2022/03/06 by Shan Shan, Ingrid Daubechies, Shan, Shan +1 · 1 citation
Computer Science · Engineering · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2203.02867
openalex publication_date 2022/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. The DM procedure consists in constructing a spectral parametrization for the manifold from simulated random walks or diffusion paths on the data set. 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 t. Experiments show that this principled approach is effective and robust.