Abstract:

Over the past five years, the witnessed capabilities of Topological Data Analysis (TDA) have elevated it from a specialized mathematical domain into a foundational enabling technology for the modern scientific data science community. By capturing the invariant “shape” of complex systems, TDA now serves as a robust and scalable regularizing-type methodology capable of modeling, integrating, and interrogating high-dimensional environments.

As DDDAS seeks to combine physics-based modeling with data-driven methods, TDA has shown the power to combine simulated data with collection measurements into a combined feature space to improve object recognition, materials awareness, and cyber analytics.  Among these contributions, TDA could be a sensor agnostic and scalable approach for dynamic digital twin technology.

This workshop demonstrates TDA-enabled technology by presenting multi-modal data fusion and deep network explainability as two comprehensive case studies. The first case study explores the Topological Data Analysis Machine Learning (TDAML) framework. Participants will be guided through the TDAML’s existing open-source Pythonic resources involving persistent homology, simplicial filtrations, and time-delay embeddings to construct finite dimensional topological feature engine spaces based on a taxonomy of stable TDA metrics. Throughout these demonstrations, attendees will witness the construction of TDA-based representations to physical systems collected in real world testing environments by transforming acoustic time-series, EO/IR video frames, and their fused data aggregates into topological signals amenable to custom Keras/TensorFlow networks for object classification. A selection of theoretical and implementation takeaways will be provided to reinforce the audience’s ability to reproductively incorporate TDAML type approaches into their R&D workflows in a productive and effective manner.

The second case study explores neural network architectures via the Topologically Aware Explainability (TopAX) workflow. The TopAX framework constructs activation-based Mapper graphs—utilizing UMAP data filtration and DBSCAN pre-image clustering—to inspect global feature manifold reorganization. By injecting Additive White Gaussian Noise (AWGN) into ResNet blocks or Vision Transformer layers, feature degradation is measured from the mapper graph using global Silhouette scores and topological sensitivity heatmaps in datasets such as ImageNet, aerial (UCM), and thermal infrared (FLIR) datasets.

Andreas Savakis (Rochester Institute of Technology – RIT) & Paul Schrader (Air Force Research Laboratory)

Andreas Savakis bio: Andreas Savakis is distinguished professor in the department of Computer Engineering at Rochester Institute of Technology (RIT). He received the B.S. and M.S. degrees in Electrical Engineering from Old Dominion University, and the Ph.D. in Electrical and Computer Engineering with Mathematics Minor from North Carolina State University. He was Senior Research Scientist with the Kodak Research Labs before joining RIT. At RIT he served as department head of computer engineering and director of the Center for Human-aware Artificial Intelligence (CHAI). He is the founder and director of the Vision and Image Processing Lab. His research interests include computer vision, deep learning, efficient and robust learning, explainable and responsible AI, human pose estimation and scene analysis.  Dr. Savakis has co-authored over 150 publications and holds 12 U.S. patents.  He is a Fellow of SPIE and has received the NYSTAR Technology Transfer Award for Economic Impact, the IEEE Region 1 Award for Outstanding Teaching, and the RIT Trustees Scholarship Award.

Paul Schrader bio: Dr. Paul T. Schrader is a Senior Research Mathematician for the Air Force Research Laboratory’s Information and Spectrum Warfare Directorate (AFRL/RF). A non-traditional student originally working for years in the wholesale distribution and welded fabrication industries, he received his BA (2011) and MS (2013) in mathematics from Cleveland State University where he began his SME studies in topological data analysis (TDA). In 2018 he obtained a PhD in mathematics from Bowling Green State University specializing in non-associative algebras and monoidal/tensor/modular categories. Prior to the AFRL/RF he was a tenure track Assistant Professor of Mathematics at Southern Arkansas University from 2018-2022. With multiple publications and patents pending in a variety of TDA, mathematics, math education, and AI/ML based mission relevant subjects, his current research includes the applications of TDA and other novel mathematical approaches to deployable modality/model agnostic data driven information fusion for collaborative/distributive/edge amenable autonomy in: target recognition and continuous custody, arbitrary tactical/strategic sensing grids, systems/materials/high-rate health monitoring, tactical/strategic situational/state awareness in terrestrial/maritime/aerial/cislunar OEs, network/data/cyber assurance, user uncertainty quantification, OOD detection and mitigation, battle/natural disaster damage assessment, and general dynamic data-driven applications systems/phenomena in DDIL/extreme environments.