Optimal Feature Extraction and Classification of Tensors via Matrix Product State Decomposition

Big data consists of large multidimensional datasets that would often be difficult to analyze if working with the original tensor. There is a rising interest in the use of tensor decompositions for feature extraction due to the ability to extract necessary features from a large dimensional feature space. In this paper the matrix product state (MPS) decomposition is used for feature extraction of large tensors. The novelty of the paper is the introduction of a single core tensor obtained from the MPS that not only contains a significantly reduced feature space, but can perform classification with high accuracy without the need of feature selection methods.