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Multilinear (tensor) manifold data modeling

October 28, 2008
Keywords:
  • Multilinear
MSC:
  • 47A07
Abstract
Most observable data such as images, videos, human motion capture data, and speech are the result of multiple factors (hidden variables) that are not directly measurable, but which are of interest in data analysis. In the context of computer vision and graphics, we deal with natural images, which are the consequence of multiple factors related to scene structure, illumination, and imaging. Multilinear algebra offers a potent mathematical framework for extracting and explicitly representing the multifactor structure of image datasets. I will present two multilinear models for learning (nonlinear) manifold representations of image ensembles in which the multiple constituent factors (or modes) are disentangled and analyzed explicitly. Our nonlinear models are computed via a tensor decomposition, known as the M-mode SVD, which is an extension to tensors of the conventional matrix singular value decomposition (SVD), or through a generalization of conventional (linear) ICA called Multilinear Independent Components Analysis (MICA). I will demonstrate the potency of our novel statistical learning approach in the context of facial image biometrics, where the relevant factors include different facial geometries, expressions, lighting conditions, and viewpoints. When applied to the difficult problem of automated face recognition, our multilinear representations, called TensorFaces (M-mode PCA) and Independent TensorFaces (MICA), yields significantly improved recognition rates relative to the standard PCA and ICA approaches. Recognition is achieved with a novel Multilinear Projection Operator. Bio: M. Alex O. Vasilescu is an Assistant Professor of Computer Science at Stony Brook University (SUNY). She received her education at MIT and the University of Toronto. She was a research scientist at the MIT Media Lab from 2005-07 and at New York University's Courant Insitute from 2001-05. She has also done research at IBM, Intel, Compaq, and Schlumberger corporations, and at the MIT Artificial Intelligence Lab. She has published papers in computer vision and computer graphics, particularly in the areas of face recognition, human motion analysis/synthesis, image-based rendering, and physics-based modeling (deformable models). She has given several invited talks about her work and has several patents pending. Her face recognition research, known as TensorFaces, has been funded by the TSWG, the Department of Defense's Combating Terrorism Support Program. She was named by MIT's Technology Review Magazine to their 2003 TR100 List of Top 100 Young Innovators. http://www.cs.sunysb.edu/~maov