Making tensor factorizations robust to non-gaussian noise.

Chi, Eric C. (Rice University, Houston, TX) ; Kolda, Tamara Gibson

关键词: TENSORS;    GAUSS FUNCTION;    ALGORITHMS;    FACTORIZATION;    PERFORMANCE;   

DOI  :  10.2172/1011706
RP-ID  :  SAND2011-1877
PID  :  OSTI ID: 1011706
Others  :  TRN: US201109%%675

学科分类：数学（综合）

美国|英语

来源: SciTech Connect

【 摘 要 】

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 independent and identically distributed (i.i.d.) Gaussian noise. We demonstrate that this loss function can 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 (MM) algorithm for fitting a CP model using our proposed loss function (CPAL1) and compare its performance to the workhorse algorithm for fitting CP models, CP alternating least squares (CPALS).