Jung, Andreas and Kaiser, Andreas (2003) Considering temporal structures in Independent Component Analysis. ICA 2003 Proceedings.
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In this work we show how temporal structures in time series can be used in the framework of independent component analysis assuming the signals arise from Markov chains with finite order. Taking into account the past of the underlying processes, by using time embedding vectors, not only instantaneous independent but also uncoupled sources can be found. As a result signals which are gaussian distributed at each time can be decomposed as long as the time embedding vectors are non-gaussian. Using the model of independent time embedding vectors, we derive an algorithm (FastTeICA) which is similar to the well known FastICA algorithm introduced by Hyv¨rinen (1999). A weakening of the strict assumption of independent embedding vectors which still takes into account the dynamics of the processes for signal decomposition can be achieved by assuming independent increments, i.e. the change of state of the processes. Both approaches, independent states and independent dynamics, are a special case of the independence of the time embedding vectors.
|Institutions:||Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter|
|Projects:||Graduiertenkolleg Nichtlinearität und Nichtgleichgewicht|
|Subjects:||500 Science > 530 Physics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Deposited On:||20 Mar 2007|
|Last Modified:||20 Jul 2011 20:58|