From Hyperbolic Geometry to Data Clustering

Explore the intersection of hyperbolic geometry and data clustering in this 39-minute conference talk by Jesse Johnson at BDF 2015. Discover how concepts from knot theory and hyperbolic three-manifolds led to the development of the Topologically Intrinsic Lexicographic Ordering (TILO) clustering algorithm. Delve into topics such as data analysis, classification, higher dimensional geometry, topology, similarity graphs, ontology, eigenvectors, exponential partitions, and knots. Learn how geometric patterns and shapes in data collections can be leveraged to solve common data science problems using abstract geometric tools. Gain insights into practical and complex applications of these concepts in fields like ecology and beyond.

Intro
Data Analysis
Classification
Clustering
Higher Dimensional Geometry
Geometry and Topology
Geometry and Ecology
Similarity Graph
Ontology
The bottleneck
Analysis of one way
Eigenvectors
Exponential Partitions
Partitioning Graphs
Knots
Scanning
Practical Application
Complex Application