Sparse and Low-Rank Subspace Clustering
In the era of data deluge, the development of methods for discovering structure in high-dimensional data is becoming increasingly important. Traditional approaches often assume that the data is sampled from a single low-dimensional manifold. However, in many applications in signal/image processing, machine learning and computer vision, data in multiple classes lie in multiple low-dimensional subspaces of a high-dimensional ambient space. In this talk, I will present methods from algebraic geometry, sparse representation theory and rank minimization for clustering and classification of data in multiple low-dimensional subspaces. I will show how these methods can be extended to handle noise, outliers as well as missing data. I will also present applications of these methods to video segmentation and face clustering.