Survey: From persistent homology to machine learning ......Survey: From persistent homology to...
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Survey: From persistent homology to machine learning feature vectors Henry Adams Colorado State University ICERM TRIPODS Bootcamp on ”Topology and Machine Learning” 2018
Transcript of Survey: From persistent homology to machine learning ......Survey: From persistent homology to...
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Survey:Frompersistenthomologytomachinelearningfeaturevectors
HenryAdamsColoradoStateUniversity
ICERMTRIPODSBootcampon”TopologyandMachineLearning”
2018
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Bottleneckdistance
2007
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Wassersteindistance
2011
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Computationtime
2017
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Possiblegoals
(kernelsarealsoveryuseful!)
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PersistenceLandscapes
Computationtimeismuchfaster!
2015
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PersistenceLandscapes
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PersistenceLandscapesMeansareunique!
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PersistenceLandscapes
Computations:ThePersistenceLandscapesToolbox:https://www.math.upenn.edu/~dlotko/persistenceLandscape.html
2017
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2015
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• Topologicalfeaturescanbeaddedtoimprovestate-of-the-artclassifiers
• Thenon-persistentfeaturesalsomatter!
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2016
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2015
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2015
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2017
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2015
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2015
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2018
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2018
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2015
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Unit Cube
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Circle
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Unit Sphere
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Clusters
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Clusters InsideClusters
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Torus
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Survey:Frompersistenthomologytomachinelearningfeaturevectors
