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Topology as Framework for Data Science: Ayasdi has a unique approach to machine learning and data analysis using topology. This framework represents a revolutionary way to look at and understand data that is orthogonal but complementary to traditional machine learning and statistical tools. In this presentation I will show you what is meant by this statement: How does topology help with data analysis? Why would you use topology? I will illustrate with both synthetic examples and problems we’ve solved for our clients.

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- 1. Shape as Organizing Principle for Data MLConf Seattle 2015 Anthony Bak, Principal Data Scientist
- 2. The Data Problem: Complexity
- 3. Solution: Topological Summaries
- 4. Shape as Organizing Principle for Data
- 5. Shape as Organizing Principle
- 6. Reduce Bias, Discover Models TDA tells you the data you have, not the data you want to have.
- 7. Generating Topological Summaries
- 8. Generating Topological Summaries
- 9. Generating Topological Summaries
- 10. Generating Topological Summaries
- 11. Generating Topological Summaries
- 12. Generating Topological Summaries
- 13. Generating Topological Summaries
- 14. Generating Topological Summaries
- 15. Generating Topological Summaries
- 16. Generating Topological Summaries
- 17. Generating Topological Summaries
- 18. Generating Topological Summaries
- 19. Generating Topological Summaries
- 20. Generating Topological Summaries
- 21. Generating Topological Summaries
- 22. Generating Topological Summaries
- 23. Generating Topological Summaries
- 24. Remember/Forget Use multiple lenses/metrics to get the complete picture Different lenses provide different summaries
- 25. Generating Topological Summaries
- 26. Lenses: where do they come from? Mean/Max/Min Variance n-Moment Density … Statistics PCA/SVD Autoencoders Isomap/MDS/TS NE … Machine Learning Centrality Curvature Harmonic Cycles … Geometry
- 27. Why Topology?
- 28. Key Properties of TDA Deformation Invariance Compressed Representation Coordinate Freeness
- 29. Coordinate Invariance 1. Topology of shape doesn’t depend on the coordinates used to describe the shape 1. Different feature sets can describe the same phenomena 1. While processing data, we frequently alter coordinates: scaling, rotating, whitening You want to study properties of your data that are invariant under coordinate changes
- 30. Coordinate Invariance: Gene Expression NKI GSE230
- 31. Coordinate Invariance: Disease State
- 32. Deformation Invariance • Topological features don’t change when you stretch and distort the data Advantage: Makes problems easier Noise resistance Less pre-processing of data Robust (stable) data
- 33. Deformation Invariance
- 34. Deformation Invariance
- 35. Deformation Invariance
- 36. Deformation Invariance
- 37. Compressed Representation • Replace the metric space with a combinatorial summary: a simplicial complex. • Data becomes easier to manage, search, and query while maintaining essential features. • Leverages many known algorithms from graph theory, computational topology, computational geometry.
- 38. Compressed Representation
- 39. Baby Steps: PCA
- 40. PCA
- 41. PCA
- 42. Data Stories
- 43. Model Introspection
- 44. Model Introspection
- 45. Predictive Maintenance
- 46. Customer Churn
- 47. Customer Churn
- 48. Transaction Fraud
- 49. Transaction Fraud
- 50. Transaction Fraud
- 51. We’re Hiring! http://www.ayasdi.com/company/careers/ Data Has Shape And Shape Has Meaning

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