A hybrid SEM algorithm for high-dimensional unsupervised learning using a finite generalized dirichlet mixture
A hybrid SEM algorithm for high-dimensional unsupervised learning using a finite generalized dirichlet mixture
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DOI：
10.1109/tip.2006.877379
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发表时间：
2006-09-01
影响因子：
10.6
通讯作者：
Ziou, Djemel
中科院分区：
文献类型：
--
作者：
Bouguila, Nizar;Ziou, Djemel
本文将鲁棒统计方案应用于高维数据的无监督学习问题。我们开发、分析和应用基于狄利克雷分布推广的新有限混合模型。广义狄利克雷分布具有比狄利克雷分布更一般的协方差结构，并且为对称和非对称分布的近似提供了高度灵活性和易用性。我们表明，这种分布的数学特性允许高维建模，而无需降维，因此不会丢失信息。这使得广义狄利克雷分布更加实用和有用。我们提出了一种混合随机期望最大化算法（HSEM）来估计广义狄利克雷混合的参数。该算法称为随机算法，因为它包含将数据元素随机分配给组件的步骤，以避免收敛到鞍点。形容词“混合”是通过引入牛顿-拉夫森步骤来证明的。此外，HSEM 算法通过引入凝聚项来自主选择组件的数量。我们的方法的性能是通过几个模式识别数据集的分类来测试的。广义狄利克雷混合还应用于图像恢复、图像对象识别和纹理图像数据库摘要等问题，以实现高效检索。对于纹理图像汇总问题，报告了来自 MIT 媒体实验室的 Vistex 纹理图像数据库的结果。
This paper applies a robust statistical scheme to the problem of unsupervised learning of high-dimensional data. We develop, analyze, and apply a new finite mixture model based on a generalization of the Dirichlet distribution. The generalized Dirichlet distribution has a more general covariance structure than the Dirichlet distribution and offers high flexibility and ease of use for the approximation of both symmetric and asymmetric distributions. We show that the mathematical properties of this distribution allow high-dimensional modeling without requiring dimensionality reduction and, thus, without a loss of information. This makes the generalized Dirichlet distribution more practical and useful. We propose a hybrid stochastic expectation maximization algorithm (HSEM) to estimate the parameters of the generalized Dirichlet mixture. The algorithm is called stochastic because it contains a step in which the data elements are assigned randomly to components in order to avoid convergence to a saddle point. The adjective "hybrid" is justified by the introduction of a Newton-Raphson step. Moreover, the HSEM algorithm autonomously selects the number of components by the introduction of an agglomerative term. The performance of our method is tested by the classification of several pattern-recognition data sets. The generalized Dirichlet mixture is also applied to the problems of image restoration, image object recognition and texture image database summarization for efficient retrieval. For the texture image summarization problem, results are reported for the Vistex texture image database from the MIT Media Lab.