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EE462 MLCV 1 Lecture 3-4 Clustering (1hr) Gaussian Mixture and EM (1hr) Tae-Kyun Kim

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EE462 MLCV 2 2D data vectors (green) are grouped to two homogenous clusters (blue and red). Clustering is achieved by an iterative algorithm (left to right). The cluster centers are marked x. Vector Clustering

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EE462 MLCV 3 ` RGBRGB Pixel Clustering (Image Quantisation) Image pixels are represented by 3D vectors of R,G,B values. The vectors are grouped to K=10,3,2 clusters, and represented by the mean values of the respective clusters.

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EE462 MLCV 4 dimension D … …… or raw pixels … K codewords Patch Clustering (BoW in Lecture 9-10) Image patches are harvested around feature points in a large number of images. They are represented by finite dimensional vectors, and clustered to form a visual dictionary. SIFT 20 D=400

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EE462 MLCV 5 …… Image Clustering Whole images are represented as finite dimensional vectors. Homogenous vectors are grouped together in Euclidean space.

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EE462 MLCV 6 K-means vs GMM Hard clustering: a data point is assigned only one cluster. Soft clustering: a data point is assigned multiple Gaussians probabilistically. Two representative techniques are k-means and Gaussian Mixture Model (GMM). K-means assigns data points to the nearest clusters, while GMM assigns data to the Gaussian densities that best represent the data.

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EE462 MLCV 7 Matrix and Vector Derivatives

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EE462 MLCV 8

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9 K-means Clustering

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EE462 MLCV 11 till converge

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EE462 MLCV 12 K=2 μ 1 μ 2 r nk

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EE462 MLCV 13 Convergence proof (yes) Global minimum (no)

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EE462 MLCV 14

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EE462 MLCV 15 Statistical Pattern Recognition Toolbox for Matlab tprtool/ …\stprtool\probab\cmeans.m …\stprtool\probab\cmeans_tk.m

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EE462 MLCV 16 Mixture of Gaussians

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EE462 MLCV 20 Maximum Likelihood s.t.

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EE462 MLCV 22 objective ftn. f(x) constraints g(x) max f(x) s.t. g(x)=0

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EE462 MLCV 23

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EE462 MLCV 24 till converge

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EE462 MLCV 27 Statistical Pattern Recognition Toolbox for Matlab tprtool/ …\stprtool\visual\pgmm.m …\stprtool\demos\demo_emgmm.m

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EE462 MLCV 28 Supplementary Material

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EE462 MLCV 29 Information Theory (for Lecture 7-8)

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EE462 MLCV 30

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EE462 MLCV 31 Advanced topic (optional) cv/lecture_clustering_em.pdf

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EE462 MLCV 32 EM Algorithm in General

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