Data Analysis and Manifold Learning (DAML) Lecture series by Radu HORAUD, INRIA Grenoble RhoneAlpes WinterSpring 2011 Short course description (pdf)

This is a 3D shape that is represented by an undirected weighted graph whose vertices correspond to 3D points and whose edges correspond to the local topology of the shape. Each graph vertex is projected onto the first nonnull eigenvector of the graph's Laplacian matrix. This eigenvector may be viewed as the intrinsic principal direction of the shape, invariant to such shape deformations as articulated motion. 
Brief course description 
Time and date 
Location 
Material 
Lecture #1: Introduction to spectral and graphbased methods  14h16h 7/1/2011 (Friday)  UFRIMA Grenoble: F113 
HoraudDAML1.pdf 
Lecture #2: Symmetric matrices and their properties  14h16h 14/1/2011 (Friday)  UFRIMA Grenoble: F113 
HoraudDAML2.pdf 
Lecture #3: Graphs, graph matrices, and spectral embeddings of graphs  14h16h 21/1/2011 (Friday)  UFRIMA Grenoble: F107 
HoraudDAML3.pdf 
Lecture #4: Gaussian mixtures and the EM algorithm  14h16h 4/2/2011 (Friday)  UFRIMA Grenoble: F116 
HoraudDAML4.pdf 
Lecture #5: Principal component analysis  14h16h 11/2/2011 (Friday)  UFRIMA Grenoble: F114 
HoraudDAML5.pdf 
Lecture #6: Bayesian PCA and factor analysis  14h16h 18/2/2011 (Friday)  UFRIMA Grenoble: F114 
HoraudDAML6.pdf 
Lecture #7: Laplacian embedding and spectral clustering  14h16h 25/2/2011 (Friday)  UFRIMA Grenoble: F114 
HoraudDAML7.pdf 
Lecture #8: Introduction to kernel methods, kernel PCA  14h16h 18/3/2011 (Friday)  UFRIMA Grenoble: F114 
HoraudDAML8.pdf 
Lecture #9: Diffusion kernels  14h16h 25/3/2011 (Friday)  UFRIMA Grenoble: F114 
HoraudDAML9.pdf 
Lecture #10: Spectral matching  14h16h 8/4/2011 (Friday)  UFRIMA Grenoble: F113 
HoraudDAML10.pdf 
Lecture #11: Other methods: LLE and LTSA  14h16h 22/4/2011 (Friday)  UFRIMA Grenoble: F113 
HoraudDAML11.pdf 
Lecture #12: Manifold learning applications  14h16h 13/5/2011 (Friday)  UFRIMA Grenoble: F114 
HoraudDAML12.pdf 
Brief overview of spectral and graphbased methods, such as principal component analysis (PCA), multi dimensional scaling (MDS), ISOMAP, LLE, Laplacian embedding, etc.
Further readings: L. Saul et al. Spectral Methods for Dimensionality Reduction. O. Chapelle, B. Schoelkopf, and A. Zien (eds.), Semisupervised Learning, pages 293308. MIT Press: Cambridge, MA.
Eigenvalues and eigenvectors. Practical computation for dense ans sparse matrices. Covariance matrix. Gram matrix.
What is the matrix of a graph? Properties of graph matrices. Spectral graph theory. Undirected weighted graphs and Markov chains. Graph distances. Graph construction.
The univariate and multivariate Gaussian distributions. The Gaussian mixture model. The expectactionmaximization algorithm for Gaussian mixtures. The curse of dimensionality.
Formal derivation. Linear discriminant analysis.
EM algorithm for PPCA. Bayesian PCA and model selection. Factor analysis.
Spectral clustering. Semisupervised spectral clustering. Links with other methods: Normalized cuts and random walks on graphs. Image and shape segmentation
Properties of kernels. Kernel PCA.
Heat diffusion on Riemannian manifolds. Heat diffusion on graphs. Diffusion embedding. Scalespace representation. Choosing the dimension of the embedded space.
Dense and sparse matching methods. Semisupervised matching.
A list of (short) papers related to manifold learning:
Medical image analysis, brain imagery, auditory perception, data mining, Google's PageRank algorithm, etc.