We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposedâ€¦ (More)

Many pattern classification algorithms such as Support Vector Machines (SVMs), MultiLayer Perceptrons (MLPs), and K-Nearest Neighbors (KNNs) require data to consist of purely numerical variables.â€¦ (More)

Model selection in tensor decomposition is important for real applications if the rank of the original data tensor is unknown and the observed tensor is noisy. In the Tucker model, the minimumâ€¦ (More)

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multiâ€“ modal datasets, which are often conveniently represented asâ€¦ (More)

We discuss extended definitions of linear and multilinear operations such as Kronecker, Hadamard, and contracted products, and establish links between them for tensor calculus. Then we introduceâ€¦ (More)

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representationâ€¦ (More)

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving orâ€¦ (More)