Multimedia Classification via Tensor Linear Discriminant Analysis

Linear discriminant analysis (LDA) is a well-known feature-extraction technique for data analytic and pattern classification. As the dimensionality of multimedia data has increased in this big era, it is often to characterize data by tensors. Over the past two decades, researchers have thus explored to extend LDA to the general tensor space, especially in two common ways: LDA of tensors using tensor decomposition methods (by conversion of tensors to matrices) and LDA of tensors built upon the T-product. However, both of the aforementioned approaches have restrictions thereby. A critical problem about how to carry out LDA of arbitrary scatter tensors based on the Einstein product still remains unsolved by the existing methods. Therefore, we propose a novel tensor LDA (a.k.a. TLDA) approach, which can carry out the LDA of arbitrary-dimensional scatter-tensors without any need of tensor decomposition. Besides, for reducing the computation time, we also design a parallel paradigm to execute our proposed TLDA in this work. Numerical experiments conducted over real multimedia data demonstrate the efficacy of our proposed new TLDA in terms of classification accuracy. Moreover, the comparison of the classification accuracies, computational-complexities, and memory-complexities of our proposed novel TLDA scheme and other existing tensor-based LDA methods is made. By leveraging TLDA for high-dimensional feature extraction, segmentation, and user-item interaction data processing, future multimedia recommendation systems can facilitate more accurate, engaging, and satisfactory user experience over the Internet.