Matrix Product State for Feature Extraction of Higher-Order Tensors
It addresses computational efficiency and classification accuracy for researchers and practitioners working with tensor data, though it appears incremental as it builds on existing tensor decomposition techniques.
This paper tackled the problem of feature extraction for multidimensional data represented by higher-order tensors by introducing matrix product state (MPS) decomposition, resulting in significant computational savings and better classification performance compared to existing methods like HOOI.
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). Benchmark results show that MPS can reduce significantly the feature space of data while achieving better classification performance compared to HOOI.