Matrix Product State for Higher-Order Tensor Compression and Classification

HERE is an increasing need to handle large multidimensional datasets that cannot efficiently be analyzed or processed using modern day computers. Due to the curse of dimensionality it is urgent to develop mathematical tools which can evaluate information beyond the properties of large matrices [1]. The essential goal is to reduce the dimensionality of multidimensional data, represented by tensors, with a minimal information loss by compressing the original tensor space to a lower-dimensional tensor space, also called the feature space [1]. Tensor decomposition is the most natural tool to enable such compressions [2]. Until recently, tensor compression is merely based on Tucker decomposition (TD) [3], also known as higher-order singular value decomposition (HOSVD) when orthogonality constraints on factor matrices are imposed [4].