2D compressed learning: support matrix machine with bilinear random projections

Abstract

Support matrix machine (SMM) is an efficient matrix classification method that can leverage the structure information within the matrix to improve the classification performance. However, its computational and storage costs are still expensive for high-dimensional data. To address these problems, in this paper, we consider a 2D compressed learning paradigm to learn the SMM classifier in some compressed data domain. Specifically, we use the Kronecker compressed sensing (KCS) to obtain the compressive measurements and learn the SMM classifier. We show that the Kronecker product measurement matrices used by KCS satisfies the restricted isometry property (RIP), which is a property to ensure the learnability of the compressed data. We further give a lower bound on the number of measurements required for KCS. Though this lower bound shows that KCS requires more measurements than the regular CS to satisfy the same RIP condition, KCS itself still enjoys lower computational and storage complexities. Then, using the RIP condition, we verify that the learned SMM classifier in the compressed domain can perform almost as well as the best linear classifier in the original uncompressed domain. Finally, our experimental results also demonstrate the feasibility of 2D compressed learning.