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On a statistical model of cluster stability
Published on Jul 28, 20074703 Views
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Chapter list
ON STATISTICAL MODEL OF CLUSTER STABILITY00:00
Concept00:13
Motivating works00:54
Clustering01:28
Clustering (cont)01:59
Example: a three-cluster set partitioned into 2 and 4 clusters02:26
Implication03:35
Concept03:55
Concept (cont. 1)04:18
Concept (cont. 2)04:43
Some probability metrics 06:07
Examples08:35
Ky Fan metrics 08:49
Concentration measure index09:08
Simple and Compound Metrics 10:38
Geometrical Algorithm13:38
General algorithm. Given a probability metric dis(·, ·) 14:06
Klebanov’s N-distances16:23
Simple distances (cont)17:25
Graphical illustration18:30
Graphical illustration (cont. 1) Distances between points belonging to different samples20:57
Graphical illustration (cont. 2)21:22
Remark23:23
Euclidean Minimal Spanning Tree23:56
An EMST of 60 random points24:49
How can an EMST be used in the cluster validation problem? 25:01
Graphical illustration. Stable clustering25:27
Graphical illustration. Non-stable clustering26:21
The two-sample MST-test (cont. 2)33:58
The two-sample MST-test (cont. 3)35:09
Theorem’s application35:36
Theorem’s application (cont. 1)35:59
Example: Calculation of Rn(S1,S2)36:14
Distances from normality 37:38
The Kolmogorov-Smirnov Distance38:39
Example : synthetic data39:24
Example : synthetic data (cont. 1)39:37
Membership Stability Algorithm41:42
A family of clustering algorithms42:48
Clusters correspondence problem43:41
Correspondence between labels a and ß obtained for a sample S. 44:05
Example:The Iris Flower Dataset 44:43
Graph of the normalized mean value 45:44
Graph of the normalized quartile value45:59
Histograms of the distances’ values 46:33