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Applied and Numerical Harmonic Analysis

Diffusion Maps: Using the Semigroup Property for Parameter Tuning

Publication ,  Chapter
Shan, S; Daubechies, I
January 1, 2023

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.

Duke Scholars

DOI

Publication Date

January 1, 2023

Volume

Part F6

Start / End Page

409 / 424
 

Citation

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Shan, S., & Daubechies, I. (2023). Diffusion Maps: Using the Semigroup Property for Parameter Tuning. In Applied and Numerical Harmonic Analysis (Vol. Part F6, pp. 409–424). https://doi.org/10.1007/978-3-030-45847-8_18
Shan, S., and I. Daubechies. “Diffusion Maps: Using the Semigroup Property for Parameter Tuning.” In Applied and Numerical Harmonic Analysis, Part F6:409–24, 2023. https://doi.org/10.1007/978-3-030-45847-8_18.
Shan S, Daubechies I. Diffusion Maps: Using the Semigroup Property for Parameter Tuning. In: Applied and Numerical Harmonic Analysis. 2023. p. 409–24.
Shan, S., and I. Daubechies. “Diffusion Maps: Using the Semigroup Property for Parameter Tuning.” Applied and Numerical Harmonic Analysis, vol. Part F6, 2023, pp. 409–24. Scopus, doi:10.1007/978-3-030-45847-8_18.
Shan S, Daubechies I. Diffusion Maps: Using the Semigroup Property for Parameter Tuning. Applied and Numerical Harmonic Analysis. 2023. p. 409–424.

DOI

Publication Date

January 1, 2023

Volume

Part F6

Start / End Page

409 / 424