Hierarchical ModelBased Clustering of Large Datasets Through 基于层次模型大型数据集通过聚类.pptVIP

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Hierarchical ModelBased Clustering of Large Datasets Through 基于层次模型大型数据集通过聚类.ppt

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Hierarchical ModelBased Clustering of Large Datasets Through 基于层次模型大型数据集通过聚类

Hierarchical Model-Based Clustering of Large Datasets Through Fractionation and Refractionation Jeremy Tantrum, Department of Statistics, University of Washington joint work with Alejandro Murua Werner Stuetzle Insightful Corporation University of Washington Motivating Example Goal of Clustering NonParametric Clustering NonParametric Clustering Model Based Clustering Model Based Clustering Model Based Clustering Fitting a Mixture of Gaussians Use the EM algorithm to maximize the log likelihood Estimates the probabilities of each observation belonging to each group Maximizes likelihood given these probabilites Requires a good starting point Model Based Clustering Hierarchical Clustering Provides a good starting point for EM algorithm Start with every point being it’s own cluster Merge the two closest clusters Measured by the decrease in likelihood when those two clusters are merged Uses the Classification Likelihood – not the Mixture Likelihood Algorithm is quadratic in the number of observations Likelihood Distance Bayesian Information Criterion Choose number of clusters by maximizing the Bayesian Information Criterion r is the number of parameters n is the number of observations Log likelihood penalized for complexity Fractionation Fractionation an meta-observations after the first round a2n meta-observations after the second round ain meta-observations after the ith round For the ith pass, we have ai-1n/M fractions taking O(M2) operations each Total number of operations is: Total running time is linear in n! Model Based Fractionation Use model based clustering Meta-observations contain all sufficient statistics – (ni, mi, Si) ni is the number of observations – size mi is the mean – location Si is the covariance matrix – shape and volume Model Based Fractionation Example 2 Refractionation Problem: If the number of meta-observations generated from a fraction is less than the number of groups in that fraction then two or more groups wi