Shape as Organizing Principle for Data

1. Shape as Organizing Principle for Data MLConf, SF 2014 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 Want to Discover the underlying structure without bias. TDA analyzes the data you have, not the data you want to have.

7. Generating Topological Summaries

24. Remember/Forget  Different lenses provide different summaries  Use multiple lenses/metrics to get the complete picture

26. Lenses: where do they come from? Statistics Mean/Max/Min Variance n-Moment Density … Machine Learning PCA/SVD Autoencoders Isomap/MDS/TS NE … Geometry Centrality Curvature Harmonic Cycles …

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. 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

32. Deformation Invariance

36. 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.

37. Compressed Representation

38. Baby Steps: PCA

39. PCA

40. PCA

41. Data Stories

42. Model Introspection

43. Model Introspection

44. Predictive Maintenance

45. Customer Churn

46. Customer Churn

47. Customer Churn

48. Transaction Fraud

51. Data has shape, Shape has meaning. http://www.ayasdi.com/company/careers/

Shape as Organizing Principle for Data

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