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

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Presentation on theme: "EE462 MLCV 1 Lecture 3-4 Clustering (1hr) Gaussian Mixture and EM (1hr) Tae-Kyun Kim."— Presentation transcript:

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

2 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

3 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.

4 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

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

6 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.

7 EE462 MLCV 7 Matrix and Vector Derivatives

8 EE462 MLCV 8

9 9 K-means Clustering

10 EE462 MLCV 10

11 EE462 MLCV 11 till converge

12 EE462 MLCV 12 K=2 μ 1 μ 2 r nk

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

14 EE462 MLCV 14

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

16 EE462 MLCV 16 Mixture of Gaussians

17 EE462 MLCV 17

18 EE462 MLCV 18

19 EE462 MLCV 19

20 EE462 MLCV 20 Maximum Likelihood s.t.

21 EE462 MLCV 21

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

23 EE462 MLCV 23

24 EE462 MLCV 24 till converge

25 EE462 MLCV 25

26 EE462 MLCV 26

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

28 EE462 MLCV 28 Supplementary Material

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

30 EE462 MLCV 30

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

32 EE462 MLCV 32 EM Algorithm in General

33 EE462 MLCV 33

34 EE462 MLCV 34


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