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Computing nonnegative tensor factorizations

Michael P. Friedlander (mpf***at***cs.ubc.ca)
Kathrin Hatz (khatz***at***ix.urz.uni-heidelberg.de)

Abstract: Nonnegative tensor factorization (NTF) is a technique for computing a parts-based representation of high-dimensional data. NTF excels at exposing latent structures in datasets, and at finding good low-rank approximations to the data. We describe an approach for computing the NTF of a dataset that relies only on iterative linear-algebra techniques and that is comparable in cost to the nonnegative matrix factorization. (The better-known nonnegative matrix factorization is a special case of NTF and is also handled by our implementation.) Some important features of our implementation include mechanisms for encouraging sparse factors and for ensuring that they are equilibrated in norm. The complete Matlab software package is available under the GPL license.

Keywords: N-dimensional arrays, tensors, nonnegative tensor factorization, alternating least-squares, block Gauss-Seidel, sparse solutions, regularization, nonnegative least-squares

Category 1: Applications -- Science and Engineering

Citation: Department of Computer Science Technical Report TR-2006-21, October 2006, University of British Columbia

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Entry Submitted: 10/18/2006
Entry Accepted: 10/18/2006
Entry Last Modified: 10/18/2006

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