Extended linear and multi-linear methods for multimodal signal processing

agerasiaetherealAI and Robotics

Nov 24, 2013 (3 years and 11 months ago)

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Fernando De la Torre

Carnegie Mellon University

ftorre@cs.cmu.edu


Title:

Extended linear and multi
-
linear methods for multimodal signal
processing



Abstract
:

Linear and Multilinear methods (e.g. Principal Compon
ent Analysis, Independent
Component Analysis, Tensor Factorization,) have been successfully applied in numerous
multimedia,

graphics and signal processing tasks

over the last two decades. In this
tutorial, we will provide a unified framework for several no
vel component analysis
techniques useful for modeling, classifying and clustering high dimensional multimodal
data.


In the first part of the tutorial, we will review traditional linear techniques such as
principal Component Analysis (PCA), Linear Discrimi
nant Analysis (LDA), Canonical
Correlation Analysis (CCA), NMF (Non
-
Negative Matrix Factorization), Independent
Component Analysis (ICA) among other CA methods. In the second part, several
extensions (linear and non
-
linear) to solve common problems in mult
imodal data such
audio and video (e.g. outliers, lack of training data, geometric invariance, etc.) will be
discussed. In the final part of the tutorial, we will review standard extensions of linear
models such as kernels, latent variable models and tensor

factorization.


Description
:


The outline of the tutorial will be:


1
-

Review of traditional linear models: PCA, LDA, CCA, OCA, NMF
and ICA. (1/2 hour)

2
-

Extended linear models:


(1:15 hours)

a.


Dealing with sample and intra
-
sample outliers (PCA, LDA, CCA).

b.

A
chieving geometrical invariance (PCA).

c.


Incremental computation (PCA, LDA).

d.

Learning relations between multiple data sets (CCA).

e.


Modeling multimodal distributed classes (LDA).

f.


Improving generalization when few training samples are available
(OCA, LDA, P
CA).

g.
Clustering in low dimensional spaces (PCA
-
LDA).

h.
Other extensions (illumination insensitive PCA, multiple
eigenspaces, etc.)

3
-

Standard extensions of linear models: (1:15 hours)

a.

Kernel methods.

b.

Latent variable models.

c.

Tensor factorization.



Length and I
ntended audience:

Half day
(3 hours)
. All people in multimedia signal processing will benefit from a deep
understanding of basic techniques such as SVD, LDA (Linear Discriminant Analysis),
CCA (Canonical Correlation Analysis), Tensor Factorization, Kernel
methods or latent
variable models. The course is self contained and just basic knowledge of linear algebra
is required.



Biography:


Fernando De la Torre received his B.Sc. degree in


Telecommunications, M.Sc. and
Ph. D. degrees in Electronic Engineerin
g and Ph. D, respectively, in 1994, 1996 and
2002, from La Salle School of Engineering in Ramon Llull University, Barcelona, Spain.


In 1997

and 2000 he became Assistant and Associate

Professor in

the Department of
Communications and Signal Theory in Eng
inyeria La Salle. Since 2005 he is Research
Faculty in the Robotics Institute at Carnegie Mellon University. Dr. De la Torre's
research interests include signal processing, computer vision and machine learning. Dr.
De la Torre has co
-
organized a workshop i
n human sensing from video and he has given
several tutorials at international conferences on the topic of subspace methods for
computer vision.




Sample Bibliography:


De la Torre, F. and Black, M. J.

Dynamic Coupled


Component Analysis.


IEEE Proc. Computer Vision and Pattern Recognition, CVPR'01,

Kauai, Hawaii, Vol.
II,
pp. 643
-
650, Dec. 2001.


De la Torre, F. and T. Kanade,

Multimodal Oriented Discriminant Analysis. ICML 05.


De la Torre
, F., R. Gross, S. Baker and B.V.K. Vijaka Kumar

Representational Oriented Component Analysis.

IEEE Proc. Computer Vision and Pattern Recognition, CVPR'05,

San Diego.


De la
Torre, F. and Black, M. J.


Robust Parameterized Component Analysis: Theory and applications to 2D facial
appearance models.

Computer Vision and Image Understanding. Vol. 91. pp. 53
-
71. 2003.


De la Torre, F. and Black, M. J.

A Framework for Robust Subspace Learning.

International Journal of Computer Vision. Vol. 54. Issue 1
-
3, pp. 183
-
209, Aug.
-
Oct.

2003.


De la Torre, F,

Discriminative Cluster Analysis. International Conference on Machine Learning 2006.


De la Torre, F,

Learning kernel expansions for image classification. Submitted to CVPR 2007.


S. Fidler, D. Skocaj, and A. Leonardis, "Combining reconstructive and discriminative
subspace methods for robust classification and regression by subsampling",
IEEE
Transactions on Pattern Analysis and Machine Intelligence
, Accepted for publication,
2006.

D. D. Lee and H. S. Seung.
Algorithms for Non
-
negative Matrix Factorization (2001).

Tipping, M.

E. and C.

M. Bishop (1999a)
.
Probabilistic principal component
analysis
.

Journal of the Royal Statistical Society, Series B


61
(3), 611

622. Tipping,

Marian Stewart Bartlett, Javier R. Movellan, Terrence J. Sejnowski

.
Face Recognition by
Independent Component Analysis. NIPS. 2002




Brand, M.E., "Incremental Singula
r Value Decomposition of Uncertain Data with
Missing Values",
European Conference on Computer Vision (ECCV)
, Vol 2350, pps 707
-
720, May 2002

A. Leonardis, H. Bischof, and J. Maver, "Multiple Eigenspaces",
Pattern Recognition
,
35
, no. 11, pages 2613
-
2627,
2002.

T. Melzer, M. Reiter, and H.Bischof.

Kernel CCA: A nonlinear extension of canonical correlation analysis.

IEEE Trans. on Neural Networks
, 2001.


Levin and A. Shashua.

Principal Component Analysis Over Continuous Subspaces and
Intersection of Half
-
spaces.

Proc. of the European Conference on Computer Vision

(ECCV), May 2002, Copenhagen, Denmark.