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Towards Testing the Significance of Branching Points and Cycles in Mapper Graphs
Published on Feb 4, 202531 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