The Johns Hopkins University Whiting School of Engineering Department of Electrical and Computer Engineering Advances in Algebraic Subspace Clustering PhD Proposal Seminar by Manolis Tsakiris Graduate Research Assistant (Dr. René Vidal) Electrical and Computer Engineering Abstract: High‐dimensional data arise in many instances in modern science and technology, from computer vision to computational biology. When the intrinsic structure of the data is nonlinear, the classic Principal Component Analysis (PCA) becomes ineffective as a means of dimensionality reduction. In addition, data is often multimodal, in the sense that different groups of points have been generated by different sources. A natural and powerful nonlinear model that has found success in the last 15 years is that of a union of linear subspaces (as opposed to a single linear subspace in PCA), under which different groups of points lie in different linear subspaces. This gives rise to the problem of Subspace Clustering, which is finding the number of subspaces, their dimensions, a basis for each subspace and the clustering of the points according to their subspace membership. Among a large variety of subspace clustering methods, including low‐rank and sparse representation approaches, Algebraic Subspace Clustering is unique in that it admits theoretical guarantees irrespectively of the subspace dimensions. However, a number of theoretical and practical issues have been open, such as a provably correct treatment of an unknown number of subspaces of arbitrary dimensions or robustness to noise. This thesis proposal talk, discusses recent theoretical and practical contributions in Algebraic Subspace Clustering, as well as current research directions, which combine techniques from algebraic geometry and sparse representation theory. Thursday, April 2, 2015 3p.m. Latrobe 120 FOR DISABILITY INFORMATION CONTACT: Janel Johnson (410) 516‐7031 [email protected]