A Fuzzy Least Squares Support Tensor Machines in Machine Learning

Abstract

In the machine learning field, high-dimensional data are often encountered in the real applications. Most of the traditional learning algorithms are based on the vector space model, such as SVM. Tensor representation is useful to the over fitting problem in vector-based learning, and tensor-based algorithm requires a smaller set of decision variables as compared to vector-based approaches. We also would require that the meaningful training points must be classified correctly and would not care about some training points like noises whether or not they are classified correctly. To utilize the structural information present in high dimensional features of an object, a tensor-based learning framework, termed as Fuzzy Least Squares support tensor machine (FLSSTM), where the classifier is obtained by solving a system of linear equations rather than a quadratic programming problem at each iteration of FLSSTM algorithm as compared to STM algorithm. This in turn provides a significant reduction in the computation time, as well as comparable classification accuracy. The efficacy of the proposed method has been demonstrated in ORL database and Yale database. The FLSSTM outperforms other tensor-based algorithms, for example, LSSTM, especially when training size is small.