Element rearrangement for action classification on product manifolds

Abstract

Conventional tensor-based classification algorithms unfold tensors into matrices using the standard mode-k unfoldings and perform classification using established machine learning algorithms. These methods assume that the standard mode-k unfolded matrices are the best 2-dimensional representations of N-dimensional structures. In this thesis, we ask the question: "Is there a better way to unfold a tensor?" To address this question, we design a method to create unfoldings of a tensor by rearranging elements in the original tensor and then applying the standard mode-k unfoldings. The rearrangement of elements in a tensor is formulated as a combinatorial optimization problem and tabu search is adapted in this work to solve it. We study this element rearrangement problem in the context of tensor-based action classification on product manifolds. We assess the proposed methods using a publicly available video data set, namely Cambridge-Gesture data set. We design several neighborhood structures and search strategies for tabu search and analyze their performance. Results reveal that the proposed element rearrangement algorithm developed in this thesis can be employed as a preprocessing step to increase classification accuracy in the context of action classification on product manifolds method.