Tensor-Train Discriminant Analysis

Abstract

The rapid development of information technology is making it possible to collect massive amounts of multidimensional, multimodal data with high dimensionality in a diverse set of science and engineering disciplines. Although there has been a lot of recent work in the area of unsupervised tensor learning, extensions to supervised learning, feature extraction and classification are still limited. Moreover, most of the existing supervised tensor learning approaches are based on the Tucker model. However, this model has some limitations for large tensors including high memory and execution time costs. In this paper, we introduce a supervised learning approach for tensor classification based on the tensor-train model. In particular, we introduce two computationally efficient implementations of tensor-train discriminant analysis (TT-DA). The proposed approaches are evaluated on image classification tasks with respect to computation time, storage cost and classification accuracy.