scholarly journals Kernel Analysis Based on Dirichlet Processes Mixture Models

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 857
Author(s):  
Jinkai Tian ◽  
Peifeng Yan ◽  
Da Huang
Keyword(s):  
Mixture Models ◽  
Crucial Role ◽  
Gaussian Mixture Models ◽  
Gaussian Process Regression ◽  
Gaussian Mixture ◽  
Spectral Domain ◽  
Dirichlet Processes ◽  
Number Of Components ◽  
Kernel Analysis ◽  
Nonparametric Bayesian Models

Kernels play a crucial role in Gaussian process regression. Analyzing kernels from their spectral domain has attracted extensive attention in recent years. Gaussian mixture models (GMM) are used to model the spectrum of kernels. However, the number of components in a GMM is fixed. Thus, this model suffers from overfitting or underfitting. In this paper, we try to combine the spectral domain of kernels with nonparametric Bayesian models. Dirichlet processes mixture models are used to resolve this problem by changing the number of components according to the data size. Multiple experiments have been conducted on this model and it shows competitive performance.

Estimating the number of components in Gaussian mixture models adaptively for medical image

Optik ◽  
2013 ◽  
Vol 124 (23) ◽  
pp. 6216-6221 ◽  
Author(s):  
Cong-Hua Xie ◽  
Jin-Yi Chang ◽  
Yong-Jun Liu
Keyword(s):  
Mixture Models ◽  
Medical Image ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Number Of Components

scholarly journals Identifying the number of components in Gaussian mixture models using numerical algebraic geometry

2019 ◽  
Vol 19 (11) ◽  
pp. 2050204
Author(s):  
Sara Shirinkam ◽  
Adel Alaeddini ◽  
Elizabeth Gross
Keyword(s):  
Algebraic Geometry ◽  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Information Criterion ◽  
Gaussian Mixture ◽  
Smoothing Spline ◽  
Numerical Algebraic Geometry ◽  
Automotive Manufacturing ◽  
Local Maxima ◽  
Number Of Components

Using Gaussian mixture models for clustering is a statistically mature method for clustering in data science with numerous successful applications in science and engineering. The parameters for a Gaussian mixture model (GMM) are typically estimated from training data using the iterative expectation-maximization algorithm, which requires the number of Gaussian components a priori. In this study, we propose two algorithms rooted in numerical algebraic geometry (NAG), namely, an area-based algorithm and a local maxima algorithm, to identify the optimal number of components. The area-based algorithm transforms several GMM with varying number of components into sets of equivalent polynomial regression splines. Next, it uses homotopy continuation methods for evaluating the resulting splines to identify the number of components that is most compatible with the gradient data. The local maxima algorithm forms a set of polynomials by fitting a smoothing spline to a dataset. Next, it uses NAG to solve the system of the first derivatives for finding the local maxima of the resulting smoothing spline, which represent the number of mixture components. The local maxima algorithm also identifies the location of the centers of Gaussian components. Using a real-world case study in automotive manufacturing and extensive simulations, we demonstrate that the performance of the proposed algorithms is comparable with that of Akaike information criterion (AIC) and Bayesian information criterion (BIC), which are popular methods in the literature. We also show the proposed algorithms are more robust than AIC and BIC when the Gaussian assumption is violated.

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
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