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K-means and Gaussian Mixture Model 王养浩 2013 年 11 月 20 日
Outline K-means Gaussian Mixture Model Expectation Maximum
K-means Gather data points to a few cohesive ‘Clusters’ Unsupervised Learning
Easy Fast Euclidean distance? K needs input ？ Convergence ？
Determination of K Rule of Thumb ： Elbow Method Cross Validation
K-means Convergence x (i) data points μ c(i) cluster centroids Coordinate descent
K-means Convergence Non-circle Clusters
K-means Convergence Local minimum – The optimization object is non-convex
Gaussian Mixture Model Mixture of Gaussian distribution
Gaussian Mixture Model Log likelihood Maximum likelihood – Expectation Maximum
Construct lower bound
Repeat until convergence
Generalized Expectation Maximum Difficulty in M-step
Summary K-means – Coordinate descent Gaussian Mixture Model – Expectation Maximum Expectation Maximum – MLE for models with latent variables – Generalized EM
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