Making Tensor Factorizations Robust to Non-Gaussian Noise

Details Making Tensor Factorizations Robust to Non-Gaussian Noise Making Tensor Factorizations Robust to Non-Gaussian Noise

2010-10-14

arxiv.org/abs/1010.3043v1

Mathematics

Numerical Analysis

Contributed presentation at the NIPS Workshop on Tensors, Kernels, and Machine Learning, Whistler, BC, Canada, December 10, 20

Scientific paper

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.

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