Canonical polyadic tensor decomposition in the presence of non Gaussian noise

Abstract

In this paper we describe an estimator for the canonical polyadic (CP) tensor model using order statistics of the residuals. The estimator minimizes in an iterative and alternating fashion a dispersion function given by the weighted ranked absolute residuals. Specific choices of the weights lead to either equivalent or approximate versions of the least squares estimator, least absolute deviation estimator or least trimmed squares estimators. For different noise distributions, we present simulations comparing the performance of the proposed algorithm with the standard least squares estimator. The simulated performance is equivalent in the Gaussian noise case and superior when the noise is distributed according to the Laplacian or Cauchy distributions.