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Shape as Organizing Principle for Data

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Anthony Bak
Anthony Bak
Engineering
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Shape as Organizing Principle for Data MLConf, SF 2014 Anthony Bak, Principal Data Scientist
The Data Problem: Complexity
Solution: Topological Summaries
Shape as Organizing Principle for Data
Shape as Organizing Principle
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.
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Generating Topological Summaries
Remember/Forget  Different lenses provide different summaries  Use multiple lenses/metrics to get the complete picture
Generating Topological Summaries
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 …
Why Topology?
Key Properties of TDA Deformation Invariance Compressed Representation Coordinate Freeness
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
Coordinate Invariance: Gene Expression NKI GSE230
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
Deformation Invariance
Deformation Invariance
Deformation Invariance
Deformation Invariance
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.
Compressed Representation
Baby Steps: PCA
PCA
PCA
Data Stories
Model Introspection
Model Introspection
Predictive Maintenance
Customer Churn
Customer Churn
Customer Churn
Transaction Fraud
Transaction Fraud
Transaction Fraud
Data has shape, Shape has meaning. http://www.ayasdi.com/company/careers/

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