Making Tensor Factorizations Robust to Non-Gaussian Noise

Abstract

Tensors are multi-way arrays, and the Candecomp/Parafac (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood estimate under the assumption of i.i.d. Gaussian noise. We demonstrate that this loss function can actually be highly sensitive to non-Gaussian noise. Therefore, we propose a loss function based on the 1-norm because it can accommodate both Gaussian and grossly non-Gaussian perturbations. We also present an alternating majorization-minimization algorithm for fitting a CP model using our proposed loss function.

Type
Other
Publication
In NIPS Workshop on Tensors, Kernels, and Machine Learning
Date
Tags
Tensors
Links
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Citation
E. C. Chi, T. G. Kolda. Making Tensor Factorizations Robust to Non-Gaussian Noise. In NIPS Workshop on Tensors, Kernels, and Machine Learning, Whistler, BC (2010-12-10), 2010. http://arxiv.org/abs/1010.3043

Keywords

CANDECOMP, PARAFAC, 1-norm, non-Gaussian noise

Comments

Contributed paper at the NIPS Workshop on Tensors, Kernels, and Machine Learning, Whistler, BC, Canada, December 10, 2010

BibTeX

@inproceedings{arXiv_1010.3043,  
author = {Eric C. Chi and Tamara G. Kolda}, 
title = {Making Tensor Factorizations Robust to Non-{G}aussian Noise}, 
booktitle = {NIPS Workshop on Tensors, Kernels, and Machine Learning},
venue = {Whistler, BC},
eventdate = {2010-12-10}, 
month = {October}, 
year = {2010},
eprint = {1010.3043},
eprintclass = {math.NA},
}