In the information age, data has become critical to virtually every aspect of the human experience. Data-driven decision making has afforded humans increasing levels of utility, which in turn has driven a heavier reliance on data. Additionally, artificial intelligence and machine learning (AI/ML) are being applied to critical tasks (e.g., self-driving cars), despite being trained on subcollection of all the data that could be potentially found in the wild. As the volume and complexity of this data grows, it has become increasingly necessary for both the human and the AI to have frameworks capable of making sense of large, high-dimensional, incomplete, and noisy data sets.
Topological Data Analysis (TDA) is a rigorous framework that borrows techniques from geometric and algebraic topology, category theory, and combinatorics in order to study the “shape” of such complex high-dimensional data. Research in this area has grown significantly over the last several years bringing a deeply rooted theory to bear on practical applications in areas such as genomics, natural language processing, medicine, cybersecurity, energy, and climate change. Within some of these areas, TDA has also been used to augment AI and ML techniques.
We believe there is further utility to be gained in this space that can be facilitated by a workshop bringing together experts (both theorists and practitioners) and non-experts. Currently there is an active community of pure mathematicians with research interests in developing and exploring the theoretical and computational aspects of TDA. Applied mathematicians and other practitioners are also present in community but do not represent a majority. This speaks to the primary aim of this workshop which is to grow a wider community of interest in TDA. By fostering meaningful exchanges between these groups, from across the government, academia, and industry, we hope to create new synergies that can only come through building a mutual comprehensive awareness of the problem and solution spaces.
Entropic Hyper-Connectomes Computation and Analysis Michael G. Rawson
(paper TDAatSDM/2022/3 ) A Case Study on Bifurcation and Chaos with CROCKER Plots İsmail Güzel, Elizabeth Munch, and Firas Khasawneh
(paper TDAatSDM/2022/6 ) DBSpan: Density-Based Clustering Using a Spanner, With an Application to Persistence Diagrams Brittany Terese Fasy, David L. Millman, Elliott Pryor, and Nathan Stouffer
(paper TDAatSDM/2022/7 ) Topological Data Analysis for Anomaly Detection in Host-Based Logs Thomas Davies
(paper TDAatSDM/2022/8 ) Parallel coarsening of graph data with spectral guarantees Christopher Brissette, George Slota, and Andy Huang
(paper TDAatSDM/2022/9 ) TopoEmbedding, a web tool for the interactive analysis of persistent homology Xueyi Bao, Guoxi Liu and Federico Iuricich
(paper TDAatSDM/2022/10 )