Robust tensor factorization using R1 norm

Heng Huang, Chris H. Q. Ding

Abstract: Over the years, many tensor based algorithms, e.g. two dimensional principle component analysis (2DPCA), two dimensional singular value decomposition (2DSVD), high order SVD, have been proposed for the study of high dimensional data in a large variety of computer vision applications. An intrinsic limitation of previous tensor reduction methods is the sensitivity to the presence of outliers, because they minimize the sum of squares errors (L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> norm). In this paper, we propose a novel robust tensor factorization method using R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> norm for error accumulation function using robust covariance matrices, allowing the method to be efficiently implemented instead of resorting to quadratic programming software packages as in other L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> norm approaches. Experimental results on face representation and reconstruction show that our new robust tensor factorization method can effectively handle outliers compared to previous tensor based PCA methods.