Neural networks for estimating intrinsic dimension Potapov, A; Ali, M K [Department of Physics, The University of Lethbridge, 4401 University Dr. W. Lethbridge, Alberta, T1K 3M4 (Canada)] 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; DATA PROCESSING; MATHEMATICAL MODELS; NEURAL NETWORKS; NONLINEAR PROBLEMS; TOPOLOGICAL MAPPING We consider the problem of feature extraction and determination of intrinsic dimensionality of observation data. One of the common approaches to this problem is to use autoassociative neural networks with a 'bottleneck' projecting layer. We propose a different approach in which a neural network performs a topological mapping that creates a nonlinear lower-dimensional projection of the data. The mapping preserves relative distances of neighbors. This technique can be efficiently implemented with the help of radial basis function networks, and it is significantly faster than training an autoassotiative network. We show that the proposed technique can be used for estimating the dimension of minimal mathematical model from time series data. United States 2002-04-01 English Journal Article Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 65; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevE.65.046212; (c) 2002 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); PBD: Apr 2002 Medium: X; Size: page(s) 046212-046212.7 https://doi.org/10.1103/PhysRevE.65.046212 [] 4 65 Journal ID: ISSN 1063-651X; PLEEE8; TRN: US03B6633001716 INIS 2010-12-31 20546257