Least-squares support tensor data description

Abstract

Multi-way arrays or tensors are becoming important tools to deal with multidimensional data. This paper is concerned with a one-class classification of second order tensor data. One-class classification problems arise when data from one class is the only data available. Typical vector based methods have limitations when dealing with tensor data. Least squares one-class support vector machine (LS-OCSVM) is a variant of the standard one-class support vector machine (OCSVM). It operates directly on patterns represented by vector and obtains an analytical solution directly from solving a set of linear equations instead of quadratic programming (QP). One-class support tensor machine (OCSTM) is a one-class classification tool for solving the one-class classification problem for tensors. It is based on alternating projection algorithms and quadratic programming to obtain solutions. In this paper, a new method to deal with one-classification of tensors is proposed, least squares support tensor data description (LS-STDD). The advantage of LS-STDD over one-class support tensor machine (OCSTM) is that LS-STDD has a closed form solution. It doesn’t use the alternating projection method of OCSTM and quadratic programming. Consequently, LS-STDD is easier and faster to implement than OCSTM. The efficiency of the proposed method over OCSTM is illustrated through simulations.