Brett W. Bader

Tensor Decompositions and Applications

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or

Algorithm 862: MATLAB tensor classes for fast algorithm prototyping

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Efficient MATLAB Computations with Sparse and Factored Tensors

-way array. Decompositions of higher-order tensors (i.e.,

Higher-order Web link analysis using multilinear algebra

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Temporal Analysis of Semantic Graphs Using ASALSAN

-way arrays with

Enhancing Multilingual Latent Semantic Analysis with Term Alignment Information

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An information-theoretic, vector-space-model approach to cross-language information retrieval*

) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

Latent Morpho-Semantic Analysis: Multilingual Information Retrieval with Character N-Grams and Mutual Information

Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLABs multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor_as_matrix class supports the “matricization” of a tensor, that is, the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp_tensor and tucker_tensor. We describe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.

Scenario Discovery Using Nonnegative Tensor Factorization

In this paper, the term tensor refers simply to a multidimensional or

Using DEDICOM for Completely Unsupervised Part-of-Speech Tagging

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