Diffusion Maps: Using the Semigroup Property for Parameter Tuning

Shan Shan, Ingrid Daubechies*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review


Diffusion maps (DM) constitute a classic dimension reduction technique, for data lying on or close to a (relatively) low-dimensional manifold embedded in a much larger dimensional space. It consists in constructing a spectral parametrization for the manifold from simulated random walks or diffusion paths on the dataset. However, DM is hard to tune in practice. In particular, the task to set a diffusion time t when constructing the diffusion kernel matrix is critical. We address this problem by using the semigroup property of the diffusion operator. We propose a semigroup criterion for picking the “right” value for t. Experiments show that this principled approach is effective and robust.
Original languageEnglish
Title of host publicationTheoretical Physics, Wavelets, Analysis, Genomics : An Indisciplinary Tribute to Alex Grossmann
EditorsP. Flandrin, S. Jaffard, T. Paul, B. Torresani
Publication date2023
ISBN (Print)978-3-030-45846-1
ISBN (Electronic)978-3-030-45847-8
Publication statusPublished - 2023
SeriesApplied and Numerical Harmonic Analysis


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