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.

摘要

多路数组或张量正在成为处理多维数据的重要工具。本文关注二阶张量数据的一类分类。当一类数据是唯一可用的数据时，就会出现一类分类问题。典型的基于向量的方法在处理张量数据时具有局限性。最小二乘一类支持向量机 (LS-OCSVM) 是标准一类支持向量机 (OCSVM) 的变体。它直接对向量表示的模式进行操作，并直接通过求解一组线性方程而不是二次规划 (QP) 来获得解析解。一类支持张量机（OCSTM）是一种一类分类工具，用于解决张量的一类分类问题。它基于交替投影算法和二次规划来获得解决方案。本文提出了一种处理张量一类的新方法，最小二乘支持张量数据描述（LS-STDD）。LS-STDD 相对于一类支持张量机 (OCSTM) 的优势在于 LS-STDD 具有封闭形式的解决方案。它没有使用OCSTM和二次规划的交替投影方法。因此，LS-STDD 比 OCSTM 更容易、更快速地实施。通过仿真说明了所提出的方法相对于 OCSTM 的效率。LS-STDD 相对于一类支持张量机 (OCSTM) 的优势在于 LS-STDD 具有封闭形式的解决方案。它没有使用OCSTM和二次规划的交替投影方法。因此，LS-STDD 比 OCSTM 更容易、更快速地实施。通过仿真说明了所提出的方法相对于 OCSTM 的效率。LS-STDD 相对于一类支持张量机 (OCSTM) 的优势在于 LS-STDD 具有封闭形式的解决方案。它没有使用OCSTM和二次规划的交替投影方法。因此，LS-STDD 比 OCSTM 更容易、更快速地实施。通过仿真说明了所提出的方法相对于 OCSTM 的效率。