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Towards Testing the Significance of Branching Points and Cycles in Mapper Graphs
Published on 2023-10-1231 Views
Presentation
Towards Testing the Significance of Branching Points and Cycles in Mapper Graphs00:00
Topological structure of a point cloud 00:12
Focus on cycles and branching points - 100:28
Focus on cycles and branching points - 200:33
Other possible graphs - additional cycles - 100:47
Other possible graphs - additional cycles - 201:06
Other possible graphs - additional branching points - 101:12
Other possible graphs - additional branching points - 201:19
Point cloud to graph using mapper algorithm - 101:42
Point cloud to graph using mapper algorithm - 202:19
Problem setting02:40
Checking cycles using (persistent) homology - 103:26
Checking cycles using (persistent) homology - 204:22
Significance testing of cycles04:45
Testing simple cycles05:39
Checking branching points with (persistent) relative homology06:12
Testing branching points07:18
Experiment 1: Y-shaped point cloud08:10
Experiment 1 - Mapper graph08:34
Experiment 2: 3D ant surface09:14
Experiment 2 - Mapper graph09:34
Experiment 2 - Branching points09:49
Experiment 2 - Cycles10:52
Future work11:34
Thank you for your attention!12:51