Title: The slowness principle: SFA can detect different slow components in non-stationary time series

Authors: Wolfgang Konen, Patrick Koch

Addresses: Institute for Informatics, Cologne University of Applied Sciences, Steinmullerallee 1, D-51643 Gummersbach, Germany. ' Institute for Informatics, Cologne University of Applied Sciences, Steinmullerallee 1, D-51643 Gummersbach, Germany

Abstract: Slow feature analysis (SFA) is a bioinspired method for extracting slowly varying driving forces from quickly varying non-stationary time series. We show here that it is possible for SFA to detect a component which is even slower than the driving force itself (e.g., the envelope of a modulated sine wave). It depends on circumstances like the embedding dimension, the time series predictability, or the base frequency, whether the driving force itself or a slower subcomponent is detected. Interestingly, we observe a swift phase transition from one regime to another and it is the objective of this work to quantify the influence of various parameters on this phase transition. We conclude that what is perceived as slow by SFA varies and that a more or less fast switching from one regime to another occurs, perhaps showing some similarity to human perception.

Keywords: driving forces; driving force detection; human perception; logistic map; nonlinear regression; non-stationary time series; phase transition; slow feature analysis; SFA; slowness principle; unsupervised learning; bioinspired optimisation.

DOI: 10.1504/IJICA.2011.037946

International Journal of Innovative Computing and Applications, 2011 Vol.3 No.1, pp.3 - 10

Published online: 21 Mar 2015 *

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