Accelerated Stochastic Variance Reduction Gradient Algorithms for Robust Subspace Clustering

Robust face clustering enjoys a wide range of applications for gate passes, surveillance systems and security analysis in embedded sensors. Nevertheless, existing algorithms have limitations in finding accurate clusters when data contain noise (e.g., occluded face clustering and recognition). It is known that in subspace clustering, the ℓ1- and ℓ2-norm regularizers can improve subspace preservation and connectivity, respectively, and the elastic net regularizer (i.e., the mixture of the ℓ1- and ℓ2-norms) provides a balance between the two properties. However, existing deterministic methods have high per iteration computational complexities, making them inapplicable to large-scale problems. To address this issue, this paper proposes the first accelerated stochastic variance reduction gradient (RASVRG) algorithm for robust subspace clustering. We also introduce a new momentum acceleration technique for the RASVRG algorithm. As a result of the involvement of this momentum, the RASVRG algorithm achieves both the best oracle complexity and the fastest convergence rate, and it reaches higher efficiency in practice for both strongly convex and not strongly convex models. Various experimental results show that the RASVRG algorithm outperformed existing state-of-the-art methods with elastic net and ℓ1-norm regularizers in terms of accuracy in most cases. As demonstrated on real-world face datasets with different manually added levels of pixel corruption and occlusion situations, the RASVRG algorithm achieved much better performance in terms of accuracy and robustness.