Allison Gilmore, Data Scientist, Ayasdi
summary
Claims that topology reveals data shape and implements Ayasdi's Mapper pipeline: pick a real-valued lens (y or PCA coordinates), make overlapping bins, cluster points in each bin, and connect clusters that share points to produce graphs/simplicial complexes. Demonstrates on a noisy circle recovering a single loop vs line topology, and on PCA projection that reports 98.4% variance yet hides a fourth cluster that Mapper finds, and shows real biology data where recovery and return paths form a circle not a line, so the method concretely finds meaningful structure.
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chapters (8)
- 0:00Introduction to Data Shape
- 4:29Geometry vs Topology
- 8:09The TDA Algorithm
- 12:34Complex Shape Analysis
- 13:32Understanding Graph Outputs
- 14:25Combining Methods
- 16:11Real-World Applications
- 19:17Conclusion
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