Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. The Tensor Toolbox provides the following classes for manipulating dense, sparse, and structured tensors using MATLAB's object-oriented features:

• tensor - A (dense) multidimensional array (extends MATLAB's current capabilities).
• sptensor - A sparse multidimensional array.
• tenmat - Store a tensor as a matrix, with extra information so that it can be converted back into a tensor.
• sptenmat - Store a sptensor as sparse matrix in coordinate format, with extra information so that it can be converted back into a sptensor.
• ttensor - Store a tensor decomposed as a Tucker operator (see below).
• ktensor - Store a tensor decomposed as a Kruskal operator (see below).

For more details about what tensors are, see the Glossary.

What's New in Version 2.4?

Version 2.4 adds optimization-based methods for calculating CP (even with missing data). The new functions require the Poblano Toolbox for Matlab, available separately. To see a complete list of changes, view the RELEASE_NOTES.txt file.

Download

To obtain a free license for our software, visit the Tensor Toolbox License and Registration page. Note: This code requires MATLAB2006a (version 7.2) or later.

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Join the Tensor Toolbox Mailing List to get important information on new releases and more.

How to Cite

Cite the following references for the MATLAB Tensor Toolbox Version 2.4:

• For optimization approach to CP (cp_opt code): E. Acar, T. G. Kolda and D. M. Dunlavy, An Optimization Approach for Fitting Canonical Tensor Decompositions, Technical Report Number SAND2009-0857, Sandia National Laboratories, Albuquerque, NM and Livermore, CA, February 2009.
   
• For CP with missing data (cp_wopt code): E. Acar, D. M. Dunlavy, T. G. Kolda and M. Mørup, Scalable Tensor Factorizations with Missing Data. In: SDM10: Proceedings of the 2010 SIAM International Conference on Data Mining, SIAM, April 2010.
   
• For working with sparse or structured tensors: Brett W. Bader and Tamara G. Kolda, Efficient MATLAB computations with sparse and factored tensors, SIAM Journal on Scientific Computing 30(1):205-231, December 2007.
   
• For working with dense tensors: Brett W. Bader and Tamara G. Kolda, Algorithm 862: MATLAB Tensor Classes for Fast Algorithm Prototyping, ACM Transactions on Mathematical Software, 32(4), December 2006.
   
• Toolbox: Brett W. Bader and Tamara G. Kolda, MATLAB Tensor Toolbox Version 2.4, http://www.sandia.gov/~tgkolda/TensorToolbox/, March 2010.

Cite the following references for Memory-Efficient Tucker (MET) included with the MATLAB Tensor Toolbox Version 2.4:

• T. G. Kolda and J. Sun. Scalable Tensor Decompositions for Multi-aspect Data Mining. In: ICDM 2008: Proceedings of the 8th IEEE International Conference on Data Mining, Pages 363-372, December 2008. (doi:10.1109/ICDM.2008.89)

Click here to see more Tensor Toolbox papers, including user contributions.

Questions or Comments

• Send a question or comment on the Tensor Toolbox via email
• Report a bug in Bugzilla (requires registration)
• Contribute your own code to the project

Links to Previous Versions

• Version 2.3
• Version 2.2
• Version 2.1
• Version 2.0
• Version 1.0