Publications [#371294] of Ingrid Daubechies

Papers Published

1. Shan, S; Daubechies, I, Diffusion Maps: Using the Semigroup Property for Parameter Tuning, in Applied and Numerical Harmonic Analysis, vol. Part F6 (January, 2023), pp. 409-424 [doi]
   (last updated on 2026/01/14)

   Abstract:
   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.