Learning the topology of a data set

author: Pierre Gaillard , Commissariat à l'Energie Atomique

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*Slides*
0:00	Learning the topology of a data set
0:17	Introduction
0:37	A question without answer…
0:47	An subjective answer
1:12	Why learning topology: (semi)-supervised applications
2:34	Why learning topology: unsupervised applications
3:28	Generative manifold learning
5:42	Computational topology - 1
6:13	Computational topology - 2
6:32	Computational topology - 3
6:34	Computational topology - 4
6:39	Computational topology - 5
6:42	Computational topology - 6
7:10	Application : known manifold
7:18	Approximation : manifold known throught a data set
7:26	Topology representing network - 1
7:51	Topology representing network - 2
7:52	Topology representing network - 3
7:55	Topology representing network - 4
8:07	Topology representing network - 5
8:19	Topology representing network - 6
8:23	Topology representing network - 7
8:30	Topology representing network - 8
8:45	Topology representing network: some drawbacks - 1
9:28	Topology representing network: some drawbacks - 2
9:48	Topology representing network: some drawbacks - 3
10:27	General assumptions on data generation - 1
10:31	General assumptions on data generation - 2
10:36	General assumptions on data generation - 3
10:40	General assumptions on data generation - 4
10:52	3 assumptions…1 generative model - 1
11:25	3 assumptions…1 generative model - 2
11:35	3 assumptions…1 generative model - 3
11:46	A Gaussian-point and a Gaussian-segment
12:36	Hola!
13:03	Proposed approach: 3 steps - 1
13:45	Number of prototypes
13:48	Proposed approach: 3 steps - 1
13:50	Number of prototypes
14:36	Proposed approach: 3 steps - 2
15:10	EM updates - 1
15:14	EM updates - 2
15:15	Proposed approach: 3 steps - 3
16:41	Threshold setting
17:30	Toy experiment - 1
17:34	Toy experiment - 2
17:37	Toy experiment - 3
17:41	Other applications
19:20	Comments
20:22	Other applications
20:32	Comments
20:40	Key points
21:53	Open questions
22:39	Related works
23:08	- Questions

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