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Random Swap EM algorithm for GMM and Image Segmentation Qinpei Zhao, Ville Hautamäki, Ismo Kärkkäinen, Pasi Fränti Speech & Image Processing Unit Department of Computer Science, University of Joensuu Box 111, Fin-80101 Joensuu FINLAND zhao@cs.joensuu.fi

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Outline Background & Status RS-EM Application

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Background: Mixture Model

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Background: EM algorithm EM algorithm -> {α, Θ} E-step (Expectation): M-step (Maximization): Iterate E,M step until convergence α- mixing coefficient Θ- model parameters, eg. {μ,∑}

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Local Maxima Let’s describe it as mountain climbing……

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600km 2160m 3099m

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Initialization Effect Initialization and Result(1)Initialization and Result(2)

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Sub-optimal Example The situation of local maxima trap

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Status Standard EM for Mixture Models(1977) Deterministic Annealing EM (DAEM) (1998) Split-Merge EM (SMEM) (2000) Greedy EM (2002) RS-EM coming…

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Outline Background & Status RS-EM (Random Swap) Application

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RSEM: Motivations Random manner Prevent from staying near the unstable or hyperbolic fixed points of EM. Prevent from its stable fixed points corresponding to insignificant local maxima of the likelihood function Avoid the slow convergence of EM algorithm Less sensitive to its initialization

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Formulas SMEM Greedy EM RSEM

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Random Swap EM After EM After Swap After EM

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Comparisons(1)

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Comparisons(2) Q1Q2S1S4

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Outline Background & Status RS-EM Application

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Application Image Segmentation Color Quantization Image Retrieval ……

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Conclusion Introduce Randomization into algorithm Performs better Without heavy time complexity Wider applications Thanks! ☺

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