Linear
and Multilinear (Tensor) Methods for Vision, Graphics and Signal Processing
Description:
Linear and Multilinear methods
(e.g. Principal Component Analysis, Independent Component Analysis, Multilinear
PCA, Multilinear ICA) have been successfully applied in numerous visual, graphics and signal
processing tasks over the last two decades. In this tutorial, we will
provide a unified framework for several classical and novel component analysis
techniques useful for modeling, classifying and clustering high dimensional
data.
In the first part of the tutorial, we will review
traditional linear techniques such as PCA, LDA, CCA, etc. Several extensions
(linear and non-linear) to solve common problems in computer vision/graphics
and signal processing (e.g. outliers, lack of training data, etc.) will be
discussed. In the second part, we will show how to generalize the above methods
to take advantage of the assets of multilinear
algebra, the algebra of higher order tensors. We will discuss: generalizations
of the concepts of rank and orthogonality, tensor
factorizations, as well as the generalization of the linear projection
operator. The tutorial will discuss how these techniques can be applied to
visual tracking, signal modeling (e.g. background estimation, virtual avatars),
pattern recognition (e.g. face recognition, gait recognition), computer
graphics and clustering problems.
Outline:
·
Extended
Linear Models - Fernando De La Torre
·
Generative Models
(Review of PCA/SVD,
·
Robust principal
component analysis.
·
Principal component
analysis with uncertainty/missing data.
·
Parameterized
component analysis.
·
PCA over continuous
spaces.
·
Filtered component
Analysis.
·
Component analysis and
spectral graph methods for clustering.
·
Multiple subspaces.
·
Discriminative Models
(Review of LDA, CCA, OCA)
·
Multimodal oriented discriminant analysis.
·
Representational
oriented component analysis.
·
Robust linear discriminant analysis.
·
Dynamic coupled
component analysis.
·
Standard extensions.
·
Latent variable
models.
·
Kernel methods.
· Multilinear Extensions - M. Alex O. Vasilescu
·
Generalizations of
rank and orthogonality to higher order tensors.
·
Higher order
decompositions: Multilinear SVD (M-mode SVD), Multilinear
·
Multilinear Projection Operator, Response Tensor, Contribution Tensor.
·
Multilinear Manifold Parameterization.
·
Applications to signal
processing, computer vision, computer graphics and machine learning.
Length and Intended audience:
Half day (4 hours). All people in computer vision will
benefit from a deep understanding of basic techniques such as SVD, LDA, CCA,
Tensor Factorization, etc and their extensions.
The course is self contained and just basic knowledge of linear algebra
is required.
Proposer:
Massachusetts
Institute of Technology
Biographies:
Fernando De la Torre received his B.Sc. degree in
telecommunications, M.Sc. degree in electronic engineering
and Ph. D, respectively, in 1994, 1996 and 2002, from La Salle School of
Engineering in
M. Alex O. Vasilescu was educated at MIT and the University of Toronto. She has done research at the MIT Artificial Intelligence Lab and at research centers of IBM, Intel, Compaq, and Schlumberger corporations. She is currently a research scientist at MIT Media Lab. She has published research 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 four patents pending. Her face recognition research, known as TensorFaces, was funded by the TSWG, the Department of Defense's Combating Terrorism Support Program. She has been named by MIT's Technology Review Magazine to their 2003 TR100 List of Top Young Innovators.