Unsupervised Learning of a Finite Mixture Model Based on the Dirichlet Distribution and Its Application

Finite mixture models have been used to model population heterogeneity and to relax distributional assumptions. These models are also convenient tools for clustering and classification of complex data such as, for example, repeated-measurements data. The performance of model-based clustering algorithms is sensitive to influential and outlying observations. Methods for identifying outliers in a finite mixture model have been described in the literature. Approaches to identify influential observations are less common. In this paper, we apply local-influence diagnostics to a finite mixture model with known number of components. The methodology is illustrated on real-life data.

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Image Segmentation Using a Trimmed Likelihood Estimator in the Asymmetric Mixture Model Based on Generalized Gamma and Gaussian Distributions

Mathematical Problems in Engineering ◽

10.1155/2018/3468967 ◽

2018 ◽

Vol 2018 ◽

pp. 1-17 ◽

Cited By ~ 2

Author(s):

Yi Zhou ◽

Hongqing Zhu

Keyword(s):

Image Segmentation ◽

Mixture Model ◽

Finite Mixture Model ◽

Finite Mixture ◽

Superior Performance ◽

Observation Data ◽

Likelihood Estimator ◽

Gaussian Distributions ◽

Model Based ◽

Generalized Gamma

Finite mixture model (FMM) is being increasingly used for unsupervised image segmentation. In this paper, a new finite mixture model based on a combination of generalized Gamma and Gaussian distributions using a trimmed likelihood estimator (GGMM-TLE) is proposed. GGMM-TLE combines the effectiveness of Gaussian distribution with the asymmetric capability of generalized Gamma distribution to provide superior flexibility for describing different shapes of observation data. Another advantage is that we consider the spatial information among neighbouring pixels by introducing Markov random field (MRF); thus, the proposed mixture model remains sufficiently robust with respect to different types and levels of noise. Moreover, this paper presents a new component-based confidence level ordering trimmed likelihood estimator, with a simple form, allowing GGMM-TLE to estimate the parameters after discarding the outliers. Thus, the proposed algorithm can effectively eliminate the disturbance of outliers. Furthermore, the paper proves the identifiability of the proposed mixture model in theory to guarantee that the parameter estimation procedures are well defined. Finally, an expectation maximization (EM) algorithm is included to estimate the parameters of GGMM-TLE by maximizing the log-likelihood function. Experiments on multiple public datasets demonstrate that GGMM-TLE achieves a superior performance compared with several existing methods in image segmentation tasks.

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Online quality prediction of nonlinear and non-Gaussian chemical processes with shifting dynamics using finite mixture model based Gaussian process regression approach

Chemical Engineering Science ◽

10.1016/j.ces.2012.07.018 ◽

2012 ◽

Vol 82 ◽

pp. 22-30 ◽

Cited By ~ 79

Author(s):

Jie Yu

Keyword(s):

Gaussian Process ◽

Mixture Model ◽

Gaussian Process Regression ◽

Finite Mixture Model ◽

Chemical Processes ◽

Finite Mixture ◽

Quality Prediction ◽

Model Based ◽

Regression Approach ◽

Non Gaussian

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