Artworks and Articles Meet Artworks and Articles Meet MAPPER and - - PowerPoint PPT Presentation

Artworks and Articles Meet Artworks and Articles Meet MAPPER and Persistent MAPPER and Persistent Homology Homology

Presented by Alicia Ledesma Alonso and Hongyuan Zhang

Presentation design adapted from slidesgala.com https://slidesgala.com/sheldon/

Why TDA? Why TDA?

• Coordinate freeness
• Deformation invariance
• Compressed representations

• Topology and topological

spaces

• Distance and metrics
• Simplicial Complex
• Persistent Homology

Topology Topology

Cleaned/Filtered data Cleaned/Filtered data Raw Data Raw Data Analyze Analyze Persistent Homology Persistent Homology Mapper Mapper

Pipeline Pipeline

What is persistent homology What is persistent homology?

Filtration example Filtration example Barcodes Barcodes

Ideally, we can recover the topological features of the original data cloud from the resulting simplicial complex.

What is Mapper? What is Mapper?

Credit to: “A User’s Guide to Topological Data Analysis” by Elizabeth Munch

arXiv arXiv

• arXiv Data
• arXiv online API and AmazonS3
• arXiv persistent homology
• Select random samples
• Identify persistent intervals
• Identify differences
• arXiv Mapper
• Color by academic categories
• Explore various lenses
• Compare

arXiv metric arXiv metric

How do we measure distance between two articles?

• L. Carlsson, G. Carlsson, and M.

Vejdemo-Johansson. Fibres of Failure: Classifying errors in predictive

• processes. arXiv e
• prints, February 2018.

arXiv Persistent Homology arXiv Persistent Homology - Dionysus Dionysus

arXiv Color Function arXiv Color Function

Met Met

• Met Data
• Official MET GitHub
• Met persistent homology
• Select random samples
• Identify persistent intervals
• Identify differences
• Met Mapper
• Identify subgroups
• Select significant features
• Compare

Met Metric Met Metric

Q: How to measure distance between two artworks? A: Mixed type of data->measure each type using different metrics For categorical features->Jaccard distance For numerical features->difference divided by max distance

Met Mapper Met Mapper

Statistical Analysis Statistical Analysis

Model Comparison Model Comparison

Model 1: “Is Public Domain” ~ “Drawings and Prints” Model 2: “Is Public Domain” ~ all variables Model Accuracy Scores (using Python Sklearn score() method): Model 1 52.17% Model 2 73.83%

Mapper is effective in guiding feature selection!

Met Persistent Homology Met Persistent Homology

[4, 5) is a relatively persistent interval for both groups in Dimension 1! Persistent Homology can help classification! comparing the number

• f persistent barcodes

and the distributions of variables

Thank you to Professor Marcos Ortiz for his mentorship, Grinnell College and the NSF for providing funding, and the Department of Mathematics and Statistics of Grinnell College for providing this opportunity.

Thank you!