scholarly journals BM: An iterative algorithm to learn stable non-linear dynamical systems with Gaussian mixture models

2010 ◽  
Author(s):  
S Mohammad Khansari-Zadeh ◽  
Aude Billard
Keyword(s):  
Dynamical Systems ◽  
Mixture Models ◽  
Iterative Algorithm ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Linear Dynamical Systems ◽  
Non Linear

A robust non-rigid point set registration method based on inhomogeneous Gaussian mixture models

2017 ◽  
Vol 34 (10) ◽  
pp. 1399-1414 ◽  
Author(s):  
Wanxia Deng ◽  
Huanxin Zou ◽  
Fang Guo ◽  
Lin Lei ◽  
Shilin Zhou ◽  
...  
Keyword(s):  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Registration Method ◽  
Point Set Registration ◽  
Point Set

scholarly journals Data Assimilation with Gaussian Mixture Models Using the Dynamically Orthogonal Field Equations. Part I: Theory and Scheme

2013 ◽  
Vol 141 (6) ◽  
pp. 1737-1760 ◽  
Author(s):  
Thomas Sondergaard ◽  
Pierre F. J. Lermusiaux
Keyword(s):  
Data Assimilation ◽  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Expectation Maximization Algorithm ◽  
Planck Equation ◽  
Information Criterion ◽  
Gaussian Mixture ◽  
Field Equations ◽  
Dynamical Equations ◽  
Prior Probabilities

Abstract This work introduces and derives an efficient, data-driven assimilation scheme, focused on a time-dependent stochastic subspace that respects nonlinear dynamics and captures non-Gaussian statistics as it occurs. The motivation is to obtain a filter that is applicable to realistic geophysical applications, but that also rigorously utilizes the governing dynamical equations with information theory and learning theory for efficient Bayesian data assimilation. Building on the foundations of classical filters, the underlying theory and algorithmic implementation of the new filter are developed and derived. The stochastic Dynamically Orthogonal (DO) field equations and their adaptive stochastic subspace are employed to predict prior probabilities for the full dynamical state, effectively approximating the Fokker–Planck equation. At assimilation times, the DO realizations are fit to semiparametric Gaussian Mixture Models (GMMs) using the Expectation-Maximization algorithm and the Bayesian Information Criterion. Bayes’s law is then efficiently carried out analytically within the evolving stochastic subspace. The resulting GMM-DO filter is illustrated in a very simple example. Variations of the GMM-DO filter are also provided along with comparisons with related schemes.

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