Ternary tree-based structural twin support tensor machine for clustering

Abstract

Most of the real-life applications usually involve complex data, e.g., grayscale images, where information is distributed spatially in the form of two-dimensional matrices (elements of second-order tensor space). Traditional vector-based clustering models such as k-means and support vector clustering rely on low-dimensional features representations for identifying patterns and are prone to loss of useful information which is present in spatial structure of the data. To overcome this limitation, tensor-based clustering models can be utilized for identifying relevant patterns in matrix data as they take advantage of structural information present in multi-dimensional framework and reduce computational overheads as well. However, despite these numerous advantages, tensor clustering has still remained relatively unexplored research area. In this paper, we propose a novel clustering framework, termed as Ternary Tree-based Structural Least Squares Support Tensor Clustering (TT-SLSTWSTC), that builds a cluster model as a hierarchical ternary tree, where at each node non-ambiguous data are dealt separately from ambiguous data points using the proposed Ternary Structural Least Squares Support Tensor Machine (TS-LSTWSTM). The TS-LSTWSTM classifier considers the structural risk minimization of data alongside a symmetrical L2-norm loss function. Also, initialization framework based on tensor k-means has been used in order to overcome the instability disseminated by random initialization. To validate the efficacy of the proposed framework, computational experiments have been performed on human activity recognition and image recognition problems. Experimental results show that our method is not only fast but yields significantly better generalization performance and is comparatively more robust in order to handle heteroscedastic noise and outliers when compared to related methods.