Learning Separable Dictionaries for Sparse Tensor Representation: An Online Approach

Abstract

Dictionary learning (DL) for sparse tensor representation aims to train a set of dictionaries for each dimension using tensor samples based on the Tucker decomposition. However, their applications are limited by the fact that all the training samples must be input simultaneously, and that there is no direct way to extend the existing online DL methods for the vector-based model to the Tucker-decomposition-based model. To overcome this limitation, in this brief, we develop a Tucker-decomposition-based strategy to achieve a warm start for updating dictionaries, based on which, an online tensor DL (TDL) algorithm is proposed. The proposed algorithm processes a single new training sample at a time, such that it can be used not only for offline learning from static samples, but also for online learning from dynamic samples, under the framework of the Tucker model. When new training samples are input, only the newly added samples need to be used for retraining the dictionaries. We verify the convergence and low-complexity of the proposed algorithm via theoretical analysis as well as online learning simulations. We also perform offline learning simulations, the results of which demonstrate that our algorithm has an obvious advantage in training accuracy over existing TDL algorithms. The proposed algorithm has the potential to be used in fields such as multidimensional signal processing, compressive sensing, and machine learning.