Research & Projects
Topology & its prevalence in real-world data
Richard M Levenson , Yashbir Singh , Bastian Grossenbacher-Rieck, Quincy Hathaway, Colleen Farrelly, Jennifer Z Rozenblit, Prateek Prasanna, Bradley Erickson, Ashok Choudhary, Gunnar Carlsson, Deepa Deepa
We review the quantification of topological uncertainty in AI applications for medical imaging, highlighting the importance of understanding spatial, structural, and shape-related characteristics in imaging data. Further, we explore various types of uncertainties, such as measurement and model uncertainties, and evaluate current methodologies for managing these uncertainties to improve diagnostic accuracy and treatment planning. Our review emphasizes the need for standardized frameworks and robust methods to ensure the reliable and ethical deployment of AI in medical settings, suggesting avenues for future research to enhance AI's clinical utility.
Hrishi Patel, Colleen Farrelly, Quincy Hathaway, JR, Deepa Deepa, Yashbir Singh, Ashok Chaudhary, Yassine Himeur, Wathiq Mansoor and Shadi Atalls (2023)
Generative Adversarial Networks (GANs) have gained prominence in medical imaging due to their ability to generate realistic images. Traditional GANs, however, often fail to capture intricate topological features such as holes and connectivity components in real images. This study applies TopoGAN, a recently developed model tailored for medical imaging. TopoGAN dynamically learns and incorporates topological features like connectedness and loops, addressing a real-world medical data augmentation problem.
This workshop will explore the integration of Topological Data Analysis (TDA) techniques with current computational methods to advance medical data analysis, focusing on enhancing performance, generalizability, and explainability. By combining TDA with other computational approaches, such as deep learning, the event aims to tackle complex medical data challenges across various domains including disease diagnosis and personalized medicine. The workshop will serve as an interdisciplinary forum, bringing together professionals from mathematics, engineering, computer science, and medicine to discuss novel applications, share insights, and outline future directions in the field.
Topology & Machine Learning
Exploring novel adaptations of topological algorithms with the goal of enhancing effectiveness of generative AI and its role in improving variability of neural network training.
Developing software to apply TDA techniques to real-world datasets from various domains to implement fast versions of both distance and kernel calculations for pairs of persistence diagrams; contributing tools for the interpretation of persistence diagrams with goal to parallelize methods for machine learning and inference
Previous Talks:
Graph Neural Networks: A Comparitive Analysis (UT Austin)
Topological Graph Layer: Topology in NN's (UT Austin, Junior Applied Mathematics Seminar)
Introduction to Topological Data Analysis: Unvieling the Shape of Data (Austin Women in Data Science)
Appications of Topology (UT Ausitn, Junior Topology Seminar)
Hippocampal Spatial Rep, exhibit Hyperbolic Geometry that Expands with Experience (Computational Neuroscience Seminar, UT Austin)
A Topological Paradigm for Hippocampal Spatial Representation using Persistent Homology (Computational Neuroscience Seminar, UT Austin)
Topology in Neuroscience (UT Austin, Junior Topology)