Topological Data Analysis

author:Neža Mramor Kosta, Faculty of computer and information science, University of Ljubljana
published: Jan. 18, 2010,   recorded: December 2009,   views: 41
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Slides

Slides
0:00 Topological data analysis: Between topology and computer science
1:12 What is computational (algebraic) topology? - 1
1:45 What is computational (algebraic) topology? - 2
2:26 What is computational (algebraic) topology? - 3
2:50 What is computational (algebraic) topology? - 4
3:00 What is computational (algebraic) topology? - 5
3:58 Topological data analysis - 1
7:24 Topological data analysis - 2
7:50 Topological data analysis - 3
8:11 Topological data analysis - 4
8:29 Topological data analysis - 5
9:12 Topological data analysis - 6
9:53 Topological data analysis - 7
10:04 Topological data analysis - 8
10:47 Topological data analysis - 9
11:21 Topological data analysis - 10
11:34 Topological data analysis - 11
11:46 Topological data analysis - 12
12:27 Topological data analysis - 13
13:32 Sampled functions - 1
14:11 Sampled functions - 2
14:31 Sampled functions - 3
15:30 Topological model: Morse theory - 1
15:45 Topological model: Morse theory - 2
16:06 Topological model: Morse theory - 3
17:12 Topological model: Morse theory - 4
18:43 Topological model: Morse theory - 5
24:55 Topological model: Morse theory - 6
25:50 Discrete Morse theory - 1
26:27 Discrete Morse theory - 2
26:48 Discrete Morse theory - 3
27:30 Discrete Morse theory - 4
27:50 Discrete Morse theory - 5
32:11 Discrete Morse theory - 6
32:58 Advantages - 1
34:05 Advantages - 2
34:41 Advantages - 3
35:19 Contributions - 1
37:24 Contributions - 2
37:40 Contributions - 3
37:41 Contributions - 4
38:20 Contributions - 5
38:30 Contributions - 6
38:52 Contributions - 7
43:14 Applications in image analysis - 1
44:03 Applications in image analysis - 2

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Description

Computational topology is a relatively new field between mathematics and computer science which, on one hand, uses concepts and methods from topology to formalize and solve problems in computer science and, on the other hand, designs algorithms for computing complex invariants of algebraic topology. In this talk we will present several topological approaches to data and image analysis.

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