Explore the fundamentals of the Mapper construction, a key technique in topological data analysis (TDA), in this 55-minute lecture by Bala Krishnamoorthy. Learn how this data visualization method produces insightful representations of complex datasets, revealing hidden structures through clustering and simplicial complex construction. Discover the mathematical foundations, robustness, and growing applications of Mapper, including its use in identifying subpopulations with distinct behaviors. Examine real-world examples that demonstrate Mapper's effectiveness in uncovering hidden patterns in large datasets, from medical research to energy landscapes. Gain insights into the interpretation of Mapper graphs, including structures like paths and flares, and understand how this versatile tool for partial clustering can provide compact yet meaningful representations of data.
Overview
Syllabus
THE MAPPER: AN INTRODUCTION
THE DATASAURUS DOZEN!
ANSCOMBE'S QUARTET Anscombe, 1973
TOPOLOGY? * branch of mathematics that studies how
DATA:CLUSTERING
TOPOLOGICAL DATA ANALYSIS TDA
TYPE 2 DIABETES SUBTYPES
INFECTION RESILIENCE Tonnes et al. 2016 PLoS Bidogy
PATIENT TRAJECTORIES
MAPPER: CDOT,DSA, UNITS
MAPPER: CDOT,DSA, AGENTS
MAPPER: FLARES
MAPPER: FOUNDATIONS
ENERGY LANDSCAPES * Kepler Mapper demo: Na-OH association in water
ENERGY LANDSCAPES * Kepler Mapper demo: Ma-OH association in water
MAPPER: THE TAKEAWAY versatile tool for partial clustering
Taught by
Applied Algebraic Topology Network
