Improved L1-Tucker via L1-Fitting

Mahsa Mozaffari, Panos P. Markopoulos, Ashley Prater-Bennette

Abstract: Tucker decomposition is the generalization of Principal Component Analysis to high-order tensors. The L2-norm-based formulation of standard Tucker suffers from severe sensitivity to outliers. L1-norm-based Tucker (L1-Tucker) has been proposed as an outlier-resistant alternative with documented success in an array of applications. L1-HOSVD is a straightforward solver for L1-Tucker that computes each basis by conducting L1-PCA on the matrix that is derived by flattening the data tensor across the corresponding mode. In this paper, L1-HOSVD is further enhanced via an additional L1-fitting step. The proposed method combines the outlier-resistance of L1-HOSVD with that of L1-fitting and returns jointly-computed bases of enhanced robustness, as corroborated by our numerical studies on synthetic and real-world datasets.