Introduction to the Issue on Robust Subspace Learning and Tracking: Theory, Algorithms, and Applications

The papers in this special section focus on robust subspace learning and tracking. Subspace learning theory for dimensionality reduction was initiated with the Principal Component Analysis (PCA) formulation proposed by Pearson in 1901. PCA was first widely used for data analysis in the field of psychometrics and chemometrics but today it is often the first step in more various types of exploratory data analysis, predictive modeling, classification and clustering problems. It finds modern applications in signal processing, biomedical imaging, computer vision, process fault detection, recommendation system design and many more domains. Since one century, numerous other subspace learning models, either reconstructive and discriminative, were developed over time in literature to address dimensionality reduction while keeping the relevant information in a different manner from PCA. However, PCA can also be viewed as a soft clustering method that seeks to find clusters in different subspaces within a dataset, and numerous clustering methods are based on dimensionality reduction. These methods are called subspace clustering methods that are extension of traditional PCA based clustering, and divide data points belonging to the union of subspaces (UoS) into the respective subspaces. In several modern applications, the main limitation of the subspace learning and clustering models are their sensitivity to outliers. Thus, further developments concern robust subspace learning which refers to the problem of subspace learning in the presence of outliers. In fact, even the classical subspace learning problem with speed or memory constraints is not a solved problem.