How slow is slow? SFA detects signals that are slower than the driving force

Publication: Wolfgang Konen, Patrick Koch, How slow is slow? SFA detects signals that are slower than the driving force, In: B. Filipic, J. Silc (eds.), Proc. 4th Int. Conf. on Bioinspired Optimization Methods and their Applications, BIOMA 2010, May 2010, Ljubljana, Slovenia (PDF)

Abstract:

Slow feature analysis (SFA) is a bioinspired method for extracting slowly
varying driving forces from quickly varying nonstationary 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 in
uence 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.