Topological Techniques for Unsupervised Learning
summary
Claims that a combinatorial translation of metric spaces yields a practical dimension reducer and clustering pipeline: implements UMAP by mapping to a fuzzy simplicial set, optimizes a cross-entropy objective via gradient descent, and produces a force‑directed low‑dimensional layout. Works on MNIST, Fashion‑MNIST and Yelp word cooccurrence: separates digit and clothing classes, reveals internal cluster structure, and yields a probabilistic anomaly score. Code and GPU support are available on GitHub.
AI-written summary · about
chapters (8)
- 0:00Topological techniques intro
- 5:30Topology and simplicial complexes
- 10:07Manifold learning basics
- 17:33Dimension reduction demo
- 21:24Topological word embeddings
- 27:26Topological clustering
- 33:46Anomaly detection via topology
- 35:11Conclusion
related talks
28mUnderstanding UMAP Internal Workings of a State of the Art Clustering Algorithm
37mA Bluffer's Guide to Dimension Reduction
34mDimensionally reducing data squeezing out the good stuff
49mMetric Representations: Algorithms and Geometry
38mManifold Learning and Dimensionality Reduction for Data Visualization
45mWords in Space: A Visual Exploration of Distance, Documents, and Distributions...
25mThe Art of Clustering: The Good, The Bad and The Beautiful
11mGeometric Methods for Machine Learning and Optimization