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On the relation between slow feature analysis and independent component analysis
Tobias Blaschke
Pietro Berkes

At a first glance Slow Feature Analsysis (SFA) and Independent Component Analysis (ICA) optimize very different objectives. SFA is a nonlinear method that extracts uncorrelated slowly-varying features; ICA is a linear method that extracts statistically independent components, often based on higher-order moments and ignoring any time structure of the signals. Slowness and statistical independence are even conflicting objectives, because two slowly varying signals are more likely to be statistically dependent than quickly varying ones.

However, if one considers linear SFA and ICA based on second-order moments, one can actually relate the two algorithms quite nicely. In fact, linear SFA and second-order ICA based on correlation matrices with a time delay of one time step are equivalent to each other. This is an analytical result that provides and interesting link between two very different principles. It also provides the basis for an integration of ICA and SFA leading to an algorithm for performing nonlinear blind-source-separation, see project Independent Slow Feature Analysis and Nonlinear Blind Source Separation.

The Institut für Neuroinformatik (INI) is a central research unit of the Ruhr-Universität Bochum. We aim to understand the fundamental principles through which organisms generate behavior and cognition while linked to their environments through sensory systems and while acting in those environments through effector systems. Inspired by our insights into such natural cognitive systems, we seek new solutions to problems of information processing in artificial cognitive systems. We draw from a variety of disciplines that include experimental approaches from psychology and neurophysiology as well as theoretical approaches from physics, mathematics, electrical engineering and applied computer science, in particular machine learning, artificial intelligence, and computer vision.

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