MIA: Chad Giusti, What can persistent homology see?; Ann Sizemore, Topological data analysis

October 12, 2016

MIA Meeting:    • MIA: Chad Giusti, What can persistent...  

Chad Giusti
Warren Center for Network and Data Sciences
Complex Systems Group & Department of Mathematics
University of Pennsylvania

What can persistent homology see?

Abstract: The usual framework for TDA takes as its starting point that a data set is sampled (noisily) from a manifold embedded in a high dimensional space, and provides a reconstruction of topological features of that manifold. However, the underlying algebraic topology can be applied to data in a much broader sense, carries much richer information about the system than just the barcodes, and can be fine-tuned so it sees only features of the data we want it to see. I will discuss this framework broadly, with focus on few of these alternative viewpoints, including applications to neuroscience and matrix factorization.

Ann Sizemore
Functional Cancer Genomics
Broad Institute of MIT and Harvard

Primer: What is persistent homology?

Abstract: A fundamental question in big data analysis is if or how these points may be sampled, noisily, from an intrinsically low-dimensional geometric shape, called a manifold, embedded in a high dimensional “sensor” space. Topological data analysis (TDA) aims to measure the “intrinsic shape” of data and identify this manifold despite noise and the likely nonlinear embedding. I will discuss the basics of the fundamental tool in TDA called persistent homology, which assigns to a point cloud a count of topological features –roughly “holes” of various dimensions – with a measure of importance of each feature recorded in a “barcode” of the data to help distinguish the significant features from the noise.

For more information visit:
http://www.broadinstitute.org/mia

Copyright Broad Institute, 2016. All rights reserved.