Clustering

author: Shai Ben-David, University of Waterlo

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*Slides*
0:00	Theoretical Foundations of Clustering - Some Progress, Many Challenges
1:01	The Theory - Practice Gap
2:29	Inherent Obstacles
3:48	There are Many Clustering Tasks - 1
4:08	There are Many Clustering Tasks - 2
4:19	Some More Examples
4:28	Common Solutions - 1
6:20	Common Solutions - 2
8:07	Quest for a General Theory
8:28	What Questions Should Research Address?
10:12	The Basic Setting
12:09	- Questions
19:04	Note that Any Pair Is Realizable
19:11	Kleinberg’s Impossibility Result
21:35	- Questions
23:11	- Questions
24:22	- Questions
28:30	Ideal Theory
31:50	Axioms as a Tool for a Taxonomy of Clustering Paradigms
33:49	Types of Axioms/Properties
34:51	Relaxations of Consistency
40:02	- Questions
48:38	Some Open Questions
48:49	A Different Approach
49:30	Stability Basic Idea
51:00	A Different Perspective – Replication
51:56	- Questions
54:38	Negative Observation
55:34	Another ‘Unstable’ Example
57:39	Yet Another ‘Unstable’ Example - 1
58:01	Yet Another ‘Unstable’ Example - 2
58:22	An Optimistic View of the “Negative ”Observations
58:37	Stability as a Model-Selection Tool
59:05	Examples of Stability Success as a Model-Selection Tool
60:07	Single Linkage Clustering of Swiss-Roll – Varying the Cutoff Distance - 1
60:46	Single Linkage Clustering of Swiss-Roll – Varying the Cutoff Distance - 2
60:56	Single Linkage Clustering of Swiss-Roll – Varying the Cutoff Distance - 3
61:45	Instability Detects the ‘Correct’ Clustering Parameter
62:13	Conclusions
62:48	Have We Found a Good Answer?
63:18	Some Bothersome Examples
64:27	The Bottom Line of a Formal Analysis
65:12	The Formal Results
66:08	Some Bothersome Examples
66:41	Proof Idea 1: Uniqueness Implies Stability
66:46	- Questions
67:14	Proof Idea 1: Uniqueness Implies Stability
67:17	Proof Idea 2: Multiple Solutions Imply Instability
67:18	Proof Idea (Continued) - 1
67:27	Proof Idea (Continued) - 2
67:29	- Questions
69:08	Some Examples - 1
69:47	Some Examples - 2
70:00	Some Examples - 3
70:11	- Questions
70:40	Some Examples - 5
71:02	Some Examples - 6
71:12	Some Examples - 7
71:38	Some Examples - 8
71:42	- Questions
72:40	Some Examples - 8
72:51	Some Examples - 9
73:15	- Questions
77:19	- Questions
80:21	A Promising Direction
82:24	- Questions

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