A SUBSPACE ELIMINATION STRATEGY FOR ACCELERATING SUPPORT MATRIX MACHINE

摘要

Support matrix machine (SMM) is an effective method for classification problems with matrixform. However, it is time-consuming to solve it, since the complexity increases quickly with the size of matrix variable. Currently, screening methods can efficiently improve the computational speed of SVM models, however they are not applicable to SMM because the SMM has nuclear norm regularization and cannot be expressed as a vector norm. To deal with this issue, in this paper, we introduce a support matrix machine based on squared hinge loss (L-2-SMM), which employs a smoothed substitution formula. It allows the solver to be accelerated without significantly affecting performance. Additionally, we construct a subspace elimination strategy for L-2-SMM (SES-L-2-SMM) to expedite the speed of its training process. To the best of our knowledge, this is the first attempt to introduce a subspace elimination strategy to SMMs models. At each step, an active subspace is chosen so that we can solve a lower-dimensional optimization problem. Later, we use the alternating direction method of multipliers (ADMM) algorithm to resolve the problem. Extensive comparative experiments on multiple real-world datasets demonstrate the efficacy of SES-L-2-SMM.