Low-cost orthogonal basis-core extraction for classification and reconstruction using tensor ring

Tensor based methods have gained popularity for being able to represent multi-aspect real world data in a lower dimensional space. Among them, methods with orthogonal factors perform relatively better in classification. However, most of them cannot handle higher order data. Recently, Tensor Ring (TR) based methods are proposed to combat with the higher order issue more effectively focusing on both classification and reconstruction. A TR-based method with orthogonal cores performs reasonably well for a given error. However, its computational complexity is very high and might produce extra features. To solve these issues, in this paper, we propose a method named as Orthogonal basis-core extraction using Tensor Ring (OTR) that can facilitate better discrimination and reconstruction at a lower cost. To maintain the ring property, we also show, theoretically, that reshaping of the product of semi-orthogonal reshaped cores remains semi-orthogonal. Rigorous experiments over eighteen benchmark datasets from different fields demonstrate the superiority of OTR over state-of-the-art methods in terms of classification and reconstruction.