NDLI: A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates

Content Provider	Springer Nature Link
Author	Pulkkinen, Seppo Mäkelä, Marko Mikael Karmitsa, Napsu
Copyright Year	2011
Abstract	Gaussian mixtures (i.e. linear combinations of multivariate Gaussian probability densities) appear in numerous applications due to their universal ability to approximate multimodal probability distributions. Finding the modes (maxima) of a Gaussian mixture is a fundamental problem arising in many practical applications such as machine learning and digital image processing. In this paper, we propose a computationally efficient method for finding a significant mode of the Gaussian mixture. Such a mode represents an area of large probability, and it often coincides with the global mode of the mixture. The proposed method uses a Gaussian convolution in order to remove undesired local maxima of the Gaussian mixture and preserve its underlying structure. The transformation between the maximizers of the smoothed Gaussian mixture and the original one is formulated as a differential equation. A robust trust region method for tracing the solution curve of this differential equation is described. Our formulation also allows mixtures with negative weights or even negative values, which occur in some applications related to machine learning or quantum mechanics. The applicability of the method to mode-finding of Gaussian kernel density estimates obtained from experimental data is illustrated. Finally, some numerical results are given to demonstrate the ability of the method to find significant modes of Gaussian mixtures and kernel density estimates.
Starting Page	459
Ending Page	487
Page Count	29
File Format	PDF
ISSN	09255001
Journal	Journal of Global Optimization
Volume Number	56
Issue Number	2
e-ISSN	15732916
Language	English
Publisher	Springer US
Publisher Date	2011-12-28
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mode-finding Gaussian mixture Convolution Continuation Trust region Predictor-corrector Kernel density estimation Operations Research/Decision Theory Computer Science Real Functions Optimization
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics Management Science and Operations Research Business, Management and Accounting Computer Science Applications

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