Applied and Numerical Harmonic Analysis
Diffusion Maps: Using the Semigroup Property for Parameter Tuning
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, 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