ICA 1.1a - Independent Component Analysis (21 min)
Channel: Prof. Laurenz Wiskott
Date: 26/01/2017

LECTURE 1 VIDEO 1 of the

Lecture Notes on Independent Component Analysis

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

Independent Component Analysis (ICA) works under the assumption that the data at hand is
a mixture of statistically independent signals.  These lectures cover the standard case,
where the mixture is linear and there are as many data components as there were signals,
although there exist extensions that go beyond that.  The goal of ICA is to recover the
original signals without knowing anything about the mixing process of the signals
themselves, and it can therefore be used for blind source separation.  There are many
different approaches to ICA.  I present here a method based on cumulants, which are a
form of statistical moments.

========================================================== LECTURE 1 [88 min]
---------------------------------------------------------------------- VIDEO 1 (21 min, https://youtu.be/3eWuUWODE4o)
1 Intuition
1.1 Mixing and unmixing
---------------------------------------------------------------------- VIDEO 2 (34 min, https://youtu.be/ugiMhRbFnTo)
1.1 Mixing and unmixing (continued)
1.2 How to find the unmixing matrix?
1.3 Sources can only be recovered up to permutation and rescaling
1.4 Whiten the data first
1.5 A generic ICA algorithm
---------------------------------------------------------------------- VIDEO 3 (29 min, https://youtu.be/o3eNcNmdldQ)
2 Formalism based on cumulants
2.1 Moments and cumulants
2.2 Cross-cumulants of statistically independent components are zero
2.3 Components with zero cross-cumulants are statistically independent
========================================================== LECTURE 2 [30 min]
---------------------------------------------------------------------- VIDEO 1 (20 min, https://youtu.be/sPzInwrpaWc)
2.4 Rotated cumulants
2.5 Contrast function
2.6 Givens-rotations
---------------------------------------------------------------------- VIDEO 2 (10 min, https://youtu.be/jniTIes-V-I)
2.7 Optimizing the contrast function
2.8 The algorithm
----------------------------------------------------------------------
==========================================================

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

Keywords: Machine Learning, Unsupervised Learning, Independent Component Analysis.