期刊
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
卷 44, 期 3, 页码 759-773出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2015.06.008
关键词
Diffusion maps; Repeated eigendirections; Chemotaxis
资金
- Department of Energy Computational Science Graduate Fellowship (CSGF) [DE-FG02-97ER25308]
- National Science Foundation Graduate Research Fellowship [DGE 1148900]
- European Union [630657]
- Horev Fellowship
- National Science Foundation (CSE program) [1310173, 1309858]
- US AFOSR [FA9550-12-1-0332]
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1310173, 1309858] Funding Source: National Science Foundation
Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One such challenge is the existence of repeated eigendirections, which obscures the detection of the true dimensionality of the underlying manifold and arises when several embedding coordinates parametrize the same direction in the intrinsic geometry of the data set. We propose an algorithm, based on local linear regression, to automatically detect coordinates corresponding to repeated eigendirections. We construct a more parsimonious embedding using only the eigenvectors corresponding to unique eigendirections, and we show that this reduced diffusion maps embedding induces a metric which is equivalent to the standard diffusion distance. We first demonstrate the utility and flexibility of our approach on synthetic data sets. We then apply our algorithm to data collected from a stochastic model of cellular chemotaxis, where our approach for factoring out repeated eigendirections allows us to detect changes in dynamical behavior and the underlying intrinsic system dimensionality directly from data. (c) 2015 Elsevier Inc. All rights reserved.
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