3.2 Principal Component Analysis (PCA) | 3 Dimensionality Reduction | Pattern Recognition Class 2012

The Pattern Recognition Class 2012 by Prof. Fred Hamprecht.
It took place at the HCI / University of Heidelberg during the summer term of 2012.
Website: http://hci.iwr.uni-heidelberg.de/MIP/...
Playlist with all videos: http://goo.gl/gmOI6

Contents of this recording:
00:01:10 - Principal Component Analysis (PCA)
00:06:52 - MNIST digits
00:22:50 - Rayleigh–Ritz method
00:37:00 - Laplace regression
00:51:42 - extensions of PCA
00:41:45 - Hebbian learning of PCA
00:52:38 - kernel PCA
00:53:06 - robust PCA
00:53:20 - sparse PCA
00:53:50 - probabilistic PCA
00:55:10 - Singular Value Decomposition (SVD)
01:39:48 - Eigenfaces


Syllabus:
1. Introduction
1.1 Applications of Pattern Recognition
1.2 k-Nearest Neighbors Classification
1.3 Probability Theory
1.4 Statistical Decision Theory

2. Correlation Measures, Gaussian Models
2.1 Pearson Correlation
2.2 Alternative Correlation Measures
2.3 Gaussian Graphical Models
2.4 Discriminant Analysis

3. Dimensionality Reduction
3.1 Regularized LDA/QDA
3.2 Principal Component Analysis (PCA)
3.3 Bilinear Decompositions

4. Neural Networks
4.1 History of Neural Networks
4.2 Perceptrons
4.3 Multilayer Perceptrons
4.4 The Projection Trick
4.5 Radial Basis Function Networks

5. Support Vector Machines
5.1 Loss Functions
5.2 Linear Soft-Margin SVM
5.3 Nonlinear SVM

6. Kernels, Random Forest
6.1 Kernels
6.2 One-Class SVM
6.3 Random Forest
6.4 Random Forest Feature Importance

7. Regression
7.1 Least-Squares Regression
7.2 Optimum Experimental Design
7.3 Case Study: Functional MRI
7.4 Case Study: Computer Tomography
7.5 Regularized Regression

8. Gaussian Processes
8.1 Gaussian Process Regression
8.2 GP Regression: Interpretation
8.3 Gaussian Stochastic Processes
8.4 Covariance Function

9. Unsupervised Learning
9.1 Kernel Density Estimation
9.2 Cluster Analysis
9.3 Expectation Maximization
9.4 Gaussian Mixture Models

10. Directed Graphical Models
10.1 Bayesian Networks
10.2 Variable Elimination
10.3 Message Passing
10.4 State Space Models

11. Optimization
11.1 The Lagrangian Method
11.2 Constraint Qualifications
11.3 Linear Programming
11.4 The Simplex Algorithm

12. Structured Learning
12.1 structSVM
12.2 Cutting Planes

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