks of output-related modeling and detection. Besides, we separate sparse items from the raw measurements to suppress the effects of outliers. An efficient optimization algorithm is designed to solve the optimization problem of RSSL. We further conduct post orthogonal decomposition upon the subspaces provided by RSSL so that the trimmed subspaces are more suitable for output-related detection. The efficacy of the proposed method is extensively verified by synthesis data and benchmark data.