Principal Component Analysis - In a nutshell (18 min)
Channel: Prof. Laurenz Wiskott
Date: 29/01/2017

Principal Component Analysis - In a nutshell (18 min)


LECTURE 1 VIDEO 1 of the

Lecture Notes on Principal Component Analysis

Prof. Laurenz Wiskott
Institut für Neuroinformatik
Ruhr-Universität Bochum, Germany, EU

==================================================================== LECTURE 1 [21 min]
---------------------------------------------------------------------- VIDEO 1 (21 min, on YouTube https://youtu.be/9H-1FH1gn6w)
In a nutshell
---------------------------------------------------------------------- VIDEOS (not done yet)
1 Intuition
1.1 Problem statement
1.2 Projection and reconstruction error
1.3 Reconstruction error and variance
1.4 Covariance matrix
1.5 Covariance matrix and higher order structure
1.6 PCA by diagonalizing the covariance matrix
----------------------------------------------------------------------
==================================================================== LECTURE 2 [] (not done yet)
2 Formalism
2.1 Definition of the PCA-optimization problem
2.2 Matrix V^T: Mapping from high-dimensional old coordinate system to low-dimensional new coordinate system
2.3 Matrix V: Mapping from low-dimensional new coordinate system to subspace in old coordinate system
2.4 Matrix (V^T V): Identity mapping within new coordinate system8
2.5 Matrix (V V^T): Projection from high- to low-dimensional (sub)space within old coordinate system
2.6 Variance
2.7 Reconstruction error
2.8 Covariance matrix
2.9 Eigenvalue equation of the covariance matrix
2.10 Total variance of the data x
2.11 Diagonalizing the covariance matrix
==================================================================== LECTURE 3 [] (not done yet)
2.12 Variance of y for a diagonalized covariance matrix
2.13 Constraints of matrix V
2.14 Finding the optimal subspace
2.15 Interpretation of the result
2.16 PCA Algorithm
2.17 Intuition of the Results
2.18 Whitening or sphering
2.19 Singular value decomposition +
3 Application
3.1 Face processing
====================================================================

More material is available at
https://www.ini.rub.de/PEOPLE/wiskott/Teaching/Material/index.html

#MachineLearning #UnsupervisedLearning #PrincipalComponentAnalysis #PCA