Matrix Product State for Feature Extraction of Higher-Order Tensors

Understand

This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors.

• Regardless of tensor order, MPS extracts its relevant features to the so-called core tensor of maximum order three which can be used for classification.
• Mainly based on a successive sequence of singular value decompositions (SVD), MPS is quite simple to implement without any recursive procedure needed for optimizing local tensors.
• Thus, it leads to substantial computational savings compared to other tensor feature extraction methods such as higher-order orthogonal iteration (HOOI) underlying the Tucker decomposition (TD).