1W-MINDS, Feb 13 2025: Ryan Murray, NCSU, A variational approach to studying dimension reduction...
Автор: Mark Iwen
Загружено: 2025-02-14
Просмотров: 130
Title: A variational approach to studying dimension reduction algorithms
Abstract: Dimension reduction algorithms, such as principal component analysis (PCA), multidimensional scaling (MDS), and stochastic neighbor embeddings (SNE and tSNE), are an important tool for data exploration, visualization, and subgroup identification. While these algorithms see broad application across many scientific fields, our theoretical understanding of non-linear dimension reduction algorithms remains limited. This talk will describe new results that identify large data limits for MDS and tSNE using tools from the Calculus of Variations. Along the way, we will showcase situations where standard libraries give outputs that are misleading, and propose new computational algorithms to mitigate these issues and improve efficiency. Connections with the celebrated Gromov-Wasserstein distance and manifold learning will also be highlighted. This talk will aim to be accessible to a broad mathematical audience.
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