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Topological Data Analysis What is it? What is it good for? How can it be used to study plant morphology?
- 1. Topological Data Analysis What is it? What is it good for? How can it be used to study plant morphology?
- 2. Liz Munch Computational Mathematics, Science & Engineering Michigan State University Topologists Mao Li Donald Danforth Plant Science Center St. Louis, Missouri USA
- 3. What are topological features? A way to measure global qualitative features from complicated geometric structures
- 4. What are topological features? A way to measure global qualitative features from complicated geometric structures There are ways to do this statistically, without topology . . .
- 5. What are topological features? Not spatial positions Chitwood et al. 2016 Plant Physiol Climate and developmental plasticity: Interannual variability in grapevine leaf morphology
- 6. What are topological features? Not spatial positions Chitwood et al. 2016 Plant Physiol Climate and developmental plasticity: Interannual variability in grapevine leaf morphology
- 7. What are topological features? Not a Fourier transform Chitwood 2014 PLOS One Imitation, genetic lineages, and time influenced the morphological evolution of the violin https://en.wikipedia.org/wiki/Fourier_transform#/media/ File:Fourier_transform_time_and_frequency_domains_(small).gif Wikipedia
- 8. What are topological features? Not a Fourier transform New York Times, International Arts, Stephen Heyman How Stradivari came to dictate violin design
- 9. Betti # Blobs Holes Voids Up to N dimensions What are topological features? Blobs, holes, and voids “Properties of space preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing” –Topology, wikipedia Elizabeth Munch A User’s Guide to Topological Data Analysis Journal of Learning Analytics, 2017
- 10. https://en.wikipedia.org/wiki/Homotopy#/media/File:Mug_and_Torus_morph.gif Wikipedia What are topological features? Blobs, holes, and voids “Properties of space preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing” –Topology, wikipedia
- 11. What is a simplicial complex? A collection of simplices 0-simplex = 1 vertex 1-simplex = 2 vertices, an edge 2-simplex = 3 vertices, a triangle 3-simplex = 4 vertices, a tetrahedron n-simplex = n + 1 vertices Simplicial complex = a network!!! Elizabeth Munch A User’s Guide to Topological Data Analysis Journal of Learning Analytics, 2017
- 12. Vietoris-Rips complex (Rips complex) A simplicial complex of your data But pick a value t so if distance between two vertices <=t, then an edge Elizabeth Munch A User’s Guide to Topological Data Analysis Journal of Learning Analytics, 2017
- 13. Vietoris-Rips complex (Rips complex) A simplicial complex of your data But pick a value t so if distance between two vertices <=t, then an edge Elizabeth Munch A User’s Guide to Topological Data Analysis Journal of Learning Analytics, 2017
- 14. Persistent homology A continuum of values to create a simplicial complex Elizabeth Munch A User’s Guide to Topological Data Analysis Journal of Learning Analytics, 2017
- 15. Vietoris-Rips complex (Rips complex) A simplicial complex of your data Huang et al., 2018 arXiv Demonstration of Topological Data Analysis on a Quantum Processor
- 16. Huang et al., 2018 arXiv Demonstration of Topological Data Analysis on a Quantum Processor Persistent homology A continuum of values to create a simplicial complex
- 17. Persistence diagrams The birth and death of features across a function Elizabeth Munch A User’s Guide to Topological Data Analysis Journal of Learning Analytics, 2017
- 18. Bottleneck distance The distance between two persistence diagrams GUDHI http://gudhi.gforge.inria.fr/doc/latest/group__bottleneck__distance.html
- 19. Mapper Converting structure to a graph Elizabeth Munch A User’s Guide to Topological Data Analysis Journal of Learning Analytics, 2017
- 20. Mapper Converting structure to a graph Elizabeth Munch A User’s Guide to Topological Data Analysis Journal of Learning Analytics, 2017
- 21. Topological Data Analysis What is it? What is it good for? How can it be used to study plant morphology?
- 22. How is topology useful for plants? Complex plant morphologies Mao Li, Keith Duncan, Chris Topp, Dan Chitwood Persistent homology and the branching topologies of plants Am J Bot, 104(3):349-353
- 23. Daniel Schachtman, Keith Duncan, Ni Jiang, Mao Li How is topology useful for plants? Complex plant morphologies
- 24. How is topology useful for plants? Complex plant morphologies Mary Lu Arpaia, Eric Focht UC Riverside
- 25. How is topology useful for plants? Complex plant morphologies Jacob Landis, Daniel Koenig UC Riverside
- 26. How is topology useful for plants? Complex plant morphologies Mitchell Eithun Liz Munch
- 27. How is topology useful for plants? Complex plant morphologies Amy Litt UC Riverside
- 28. How is topology useful for plants? Complex plant morphologies Carolyn Rasmussen UC Riverside
- 29. How is topology useful for plants? Complex plant morphologies Peter Cousins (Gallo), Keith Duncan
- 30. Chopping down the cherry tree Isolating the inner tree Jimmy Larson Mitchell Eithun Liz Munch Greg Lang
- 31. Jimmy Larson Mitchell Eithun Liz Munch Greg Lang Chopping down the cherry tree Isolating the inner tree
- 32. Jimmy Larson Mitchell Eithun Liz Munch Greg Lang Chopping down the cherry tree Isolating the inner tree
- 33. Jimmy Larson Mitchell Eithun Liz Munch Greg Lang Chopping down the cherry tree Isolating the inner tree
- 34. Jimmy Larson Mitchell Eithun Liz Munch Greg Lang Chopping down the cherry tree Isolating the inner tree MSU Museum
- 35. Jimmy Larson Mitchell Eithun Liz Munch Greg Lang Chopping down the cherry tree Isolating the inner tree
- 36. Topological Data Analysis What is it? What is it good for? How can it be used to study plant morphology?
- 37. Are there applications to plant morphology? 2D • Shapes • Local features: leaf serrations • First order homology: loops Branching architectures • Shoots and roots
- 38. 16 annuli Density estimator A tool: Subset and smooth Side view A persistent homology morphometric method: Blind to size, position, and orientation 2D point cloud Mao Li
- 39. plane height (level value) connectedcomponent The function is pixel density subsetted by a ring Persistent homology measures topology, or connected components, across the scale of the function Mao Li
- 40. plane height (level value) connectedcomponent Mao Li The function is pixel density subsetted by a ring Persistent homology measures topology, or connected components, across the scale of the function
- 41. plane height (level value) connectedcomponent Mao Li The function is pixel density subsetted by a ring Persistent homology measures topology, or connected components, across the scale of the function
- 42. plane height (level value) connectedcomponent Mao Li The function is pixel density subsetted by a ring Persistent homology measures topology, or connected components, across the scale of the function
- 43. plane height (level value) connectedcomponent Mao Li The function is pixel density subsetted by a ring Persistent homology measures topology, or connected components, across the scale of the function
- 44. plane height (level value) connectedcomponent Mao Li The function is pixel density subsetted by a ring Persistent homology measures topology, or connected components, across the scale of the function
- 45. plane height (level value) connectedcomponent Mao Li The function is pixel density subsetted by a ring Persistent homology measures topology, or connected components, across the scale of the function
- 46. plane height (level value) connectedcomponent Mao Li The function is pixel density subsetted by a ring Persistent homology measures topology, or connected components, across the scale of the function
- 47. plane height (level value) connectedcomponent Mao Li The function is pixel density subsetted by a ring Persistent homology measures topology, or connected components, across the scale of the function
- 48. plane height (level value) connectedcomponent Mao Li The function is pixel density subsetted by a ring Persistent homology measures topology, or connected components, across the scale of the function
- 49. plane height (level value) connectedcomponent Mao Li The function is pixel density subsetted by a ring Persistent homology measures topology, or connected components, across the scale of the function
- 50. Morphometrics with persistent homology Compares simple, deeply lobed, and compound leaf shapes
- 52. Where do the leaves come from? “Transect” and Leafsnap data Transect data Dana Royer, Wesleyan University Daniel Peppe, Baylor University Peter Wilf, Penn State Huff PM, Wilf P, Azumah EJ. 2003. Digital future for paleoclimate estimation from fossil leaves? Preliminary results. Palaios 18: 266-274. Royer DL, Wilf P, Janesko DA, Kowalski EA, Dilcher DL. 2005. Correlations of climate and plant ecology to leaf size and shape: potential proxies for the fossil record. American Journal of Botany 92: 1141-1151. Peppe DJ, Royer DL, Cariglino B, Oliver SY, Newman S, Leight E, Enikolopov G, Fernandez-Burgos M, Herrera F, Adams JM, Correa E, Currano ED, Erickson JM, Hinojosa LF, Iglesias A, Jaramillo CA, Johnson KR, Jordan GJ, Kraft N, Lovelock EC, Lusk CH, Niinemets U, Penuelas J, Rapson G, Wing SL, Wright IJ. 2011. Sensitivity of leaf size and shape to climate: global patterns and paleoclimatic applications. New Phytologist, 190: 724-739. Leafsnap: A Computer Vision System for Automatic Plant Species Identification Neeraj Kumar, Peter N. Belhumeur, Arijit Biswas, David W. Jacobs, W. John Kress, Ida C. Lopez, João V. B. Soares Proceedings of the 12th European Conference on Computer Vision (ECCV), October 2012
- 53. Analysis Mao Li, Danforth Center Isolation Rebekah Mohn, Miami University Potato Shelley Jansky, USDA, Wisconsin- Madison Diego Fajardo, National Center for Genome Resources Pepper Allen van Deynze, UC Davis Theresa Hill, UC Davis Tomato Viktoriya Coneva, Danforth Center Margaret Frank, Danforth Center Chris Topp, Danforth Center Arabidopsis Ruthie Angelovici, University of Missouri, Columbia Batushansky Albert, University of Missouri, Columbia Clement Bagaza, University of Missouri, Columbia Edmond Riffer, University of Missouri, Columbia Braden Zink, University of Missouri, Columbia Brassica J. Chris Pires, University of Missouri, Columbia Hong An, University of Missouri, Columbia Sarah Gebken, University of Missouri, Columbia Cotton Vasu Kuraparthy, North Carolina State University Grape Allison Miller, Saint Louis University Jason Londo, USDA/ARS, Geneva, NY Laura Klein, Saint Louis University Passiflora Wagner Otoni, Universidade Federal de Vicosa Viburnum Erika Edwards, Brown University Elizabeth Spriggs, Yale University Michael Donoghue, Yale University Sam Schmerler, American Museum of Natural History Grasses Lynn Clark, Iowa State Timothy Gallaher, Iowa State Phillip Klahs, Iowa State Where do the leaves come from? Specific plant taxa
- 54. Morphometrics with persistent homology A morphospace for leaf shape
- 55. Mao Li, Margaret Frank, Viktoriya Coneva, Washington Mio, Chris Topp, Dan Chitwood Persistent homology: a tool to universall measure plant morphologies across organs and scales bioRxiv, 2018 How is topology useful for plants? Local features: serrations
- 56. Mao Li, Margaret Frank, Viktoriya Coneva, Washington Mio, Chris Topp, Dan Chitwood Persistent homology: a tool to universall measure plant morphologies across organs and scales bioRxiv, 2018 How is topology useful for plants? First order homology: loops
- 57. How is topology useful for plants? Genetics and persistent homology
- 58. Mao Li, Keith Duncan, Chris Topp, Dan Chitwood Persistent homology and the branching topologies of plants Am J Bot, 104(3):349-353 How is topology useful for plants? Branching architectures
- 59. Mao Li
- 60. Mao Li
- 61. Mao Li, Keith Duncan, Chris Topp, Dan Chitwood Persistent homology and the branching topologies of plants Am J Bot, 104(3):349-353 How is topology useful for plants? Branching architectures
- 62. Bottleneck distances Overall differences in morphology Mao Li, Keith Duncan, Chris Topp, Dan Chitwood Persistent homology and the branching topologies of plants Am J Bot, 104(3):349-353 Mao Li
- 63. Bottleneck distances Overall differences in morphology Mao Li
- 64. Scan all the things!!! MSU Museum and the Broad
- 65. Scan all the things!!! MSU Museum and the Broad
- 66. Scan all the things!!! MSU Museum and the Broad