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Gaussian Mixture Example: Start

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After First Iteration

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After 2nd Iteration

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After 3rd Iteration

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After 4th Iteration

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After 5th Iteration

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After 6th Iteration

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After 20th Iteration

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A Gaussian Mixture Model for Clustering Assume that data are generated from a mixture of Gaussian distributions For each Gaussian distribution Center: i Variance: (ignore) For each data point Determine membership

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Learning Gaussian Mixture Model with the known covariance

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Log-likelihood of Data Apply MLE to find optimal parameters

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Learning a Gaussian Mixture (with known covariance)

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E-Step Learning Gaussian Mixture Model

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M-Step Learning Gaussian Mixture Model

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Mixture Model for Document Clustering A set of language models

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Mixture Model for Documents Clustering A set of language models Probability

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A set of language models Probability Mixture Model for Document Clustering

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A set of language models Probability Introduce hidden variable z ij z ij : document d i is generated by the j-th language model j.

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Learning a Mixture Model E-Step K: number of language models

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Learning a Mixture Model M-Step N: number of documents

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