期刊
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
卷 36, 期 1, 页码 79-107出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2013.03.001
关键词
Diffusion distance; Graph Laplacian; Manifold learning; Dynamic graphs; Dimensionality reduction; Kernel method; Spectral graph theory
资金
- Air Force Office of Scientific Research STTR [FA9550-10-C-0134]
- Army Research Office MURI [W911NF-09-1-0383]
Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on some set of parameters. We analyze this type of data in terms of the diffusion distance and the corresponding diffusion map. As the data changes over the parameter space, the low dimensional embedding changes as well. We give a way to go between these embeddings, and furthermore, map them all into a common space, allowing one to track the evolution of X in its intrinsic geometry. A global diffusion distance is also defined, which gives a measure of the global behavior of the data over the parameter space. Approximation theorems in terms of randomly sampled data are presented, as are potential applications. (C) 2013 Elsevier Inc. All rights reserved.
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