# 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
Publication
In NIPS Workshop on Tensors, Kernels, and Machine Learning
Date
Tags
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

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},
}