The tensor product of two arrays is notionally an outer
        product of the arrays collapsed in specific extents by summing
        along the appropriate diagonals.

Provides convenience functions for advanced
        linear algebra with tensors and computation with data sets of
        tensors on a higher level abstraction. It includes Einstein and
        Riemann summing conventions, dragging, co- and contravariate
        indices, parallel computations on sequences of tensors.

Bayesian Tensor Factorization for decomposition of tensor data sets using the trilinear CANDECOMP/PARAFAC (CP) factorization, with automatic component selection. The complete data analysis pipeline is provided, including functions and recommendations for data normalization and model definition, as well as missing value prediction and model visualization. The method performs factorization for three-way tensor datasets and the inference is implemented with Gibbs sampling.

Contains several utility functions for manipulating tensor-valued data (centering, multiplication from a single mode etc.) and the implementations of the following blind source separation methods for tensor-valued data: 'tPCA', 'tFOBI', 'tJADE', k-tJADE', 'tgFOBI', 'tgJADE', 'tSOBI', 'tNSS.SD', 'tNSS.JD', 'tNSS.TD.JD', 'tPP' and 'tTUCKER'.

Performs model-based tensor clustering methods including Tensor Gaussian Mixture Model (TGMM), Tensor Envelope Mixture Model (TEMM) by Deng and Zhang (2021) <DOI: 10.1111/biom.13486>, Doubly-Enhanced EM (DEEM) algorithm by Mai, Zhang, Pan and Deng (2021) <DOI: 10.1080/01621459.2021.1904959>.

Efficient algorithms for tensor noise reduction and completion. This package includes a suite of parametric and nonparametric tools for estimating tensor signals from noisy, possibly incomplete observations. The methods allow a broad range of data types, including continuous, binary, and ordinal-valued tensor entries. The algorithms employ the alternating optimization. The detailed algorithm description can be found in the following three references.