Geometric and Topological Approaches to Representation Learning in Biomedical Data

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High-throughput, high-dimensional data has become ubiquitous in the biomedical 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, dimensionality reduction. Next we show how to combine diffusion geometry with topology to extract multi-granular features from the data 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. Finally we will show how to learn dynamics from static snapshot data by using a manifold-regularized neural ODE-based optimal transport. Together, we will show a complete framework for exploratory and unsupervised analysis of big biomedical data.  

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. Her 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.