Robust Principal Component Analysis on Graphs

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first issue with a sparse penalty term. The second issue can be handled with the matrix factorization model, which is however non-convex. Besides, PCA based clustering can also be enhanced by using a graph of data similarity. In this article, we introduce a new model called "Robust PCA on Graphs" which incorporates spectral graph regularization into the Robust PCA framework. Our proposed model benefits from 1) the robustness of principal components to occlusions and missing values, 2) enhanced low-rank recovery, 3) improved clustering property due to the graph smoothness assumption on the low-rank matrix, and 4) convexity of the resulting optimization problem. Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with corruptions clearly reveal that our model outperforms 10 other state-of-the-art models in its clustering and low-rank recovery tasks

Structured Sparse Principal Component Analysis

We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This \emph{structured sparse PCA} is based on a structured regularization recently introduced by [1]. While classical sparse priors only deal with \textit{cardinality}, the regularization we use encodes higher-order information about the data. We propose an efficient and simple optimization procedure to solve this problem. Experiments with two practical tasks, face recognition and the study of the dynamics of a protein complex, demonstrate the benefits of the proposed structured approach over unstructured approaches

A survey of face recognition techniques under occlusion

The limited capacity to recognize faces under occlusions is a long-standing problem that presents a unique challenge for face recognition systems and even for humans. The problem regarding occlusion is less covered by research when compared to other challenges such as pose variation, different expressions, etc. Nevertheless, occluded face recognition is imperative to exploit the full potential of face recognition for real-world applications. In this paper, we restrict the scope to occluded face recognition. First, we explore what the occlusion problem is and what inherent difficulties can arise. As a part of this review, we introduce face detection under occlusion, a preliminary step in face recognition. Second, we present how existing face recognition methods cope with the occlusion problem and classify them into three categories, which are 1) occlusion robust feature extraction approaches, 2) occlusion aware face recognition approaches, and 3) occlusion recovery based face recognition approaches. Furthermore, we analyze the motivations, innovations, pros and cons, and the performance of representative approaches for comparison. Finally, future challenges and method trends of occluded face recognition are thoroughly discussed