Mixture Model

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Hui Zhang - One of the best experts on this subject based on the ideXlab platform.

  • synthetic aperture radar image segmentation by modified student s t Mixture Model
    IEEE Transactions on Geoscience and Remote Sensing, 2014
    Co-Authors: Hui Zhang, Thanh Minh Nguyen, Xingming Sun
    Abstract:

    Synthetic aperture radar (SAR) data are often affected by speckle noise, which originates in the SAR system's coherent nature. In this paper, we introduce a simple and effective algorithm to make the traditional Student's t-Mixture Model (SMM) more robust to noise. The proposed new modified SMM (MSMM) is applied for SAR image segmentation. SMM has come to be regarded as an alternative to the Gaussian Mixture Model (GMM) as it is heavy tailed and more robust to outliers. However, a major shortcoming of this method is that it does not take into account the spatial dependencies in the image. Although some existing methods incorporate the spatial relationship between neighboring pixels, they are still not robust enough to noise. The advantages of our method are as follows. First, we introduce MSMM to incorporate the local spatial information and pixel intensity value by considering the conditional probability of an image pixel influenced by the probabilities of pixels in its immediate neighborhood. Furthermore, we introduce the additional parameter α to control the extent of this influence. The larger α indicates the heavier extent of influence in the neighborhoods. Second, the prior probability of an image pixel is influenced by the probabilities of pixels in its immediate neighborhood, which incorporates local spatial and component information. Third, our Model is based on the finite Mixture Model (FMM); it is simple and easy to implement, and the expectation maximization algorithm can be applied for estimation of optimal parameters. Finally, the traditional SMM can be considered as a special case of our Model. Thus, our method is general enough for FMM-based techniques. Experimental results on both simulated and real SAR images demonstrate the improved robustness and effectiveness of our approach.

  • Bounded generalized Gaussian Mixture Model
    Pattern Recognition, 2014
    Co-Authors: Thanh Minh Nguyen, Hui Zhang
    Abstract:

    Abstract The generalized Gaussian Mixture Model (GGMM) provides a flexible and suitable tool for many computer vision and pattern recognition problems. However, generalized Gaussian distribution is unbounded. In many applications, the observed data are digitalized and have bounded support. A new bounded generalized Gaussian Mixture Model (BGGMM), which includes the Gaussian Mixture Model (GMM), Laplace Mixture Model (LMM), and GGMM as special cases, is presented in this paper. We propose an extension of the generalized Gaussian distribution in this paper. This new distribution has a flexibility to fit different shapes of observed data such as non-Gaussian and bounded support data. In order to estimate the Model parameters, we propose an alternate approach to minimize the higher bound on the data negative log-likelihood function. We quantify the performance of the BGGMM with simulations and real data.

  • a finite Mixture Model for detail preserving image segmentation
    Signal Processing, 2013
    Co-Authors: Thanh Minh Nguyen, Hui Zhang, Dibyendu Mukherjee
    Abstract:

    We present a new finite Mixture Model for image segmentation. Firstly, in order to take into account the spatial dependencies in an image, existing Mixture Models use a constant temperature parameter (@b) throughout the image for every label. The constant value of @b reduces the impact of noise in homogeneous regions but negatively affects segmentation along the border of two regions. We propose a new way to use a different value of @b throughout the image. Secondly, in order to incorporate the correlation between each center pixel and its neighboring pixels, the existing Mixture Model gives the same importance to all pixels in a neighborhood window. We assign different weights to different pixels appearing in the window, which is based on the fact that the clique strength should be reduced with distance. Thirdly, our Model is based on the Student's-t distribution, which is heavily tailed and more robust than the Gaussian. We exploit the Dirichlet distribution and Dirichlet law to incorporate the spatial relationships between pixels in an image. Finally, the expectation maximization (EM) algorithm is adopted to maximize the data log-likelihood and to optimize the parameters. The performance is compared to other existing Models based on the Model-based techniques, demonstrating the superiority of the proposed Model for image segmentation.

Thanh Minh Nguyen - One of the best experts on this subject based on the ideXlab platform.

  • synthetic aperture radar image segmentation by modified student s t Mixture Model
    IEEE Transactions on Geoscience and Remote Sensing, 2014
    Co-Authors: Hui Zhang, Thanh Minh Nguyen, Xingming Sun
    Abstract:

    Synthetic aperture radar (SAR) data are often affected by speckle noise, which originates in the SAR system's coherent nature. In this paper, we introduce a simple and effective algorithm to make the traditional Student's t-Mixture Model (SMM) more robust to noise. The proposed new modified SMM (MSMM) is applied for SAR image segmentation. SMM has come to be regarded as an alternative to the Gaussian Mixture Model (GMM) as it is heavy tailed and more robust to outliers. However, a major shortcoming of this method is that it does not take into account the spatial dependencies in the image. Although some existing methods incorporate the spatial relationship between neighboring pixels, they are still not robust enough to noise. The advantages of our method are as follows. First, we introduce MSMM to incorporate the local spatial information and pixel intensity value by considering the conditional probability of an image pixel influenced by the probabilities of pixels in its immediate neighborhood. Furthermore, we introduce the additional parameter α to control the extent of this influence. The larger α indicates the heavier extent of influence in the neighborhoods. Second, the prior probability of an image pixel is influenced by the probabilities of pixels in its immediate neighborhood, which incorporates local spatial and component information. Third, our Model is based on the finite Mixture Model (FMM); it is simple and easy to implement, and the expectation maximization algorithm can be applied for estimation of optimal parameters. Finally, the traditional SMM can be considered as a special case of our Model. Thus, our method is general enough for FMM-based techniques. Experimental results on both simulated and real SAR images demonstrate the improved robustness and effectiveness of our approach.

  • Bounded generalized Gaussian Mixture Model
    Pattern Recognition, 2014
    Co-Authors: Thanh Minh Nguyen, Hui Zhang
    Abstract:

    Abstract The generalized Gaussian Mixture Model (GGMM) provides a flexible and suitable tool for many computer vision and pattern recognition problems. However, generalized Gaussian distribution is unbounded. In many applications, the observed data are digitalized and have bounded support. A new bounded generalized Gaussian Mixture Model (BGGMM), which includes the Gaussian Mixture Model (GMM), Laplace Mixture Model (LMM), and GGMM as special cases, is presented in this paper. We propose an extension of the generalized Gaussian distribution in this paper. This new distribution has a flexibility to fit different shapes of observed data such as non-Gaussian and bounded support data. In order to estimate the Model parameters, we propose an alternate approach to minimize the higher bound on the data negative log-likelihood function. We quantify the performance of the BGGMM with simulations and real data.

  • a finite Mixture Model for detail preserving image segmentation
    Signal Processing, 2013
    Co-Authors: Thanh Minh Nguyen, Hui Zhang, Dibyendu Mukherjee
    Abstract:

    We present a new finite Mixture Model for image segmentation. Firstly, in order to take into account the spatial dependencies in an image, existing Mixture Models use a constant temperature parameter (@b) throughout the image for every label. The constant value of @b reduces the impact of noise in homogeneous regions but negatively affects segmentation along the border of two regions. We propose a new way to use a different value of @b throughout the image. Secondly, in order to incorporate the correlation between each center pixel and its neighboring pixels, the existing Mixture Model gives the same importance to all pixels in a neighborhood window. We assign different weights to different pixels appearing in the window, which is based on the fact that the clique strength should be reduced with distance. Thirdly, our Model is based on the Student's-t distribution, which is heavily tailed and more robust than the Gaussian. We exploit the Dirichlet distribution and Dirichlet law to incorporate the spatial relationships between pixels in an image. Finally, the expectation maximization (EM) algorithm is adopted to maximize the data log-likelihood and to optimize the parameters. The performance is compared to other existing Models based on the Model-based techniques, demonstrating the superiority of the proposed Model for image segmentation.

  • fast and robust spatially constrained gaussian Mixture Model for image segmentation
    IEEE Transactions on Circuits and Systems for Video Technology, 2013
    Co-Authors: Thanh Minh Nguyen
    Abstract:

    In this paper, a new Mixture Model for image segmentation is presented. We propose a new way to incorporate spatial information between neighboring pixels into the Gaussian Mixture Model based on Markov random field (MRF). In comparison to other Mixture Models that are complex and computationally expensive, the proposed method is fast and easy to implement. In Mixture Models based on MRF, the M-step of the expectation-maximization (EM) algorithm cannot be directly applied to the prior distribution ${\pi_{ij}}$ for maximization of the log-likelihood with respect to the corresponding parameters. Compared with these Models, our proposed method directly applies the EM algorithm to optimize the parameters, which makes it much simpler. Experimental results obtained by employing the proposed method on many synthetic and real-world grayscale and colored images demonstrate its robustness, accuracy, and effectiveness, compared with other Mixture Models.

Yin Shen - One of the best experts on this subject based on the ideXlab platform.

  • same clustering single cell aggregated clustering via Mixture Model ensemble
    Nucleic Acids Research, 2020
    Co-Authors: Yuchen Yang, Yuchao Jiang, Yin Shen, Yun Li
    Abstract:

    : Clustering is an essential step in the analysis of single cell RNA-seq (scRNA-seq) data to shed light on tissue complexity including the number of cell types and transcriptomic signatures of each cell type. Due to its importance, novel methods have been developed recently for this purpose. However, different approaches generate varying estimates regarding the number of clusters and the single-cell level cluster assignments. This type of unsupervised clustering is challenging and it is often times hard to gauge which method to use because none of the existing methods outperform others across all scenarios. We present SAME-clustering, a Mixture Model-based approach that takes clustering solutions from multiple methods and selects a maximally diverse subset to produce an improved ensemble solution. We tested SAME-clustering across 15 scRNA-seq datasets generated by different platforms, with number of clusters varying from 3 to 15, and number of single cells from 49 to 32 695. Results show that our SAME-clustering ensemble method yields enhanced clustering, in terms of both cluster assignments and number of clusters. The Mixture Model ensemble clustering is not limited to clustering scRNA-seq data and may be useful to a wide range of clustering applications.

  • same clustering single cell aggregated clustering via Mixture Model ensemble
    Nucleic Acids Research, 2020
    Co-Authors: Ruth Huh, Yuchen Yang, Yuchao Jiang, Yin Shen
    Abstract:

    Clustering is an essential step in the analysis of single cell RNA-seq (scRNA-seq) data to shed light on tissue complexity including the number of cell types and transcriptomic signatures of each cell type. Due to its importance, novel methods have been developed recently for this purpose. However, different approaches generate varying estimates regarding the number of clusters and the single-cell level cluster assignments. This type of unsupervised clustering is challenging and it is often times hard to gauge which method to use because none of the existing methods outperform others across all scenarios. We present SAME-clustering, a Mixture Model-based approach that takes clustering solutions from multiple methods and selects a maximally diverse subset to produce an improved ensemble solution. We tested SAME-clustering across 15 scRNA-seq datasets generated by different platforms, with number of clusters varying from 3 to 15, and number of single cells from 49 to 32 695. Results show that our SAME-clustering ensemble method yields enhanced clustering, in terms of both cluster assignments and number of clusters. The Mixture Model ensemble clustering is not limited to clustering scRNA-seq data and may be useful to a wide range of clustering applications.

Juan Shen - One of the best experts on this subject based on the ideXlab platform.

  • inference for subgroup analysis with a structured logistic normal Mixture Model
    Journal of the American Statistical Association, 2015
    Co-Authors: Juan Shen
    Abstract:

    In this article, we propose a statistical Model for the purpose of identifying a subgroup that has an enhanced treatment effect as well as the variables that are predictive of the subgroup membership. The need for such subgroup identification arises in clinical trials and in market segmentation analysis. By using a structured logistic-normal Mixture Model, our proposed framework enables us to perform a confirmatory statistical test for the existence of subgroups, and at the same time, to construct predictive scores for the subgroup membership. The inferential procedure proposed in the article is built on the recent literature on hypothesis testing for Gaussian Mixtures, but the structured logistic-normal Mixture Model enjoys some distinctive properties that are unavailable to the simpler Gaussian Mixture Models. With the bootstrap approximations, the proposed tests are shown to be powerful and, equally importantly, insensitive to the choice of tuning parameters. As an illustration, we analyze a dataset fr...

  • inference for subgroup analysis with a structured logistic normal Mixture Model
    Journal of the American Statistical Association, 2015
    Co-Authors: Juan Shen, Xuming He
    Abstract:

    In this article, we propose a statistical Model for the purpose of identifying a subgroup that has an enhanced treatment effect as well as the variables that are predictive of the subgroup membership. The need for such subgroup identification arises in clinical trials and in market segmentation analysis. By using a structured logistic-normal Mixture Model, our proposed framework enables us to perform a confirmatory statistical test for the existence of subgroups, and at the same time, to construct predictive scores for the subgroup membership. The inferential procedure proposed in the article is built on the recent literature on hypothesis testing for Gaussian Mixtures, but the structured logistic-normal Mixture Model enjoys some distinctive properties that are unavailable to the simpler Gaussian Mixture Models. With the bootstrap approximations, the proposed tests are shown to be powerful and, equally importantly, insensitive to the choice of tuning parameters. As an illustration, we analyze a dataset from the AIDS Clinical Trials Group 320 study and show how the proposed methodology can help detect a potential subgroup of AIDS patients who may react much more favorably to the addition of a protease inhibitor to a conventional regimen than other patients.

T Mukai - One of the best experts on this subject based on the ideXlab platform.

  • application of multivariate maxwellian Mixture Model to plasma velocity distribution function
    Journal of Geophysical Research, 2001
    Co-Authors: Genta Ueno, Takashi Tsuchiya, S Machida, Tohru Araki, Nagatomo Nakamura, Tomoyuki Higuchi, Yoshifumi Saito, T Mukai
    Abstract:

    Recent space plasma observations have provided us with three-dimensional velocity distributions having multiple peaks. We propose a method for analyzing such velocity distributions via a multivariate Maxwellian Mixture Model where each component of the Model represents each of the multiple peaks. The parameters of the Model are determined through an iterative nonlinear optimization technique, specifically the expectation-maximization (EM) algorithm. For the automatic judgment of the preferable number of components in the Mixture Model, we introduce a method of examining the number of extrema of a resulting Mixture Model. We show applications of our method to ion observations in the plasma sheet boundary layer (PSBL) and in the central plasma sheet (CPS) of the Earth's magnetotail. From an analysis of the PSBL and CPS, low-energy ions that have properties similar to those of lobe ions were detected also in the PSBL and CPS. In the PSBL, middle-energy ion component which is flowing dawnward and directed the neutral sheet was extracted. We suggested that magnetic field fluctuations in the PSBL can be explained only when the two ion components were properly treated.