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.
|Title of host publication||Theoretical Physics, Wavelets, Analysis, Genomics : An Indisciplinary Tribute to Alex Grossmann|
|Editors||P. Flandrin, S. Jaffard, T. Paul, B. Torresani|
|Publication status||Published - 2023|
|Series||Applied and Numerical Harmonic Analysis|