Analyzing and classifying large and complex datasets are generally challenging. Topology is a field of mathematics that mainly studies “shapes” and allows geometric objects to be deformed, stretched, and bent. Using machinery from topology we can summarize complex data in a compact and informative way. However, these summaries are not compatible with statistical and machine learning methods directly. In this talk, I will provide a brief introduction of how to detect shape patterns of data and produce topological summaries. A novel Bayesian inference to quantify the uncertainties of these summaries will also be presented. The beauty of this Bayesian inference is that it allows incorporating experts’ beliefs or historical data and in turn yields effective inference and machine learning schemes. Finally, I will present an application to filament networks data classification of plant cells.
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 holding an assistant professor position at UH Manoa in the Department of Mathematics. Before coming to UHM, she was working as a postdoctoral research associate funded by the ARO in mathematical data science at UTK. She has been working on building novel learning tools that rely on the shape peculiarities of data with application to biology, materials science, neuroscience, and ophthalmology. Her dissertation involves the development of analytical tools for smooth shape reconstruction from noisy data and visualization tools for utilizing information from advanced imaging devices.