Recent advances in information technologies have led to unprecedented large amounts of high-dimensional data from many emerging applications. The need for more advanced techniques to analyze such complex data calls for shifting research paradigms. In this talk, I will overview and highlight several results in the area of estimation of mixture models in high-dimensional data spaces. Applications will be presented in problems such as motion segmentation, image segmentation, face recognition, and human action categorization. Through this talk, I intend to emphasize the confluence of algebra and statistics that may lead to more advanced solutions in analyzing complex singular data structures such as mixture linear subspaces and nonlinear manifolds. In the first part of the talk, I will start by reviewing a solution to simultaneously segment and estimate mixture subspace models – Generalized Principal Component Analysis (GPCA). In contrast to traditional statistical methods, GPCA is focused on recovering a set of vanishing polynomials that globally determines mixture subspaces as its zero set. I will introduce a new algebro-geometric framework along the same approach to simultaneously segment mixture quadratic manifolds. The new solution is also robust to moderate data noise and outliers. The second part will be focused on classification of mixture subspace models, where the prior information of mixture subspaces is provided through training examples. Inspired by compressive sensing theory, the recognition problem can be reformulated via a sparse representation. Furthermore, efficient solutions exist to recover such sparse representation using fast L-1 minimization. Finally, I will discuss several open problems in the emerging field of distributed sensor perception.
Allen Y. Yang is a postdoctoral researcher in the department of EECS at UC Berkeley. His primary research is in pattern analysis of geometric and statistical models in high-dimensional data spaces, and applications in motion segmentation, image segmentation, face recognition, and distributed sensor perception. He received a BEng in Computer Science from the University of Science and Technology of China (USTC) in 2001. He received an MS in Electrical Engineering in 2003, an MS in Mathematics in 2005, and a PhD in Electrical and Computer Engineering in 2006, all from the University of Illinois (UIUC). He has published five journal papers and more than 10 conference papers. He has three US patent applications.