Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning or robust PCA (RPCA). For long data sequences, if one tries to use a single lower dimensional subspace to represent the data, the required subspace dimension may end up being quite large. For such data, a better model is to assume that it lies in a low-dimensional subspace that can change over time, albeit gradually. The problem of tracking such data (and the subspaces) while being robust to outliers is called robust subspace tracking (RST). This article provides a magazine-style overview of the entire field of robust subspace learning and tracking. In particular solutions for three problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition (S+LR), RST via S+LR, and "robust subspace recovery (RSR)". RSR assumes that an entire data vector is either an outlier or an inlier. The S+LR formulation instead assumes that outliers occur on only a few data vector indices and hence are well modeled as sparse corruptions.Comment: To appear, IEEE Signal Processing Magazine, July 201

A robust motion estimation and segmentation approach to represent moving images with layers

The paper provides a robust representation of moving images based on layers. To that goal, we have designed efficient motion estimation and segmentation techniques by affine model fitting suitable for the construction of layers. Layered representations, originally introduced by Wang and Adelson (see IEEE Transactions on Image Processing, vol.3, no.5, p.625-38, 1994) are important in several applications. In particular they are very appropriate for object tracking, object manipulation and content-based scalability which are among the main functionalities of the future MPEG-4 standard. In addition a variety of examples are provided that give a deep insight into the performance bounds of the representation of moving images using layers.Peer ReviewedPostprint (published version