Abstract
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 MATLAB's 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.
Keywords
Tensor (intrinsic definition)Computer scienceMatrix multiplicationTensor contractionTensor calculusMATLABMatrix (chemical analysis)Variety (cybernetics)Class (philosophy)AlgorithmComputational scienceTensor productTheoretical computer scienceAlgebra over a fieldMathematicsTensor fieldExact solutions in general relativityArtificial intelligencePure mathematicsProgramming languagePhysicsMathematical analysis
Affiliated Institutions
Related Publications
Efficient MATLAB Computations with Sparse and Factored Tensors
In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. ...
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 N-way array. Decompositions...
Part-Based Statistical Models for Object Classification and Detection
We propose using simple mixture models to define a set of mid-level binary local features based on binary oriented edge input. The features capture natural local structures in t...
Linear Smoothers and Additive Models
We study linear smoothers and their use in building nonparametric regression models. In the first part of this paper we examine certain aspects of linear smoothers for scatterpl...
Spatial Priors for Part-Based Recognition Using Statistical Models
We present a class of statistical models for part-based object recognition that are explicitly parameterized according to the degree of spatial structure they can represent. The...
Publication Info
- Year
- 2006
- Type
- article
- Volume
- 32
- Issue
- 4
- Pages
- 635-653
- Citations
- 448
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
448
OpenAlex
Cite This
Brett W. Bader,
Tamara G. Kolda
(2006).
Algorithm 862.
ACM Transactions on Mathematical Software
, 32
(4)
, 635-653.
https://doi.org/10.1145/1186785.1186794
Identifiers
- DOI
- 10.1145/1186785.1186794