Robust feature extraction via ℓ∞-norm based nonnegative Tucker decomposition

Feature extraction plays an indispensable role in image and video technology. However, it is difficult for traditional matrix based feature extraction methods to handle massive multi-dimensional data. This, alongside with the ubiquitous uncertainty (noise) in real-world data, resulted in many robust tensor based feature extraction models. However, these existing models did not consider the worst-case model performance (i.e., the largest fitting error among all samples), which is critically important from a robust optimization perspective. In this paper, we propose a novel robust feature extraction model via ℓ∞-norm based nonnegative Tucker decomposition. The model is to minimize the maximum sample fitting error so as to overcome the influence of data uncertainty. Although the new model is nonconvex and nonsmooth, we design an effective iterative optimization algorithm with theoretical guarantee on its convergence for it. The performance of the new model on five real-world benchmark object classification and face recognition datasets under various corruption scenarios are evaluated, and the experimental results show the excellence of the new model by comparing to many existing models.