Stability and Resampling Methods for Clustering

A formal analysis of stability - lessons and open questions

author: Shai Ben-David, University of Waterlo

Categories

Top: Computer Science: Machine Learning: Clustering

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*Slides*
0:00	A formal analysis of stability - lessons and challenges
0:25	What is a good clustering??? (1)
0:54	What is a good clustering??? (2)
1:04	In what sense is the leftmost clustering better than the middle one?
1:42	Even if we commit to a fixed cost function
13:40	Even harder questions
17:11	Quest for a general theory
18:38	A more modest approach
19:28	Stability - the basic idea
20:11	Stability - the formal definition
21:25	(In)Stability detects non-clusterability:
22:15	Stability distinguishes relevant from irrelevant clustering paradigms:
23:13	Stability detects correct k (1)
23:26	Stability detects correct k (2)
23:49	Conclusions (as of Dec. 2005)
25:00	Have we found a good answer?
25:48	Some bothersome examples
29:29	The bottom line of a formal analysis
30:12	The formal results
31:54	Proof Idea 1: Uniqueness implies stability
34:35	Proof idea (2): Multiple solutions imply instability
36:19	Proof idea (continued) (1)
36:58	Proof idea (continued) (2)
37:52	Some Examples (1)
38:16	Some Examples (2)
38:25	Some Examples (3)
38:32	Some Examples (4)
38:47	Some Examples (5)
38:57	Some Examples (6)
38:58	Some Examples (7)
39:28	Some Examples (8)
41:02	The bottom line
50:12	Other notions of stability
50:48	Two different topics for discussion
51:36	Some thoughts on the ‘finite samples’ issue
55:38	Alternative notions of clusterability

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