Tree-Based Structural Twin Support Tensor Clustering with Square Loss Function

Abstract

Most of the real-life applications involving images, videos etc. deals with matrix data (second order tensor space). Tensor based clustering models can be utilized for identifying patterns in matrix data as they take advantage of structural information in multi-dimensional framework and reduce computational overheads as well. Despite such numerous advantages, tensor clustering has still remained relatively unexplored research area. In this paper, we propose a novel clustering technique, termed as Treebased Structural Least Squares Twin Support Tensor Clustering (Tree-SLSTWSTC), that builds a cluster model as a binary tree, where each node comprises of proposed Structural Least Squares Twin Support Tensor Machine (S-LSTWSTM) classifier that considers the structural risk minimization of data alongside a symmetrical L2-norm loss function. The proposed approach results in time-efficient learning. Initialization framework based on tensor \(k{-}\)means has been proposed and implemented in order to overcome the instability disseminated by random initialization. To validate the efficacy of the proposed framework, computational experiments have been performed with relevant tensor based models on face recognition and optical digit recognition datasets.