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K-means and Gaussian Mixture Model 王养浩 2013 年 11 月 20 日

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Outline K-means Gaussian Mixture Model Expectation Maximum

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K-means Gather data points to a few cohesive ‘Clusters’ Unsupervised Learning

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K-means

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Easy Fast Euclidean distance? K needs input ？ Convergence ？

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Determination of K Rule of Thumb ： Elbow Method Cross Validation

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K-means Convergence x (i) data points μ c(i) cluster centroids Coordinate descent

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Coordinate Descent

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K-means Convergence Non-circle Clusters

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K-means Convergence Local minimum – The optimization object is non-convex

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Gaussian Mixture Model Mixture of Gaussian distribution

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Gaussian Mixture Model Log likelihood Maximum likelihood – Expectation Maximum

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Expectation Maximum

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Jenson inquality

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Expectation Maximum

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Construct lower bound

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Expectation Maximum

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Repeat until convergence

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Generalized Expectation Maximum Difficulty in M-step

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Summary K-means – Coordinate descent Gaussian Mixture Model – Expectation Maximum Expectation Maximum – MLE for models with latent variables – Generalized EM

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