Least Squares Support Matrix Machines Based on Bilevel Programming

Abstract

It is known that the classifications problems for matrix or more higher order tensor data are often met in many real-world applications. If using classical SVM-type methods for such problems, it needs to reshape matrix or tensor data into vectors, which may lead to the destruction of structure information contained in data. In order to overcome the limitation, this paper considers the classification problem with matrices as inputs directly and proposes a novel classification method named as least square support matrix machine (LSSMM). By means of bilevel programming (BP), an iteratively implemented algorithm (BP-LSSMM) for LSSMM is suggested. Experiment results indicate that BP-LSSMM is an effective and competitive classifier for matrix data classification.