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.