Topological Modeling of Complex Data

Explore topological modeling of complex data in this 55-minute AMS-MAA Invited Address from the 2018 Joint Mathematics Meetings. Delve into the challenges of big data analysis, comparing size versus complexity and examining traditional mathematical modeling approaches. Discover the limitations of algebraic modeling and clustering techniques before exploring the concept of data shape. Learn how to construct networks for data sets and apply topological modeling to various real-world scenarios, including diabetes analysis, breast cancer microarray studies, and microbiome research. Investigate feature modeling, hot spot analysis, and supervised analysis techniques. Gain insights into improving existing models, surface sub-populations in mortgage data, and leverage serendipity in exploratory data analysis.

Intro
Big Data
Size vs. Complexity
Mathematical Modeling
What Do Models Buy You?
Hierarchical Clustering
Problems with Algebraic Modeling
Problems with Clustering
The Shape of Data
How to Build Networks for Data Sets
Topological Modeling
Unsupervised Analysis - Diabetes
Unsupervised Analysis/ Hypothesis Generation
Microarray Analysis of Breast Cancer
Different Platforms for Microarrays
TDA and Clustering
Feature Modeling
Explaining the Different cohorts
UCSD Microbiome
Pancreatic Cancer
Hot Spot Analysis and Supervised Analysis
Model Diae
Create network of mortgages
Surface sub-populations
Improve existing models
Serendipity
Exploratory Data Analysis