Math Modeling Seminar: Geometric and Topological Approaches to Representation Learning in Biomedical Data

Geometric and Topological Approaches to Representation Learning in Biomedical Data

Dr. Smita Krishnaswamy
Assistant Professor
Department of Genetics, Yale School of Medicine
Department of Computer Science, Yale School of Applied Science and Engineering
Yale University

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Abstract:
High-throughput, high-dimensional data has become ubiquitous in the biomedical, health and social sciences as a result of breakthroughs in measurement technologies and data collection. While these large datasets containing millions of observations of cells, peoples, or brain voxels  hold great potential for understanding generative state space of the data, as well as drivers of differentiation, disease and progression, they also pose new challenges in terms of noise, missing data, measurement artifacts, and the so-called “curse of dimensionality.” In this talk, I will cover data geometric and topological approaches to understanding the shape and structure of the data.  First, we show how diffusion geometry and deep learning can be  used to obtain useful representations of the data that enable denoising (MAGIC), dimensionality reduction (PHATE), and factor analysis (Archetypal Analysis Network) of the data.  Next we will show how to learn dynamics from static snapshot data by using a manifold-regularized neural ODE-based optimal transport (TrajectoryNet). Finally, we cover a novel approach to combine diffusion geometry with topology to extract multi-granular features from the data (Diffusion Condensation and Multiscale PHATE) to assist in differential and predictive analysis. On the flip side, we also create a manifold geometry from topological descriptors, and show its applications to neuroscience. Together, we will show a complete framework for exploratory and unsupervised analysis of big biomedical data.

Speaker Bio:
Dr. Smita Krishnaswamy is an Associate professor in Genetics and Computer Science. She is affiliated with the applied math program, computational biology program, Yale Center for Biomedical Data Science and Yale Cancer Center. Her lab works on the development of machine learning techniques to analyze high dimensional high throughput biomedical data. Smita’s focus is on unsupervised machine learning methods, specifically manifold learning and deep learning techniques for detecting structure and patterns in data. She has developed algorithms for non-linear dimensionality reduction and visualization, learning data geometry, denoising, imputation, inference of multi-granular structure, and inference of feature networks from big data. Her group has applied these techniques to many data types such as single cell RNA-sequencing, mass cytometry, electronic health record, and connectomic data from a variety of systems. Specific application areas include immunology, immunotherapy, cancer, neuroscience, developmental biology and health outcomes. Smita has a Ph.D. in Computer Science and Engineering from the University of Michigan.

Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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The Math Modeling Seminar will recur each week throughout the semester on the same day and time. Find out more about upcoming speakers on the Mathematical Modeling Seminar Series webpage.