Generalized Principal Component Analysis GPCA: Geometric Clustering for Vision and Control Networks
Assistant Professor of Biomedical Engineering
Time and Place
Mauldin Auditorium (NSH 1305)
Refreshments 3:15 pm
Talk 3:30 pm
Data segmentation is usually though of as a "chiken-and-egg" problem. In order to estimate a mixture of models one needs to first segment the data and in order to segment the data one needs to know the model parameters. Therefore, data segmentation is usually solved in two stages (1) data clustering and (2) model fitting, or else iteratively using, e.g. the Expectation Maximization (EM) algorithm.
This talk will show that for a wide class of segmentation problems (eigenvector segmentation, mixtures of subspaces, mixtures of fundamental matrices/trifocal tensors, mixtures of linear dynamical models), the "chicken-and-egg" dilemma can be tackled using algebraic geometric techniques. In fact, it is possible to eliminate the data segmentation step algebraically and then use all the data to recover all the models without previously segmenting the data. The solution can be obtained using linear algebraic techniques and is closed form if and only if the number of groups is less than or equal to 4. Examples of the applications of GPCA to segmentation of static and dynamic scenes and identification of hybrid dynamical models systems will also be presented.
Professor Ren Vidal received his
B.S. degree in Electrical Engineering (highest honors) from the Pontificia Universidad
Catlica de Chile in 1997 and his M.S. and Ph.D. degrees in Electrical
Engineering and Computer Sciences from the
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