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Explore the theoretical foundations and practical applications of modern nonlinear dimensionality reduction techniques in this conference talk from Harvard's Center of Mathematical Sciences and Applications. Delve into stochastic neighbor embedding algorithms, including popular methods like t-SNE and UMAP, which have revolutionized data visualization and analysis of high-dimensional datasets. Examine the challenges these methods face, including limited theoretical understanding, interpretation difficulties, and parameter sensitivity issues. Discover recent theoretical breakthroughs that reveal the intrinsic mechanisms and large-sample limits of these algorithms, along with theory-informed guidelines for their reliable application in biological research. Learn about new algorithmic developments that address current limitations through improved bias reduction and enhanced stability. Gain insights into how these theoretical advances not only strengthen our understanding of nonlinear embedding methods but also create new opportunities for scientific discovery across various domains.
