A Gaussian Mixture Model Based Cost Function for Parameter
Estimation of CHaotic Biological Systems
Yasser Shekofteha,b, Sajad Jafaria, Julien Clinton Sprottc, S.
Mohammad Reza Hashemi Golpayegania, Farshad Almasganja
aBiomedical Engineering Department, Amirkabir
University of Technology, Tehran 15875-4413, Iran
bResearch Center of Intelligent Signal
Processing (RCISP), Tehran, Iran
cPhysics Department, University of Wisconsin, 1150
University Ave., Madison, WI 53706, USA
Received 21 November 2012, Received in revised form 21 November
2013, Accepted 24 May 2014, Available online 6 June 2014
As we know, many biological systems such as neurons or the heart can
exhibit chaotic behavior. Conventional methods for parameter
estimation in models of these systems have some limitations caused
by sensitivity to initial conditions. In this paper, a novel cost
function is proposed to overcome those limitations by building a
statistical model on the distribution of the real system attractor
in state space. This cost function is defined by the use of a
likelihood score in a Gaussian mixture model (GMM) which is fitted
to the observed attractor generated by the real system. Using that
learned GMM, a similarity score can be defined by the computed
likelihood score of the model time series. We have applied the
proposed method to the parameter estimation of two important
biological systems, a neuron and a cardiac pacemaker, which show
chaotic behavior. Some simulated experiments are given to verify the
usefulness of the proposed approach in clean and noisy conditions.
The results show the adequacy of the proposed cost function.
Ref: Y. Shekofteh, S. Jafari, J. C. Sprott,
S. M. R. H. Golpayegani, and F. Almasganj, Commun. Nonlinear Sci.
Numer. Simulat. 20, 469-481 (2015)
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