修正Gibbs采样的有限混合模型无监督学习算法

刘伟峰; 韩崇昭; 石勇

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修正Gibbs采样的有限混合模型无监督学习算法

更新时间：2025-12-08

- 修正Gibbs采样的有限混合模型无监督学习算法
- Unsupervised Learning for Finite Mixture Models Via Modified Gibbs Sampling
- 西安交通大学学报 2009年43卷第2期页码：15-19
- 作者机构：
  
  西安交通大学电子与信息工程学院,西安,710049
- 作者简介：
- 基金信息：
  
  : 2008-05-16. 作者简介: 刘伟峰(1973-),男,博士生;韩崇昭(联系人),男,教授,博士生导师. 基金项目: 国家自然科学基金资助项目(60574033,60602026);国家重点基础研究发展规划资助项目(2007CB311006)
- DOI：
  中图分类号： TP391
- 网络首发：2009-02-10，
  
  纸质出版：2009
- 稿件说明：
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刘伟峰, 韩崇昭, 石勇. 修正Gibbs采样的有限混合模型无监督学习算法[J]. 西安交通大学学报, 2009,43(2):15-19.

刘伟峰, 韩崇昭, 石勇. Unsupervised Learning for Finite Mixture Models Via Modified Gibbs Sampling[J]. 2009, 43(2): 15-19.
刘伟峰, 韩崇昭, 石勇. 修正Gibbs采样的有限混合模型无监督学习算法[J]. 西安交通大学学报, 2009,43(2):15-19. DOI：

刘伟峰, 韩崇昭, 石勇. Unsupervised Learning for Finite Mixture Models Via Modified Gibbs Sampling[J]. 2009, 43(2): 15-19. DOI：

摘要

针对传统有限混合模型无监督学习算法不能处理参数维数变化的问题

提出了一种基于修正Gibbs采样的无监督学习算法.该算法的关键是

在每一次完全采样之后引入分布元的合并和剔除技术

即将利用均值、协方差矩阵差值的2范数作为合并的判断准则

最小且小于阈值的分布元权重作为剔除规则.仿真实验表明

所提算法对于参数初值的选择是不敏感的

对于分布元个数的先验信息要求得更少

它不仅可以处理维数变化问题

而且不必计算跳变概率

同时能够很好地估计出分布元个数及其参数.

Abstract

Since the conventional algorithm can not deal with the variable parameter dimension in the unsupervised learning of finite mixture models(FMM)

an unsupervised learning algorithm based on the modified Gibbs sampling scheme is proposed. The key for the proposed algorithm is to adopt the component management techniques that include component combination and elimination after each complete iterative step. The 2-norm of the differences in the mean and covariance are used for the component combination rule

and the component elimination rule is that the component that has the least weight and is less than certain threshold will be discarded. Simulation results show that the proposed algorithm is robust for the parameter initialization and requires fewer prior information for the number of components. The proposed algorithm can deal with the variable dimension and avoid the calculation of the jump probability. Moreover

it can estimate the number of the components and parameters effectively.

关键词

Keywords

references

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CONSTANTINOPOULOS C, TITSIAS M K, BAYESIAN A L. Feature and model selection for Gaussian mixture models [J]. IEEE Trans Patt Anal Mach Intell, 2006, 28(6):1013-1018.

BOUGUILA N, ZIOU D. A hybrid Sem algorithm for high-dimensional unsupervised learning using a finite generalized dirichlet mixture [J]. IEEE Trans Image Processing, 2006, 15(9):2657-2668.

PEMKOPF F, BOUCHAFFRA D. Genetic based EM algorithm for learning Gaussian mixture models[J]. IEEE Trans Patt Anal Mach Intell, 2005, 27(8):1344-1348.

FIGUEIREDO M A T, JAIN A K. Unsupervised learning of finite mixture models [J]. IEEE TransPatt Anal Mach Intell, 2002, 24(3):381-396.

REDDY C K, CHIANG Hsiao-Dong, RAJARATNAM B. TRUST-TECH-based expectation maximization for learning finite mixture models[J]. IEEE Trans Patt Anal Mach Intell, 2008, 30(7):1146-1157.

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GREEN P J. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination [J]. Biomertrika, 1997, 82(4):711-732.

RICHARDSON S, GREEN P J. On Bayesian analysis of mixtures with an unkown number of components [J]. Journal of Royal Statistical Society: B, 1997, 59(4):731-792.

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