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A formal analysis of stability - lessons and open questions
Published on Jul 28, 20074778 Views
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Chapter list
A formal analysis of stability - <br>lessons and challenges00:00
What is a good clustering??? (1)00:25
What is a good clustering??? (2)00:54
In what sense is the leftmost clustering <br>better than the middle one?01:04
Even if we commit to a fixed cost<br> function01:42
Even harder questions13:40
Quest for a general theory17:11
A more modest approach18:38
Stability - the basic idea19:28
Stability - the formal definition20:11
(In)Stability detects<br> non-clusterability:21:25
Stability distinguishes relevant from <br>irrelevant clustering paradigms:22:15
Stability detects correct k (1)23:13
Stability detects correct k (2)23:26
Conclusions (as of Dec. 2005)23:49
Have we found a good answer?25:00
Some bothersome examples25:48
The bottom line of a formal analysis29:29
The formal results30:12
Proof Idea 1: <br>Uniqueness implies stability31:54
Proof idea (2):<br> Multiple solutions imply instability34:35
Proof idea (continued) (1)36:19
Proof idea (continued) (2)36:58
Some Examples (1)37:52
Some Examples (2)38:16
Some Examples (3)38:25
Some Examples (4)38:32
Some Examples (5)38:47
Some Examples (6)38:57
Some Examples (7)38:58
Some Examples (8)39:28
The bottom line41:02
Other notions of stability50:12
Two different topics for discussion50:48
Some thoughts on the <br>‘finite samples’ issue51:36
Alternative notions of clusterability55:38