@inbook{b279059463244fd9a5bc7ea113b173f4,

title = "Diffusion Maps: Using the Semigroup Property for Parameter Tuning",

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.",

author = "Shan Shan and Ingrid Daubechies",

note = "https://arxiv.org/pdf/2203.02867",

year = "2023",

doi = "10.1007/978-3-030-45847-8_18",

language = "English",

isbn = "978-3-030-45846-1",

series = "Applied and Numerical Harmonic Analysis",

publisher = "Springer",

pages = "409--424",

editor = "P. Flandrin and S. Jaffard and T. Paul and B. Torresani",

booktitle = "Theoretical Physics, Wavelets, Analysis, Genomics",

address = "Germany",

}