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Bayesian Statistics, Topology, and Machine Learning for Complex Data Analysis

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Analyzing and classifying large and complex datasets are generally challenging. Topological data analysis, that builds on techniques from topology, is a natural fit for this. Persistence diagram is a powerful tool originated in topological data analysis that allows retrieval of important topological and geometrical features latent in a dataset. Data analysis and classification involving persistence diagrams have been applied in numerous applications. In this talk, I will provide a brief introduction of topological data analysis, focusing primarily on persistence diagrams, and a Bayesian framework for inference with persistence diagrams. The goal is to provide a supervised machine learning algorithm on the space of persistence diagrams. This framework is applicable to a wide variety of datasets. I will present applications in materials science, biology, and neuroscience.
 
Speaker’s Bio: Farzana Nasrin graduated from Texas Tech University with a Ph.D. in Applied Mathematics in August 2018. Her research interests span algebraic topology, differential geometry, statistics, and machine learning. Currently she is working as a post-doctoral research associate at UTK. Here she studies supervised and unsupervised machine learning methods on the space of persistence diagrams with applications to biology, biomedical imaging, EEG, and materials data. Her dissertation involves development of analytical tools for smooth shape reconstruction from noisy data and visualization tools for utilizing information from advanced imaging devices.
 

Last Updated: May 28, 2020 - 4:06 pm