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Survey:Frompersistenthomologytomachinelearningfeaturevectors
HenryAdamsColoradoStateUniversity
ICERMTRIPODSBootcampon”TopologyandMachineLearning”
2018
Bottleneckdistance
2007
Wassersteindistance
2011
Computationtime
2017
Possiblegoals
(kernelsarealsoveryuseful!)
PersistenceLandscapes
Computationtimeismuchfaster!
2015
PersistenceLandscapes
PersistenceLandscapesMeansareunique!
PersistenceLandscapes
Computations:ThePersistenceLandscapesToolbox:https://www.math.upenn.edu/~dlotko/persistenceLandscape.html
2017
2015
• Topologicalfeaturescanbeaddedtoimprovestate-of-the-artclassifiers
• Thenon-persistentfeaturesalsomatter!
2016
2015
2015
2017
2015
2015
2018
2018
2015
01
1
0.5
Unit Cube
0.5
1
0.50 0
Circle
0
0.5
1
0
0.5
1-1
0
1
01
1
0.5
Unit Sphere
0.5
1
0.50 0
0.51
1
1
Clusters
0.5 0.8
1.5
0.60 0.4
0.61
0.8
1
Clusters InsideClusters
0.5 0.8
1.2
0.70.60 0.5
-211
0.50.5
00
0
Torus
2
Survey:Frompersistenthomologytomachinelearningfeaturevectors