Stability and Resampling Methods for Clustering

On a statistical model of cluster stability

author: Zeev Volkovich, ORT Braude College of Engineering

Categories

Top: Computer Science: Machine Learning: Clustering

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*Slides*
0:00	ON STATISTICAL MODEL OF CLUSTER STABILITY
0:13	Concept
0:54	Motivating works
1:28	Clustering
1:59	Clustering (cont)
2:26	Example: a three-cluster set partitioned into 2 and 4 clusters
3:35	Implication
3:55	Concept
4:18	Concept (cont. 1)
4:43	Concept (cont. 2)
6:07	Some probability metrics
8:35	Examples
8:49	Ky Fan metrics
9:08	Concentration measure index
10:38	Simple and Compound Metrics
13:38	Geometrical Algorithm
14:06	General algorithm. Given a probability metric dis(·, ·)
16:23	Klebanov’s N-distances
17:25	Simple distances (cont)
18:30	Graphical illustration
20:57	Graphical illustration (cont. 1) Distances between points belonging to different samples
21:22	Graphical illustration (cont. 2)
23:23	Remark
23:56	Euclidean Minimal Spanning Tree
24:49	An EMST of 60 random points
25:01	How can an EMST be used in the cluster validation problem?
25:27	Graphical illustration. Stable clustering
26:21	Graphical illustration. Non-stable clustering
33:58	The two-sample MST-test (cont. 2)
35:09	The two-sample MST-test (cont. 3)
35:36	Theorem’s application
35:59	Theorem’s application (cont. 1)
36:14	Example: Calculation of Rn(S1,S2)
37:38	Distances from normality
38:39	The Kolmogorov-Smirnov Distance
39:24	Example : synthetic data
39:37	Example : synthetic data (cont. 1)
41:42	Membership Stability Algorithm
42:48	A family of clustering algorithms
43:41	Clusters correspondence problem
44:05	Correspondence between labels a and ß obtained for a sample S.
44:43	Example:The Iris Flower Dataset
45:44	Graph of the normalized mean value
45:59	Graph of the normalized quartile value
46:33	Histograms of the distances’ values

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