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Online discrimination of nonlinear dynamics with switching differential equations

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Bitzer,  Sebastian
Department Neurology, MPI for Human Cognitive and Brain Sciences, Max Planck Society;

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Yildiz,  Izzet Burak
Department Neurology, MPI for Human Cognitive and Brain Sciences, Max Planck Society;

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Kiebel,  Stefan J.
Department Neurology, MPI for Human Cognitive and Brain Sciences, Max Planck Society;

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Citation

Bitzer, S., Yildiz, I. B., & Kiebel, S. J. (2012). Online discrimination of nonlinear dynamics with switching differential equations. arXiv, 1211.0947.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0010-19FA-A
Abstract
How to recognise whether an observed person walks or runs? We consider a dynamic environment where observations (e.g. the posture of a person) are caused by different dynamic processes (walking or running) which are active one at a time and which may transition from one to another at any time. For this setup, switching dynamic models have been suggested previously, mostly, for linear and nonlinear dynamics in discrete time. Motivated by basic principles of computations in the brain (dynamic, internal models) we suggest a model for switching nonlinear differential equations. The switching process in the model is implemented by a Hopfield network and we use parametric dynamic movement primitives to represent arbitrary rhythmic motions. The model generates observed dynamics by linearly interpolating the primitives weighted by the switching variables and it is constructed such that standard filtering algorithms can be applied. In two experiments with synthetic planar motion and a human motion capture data set we show that inference with the unscented Kalman filter can successfully discriminate several dynamic processes online.