Sparse Subspace Classification and Clustering

SpeakerDr. Rene E. Vidal
Organization Center for Imaging Science, Johns Hopkins University
LocationEngineering Building II Room 1230
DateOctober 26, 2012 12:50 PM


In many problems 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. We consider the two problems of classification and clustering of data in a union subspaces using sparse representation techniques. We use the idea that the collection of data forms a self-expressive dictionary in which a new data point can write itself as a linear combination of points from the same class/subspace. First, we consider the classification problem where the training data in each class form a few groups of the dictionary and correspond to a few subspaces. We formulate the classification problem as finding a few active subspaces in the union of subspaces using two classes of convex optimization programs. We investigate conditions under which the proposed optimization programs recover the desired solution. Next, we consider the clustering problem, where the goal is to cluster the data in a union of subspaces so that data points in each cluster correspond to points in the same subspace. We propose a convex optimization program based on sparse representation and use its solution to infer the clustering of data using spectral clustering. We investigate conditions under which the proposed convex program successfully finds a sparse representation of each point as a linear combination of points from the same subspace. We demonstrate the efficacy of the proposed classification and clustering algorithms on face classification, face clustering and motion segmentation.


Professor Vidal received his B.S. degree in Electrical Engineering (highest honors) from the Pontificia Universidad Catolica de Chile in 1997 and his M.S. and Ph.D. degrees in Electrical Engineering and Computer Sciences from the University of California at Berkeley in 2000 and 2003, respectively. He was a research fellow at theNational ICT Australia in 2003 and has been a faculty member in the Department of Biomedical Engineering and the Center for Imaging Science of The Johns Hopkins University since 2004. He has held several visiting faculty positions at ENS Paris, the Catholic University of Chile, Universite Henri Poincare, and the Australian National University. Dr.Vidal was co-editor (with Anders Heyden and Yi Ma) of the book ``Dynamical Vision" and has co-authored more than 150 articles in biomedical image analysis, computer vision, machine learning, hybrid systems, and robotics. Dr. Vidal is Associate Editor of the IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), the SIAM Journal on Imaging Sciences and the Journal of Mathematical Imaging and Vision. He was or will be program chair for ICCV 2015, CVPR 2014, WMVC 2009, and PSIVT 2007. He was or will be area chair for CVPR 2013, ICCV 2011, ICCV 2007 and CVPR 2005. Dr. Vidal is recipient of numerous awards for his work, including the 2011 Best Paper Award Finalist (with Roberto Tron and Bijan Afsari) at the Conference on Decision and Control, the 2009 ONR Young Investigator Award, the 2009 Sloan Research Fellowship, the 2005 NFS CAREER Award and the 2004 Best Paper Award Honorable Mention (with Prof. Yi Ma) at the European Conference on Computer Vision. He also received the 2004 Sakrison Memorial Prize for "completing an exceptionally documented piece of research", the 2003 Eli Jury award for "outstanding achievement in the area of Systems, Communications, Control, or Signal Processing", the 2002 Student Continuation Award from NASA Ames, the 1998 Marcos Orrego Puelma Award from the Institute of Engineers of Chile, and the 1997 Award of the School of Engineering of the Pontificia Universidad Catolica de Chile to the best graduating student of the school. He is a member of the IEEE and the ACM.

  October 2012
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