Reconstructing state spaces from multivariate data using variable delays
- 2 August 2006
- journal article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 74 (2), 026202
- https://doi.org/10.1103/physreve.74.026202
Abstract
We study two methods for constructing a nonuniform embedding for multivariate data. A nonuniform embedding is a state space reconstruction which is more flexible than the common delay coordinates with fixed delays since it contains variable delays. Using these methods, we can extract causal relationships among many variables in a more suitable way. We demonstrate that the proposed methods can give more precise predictions and simpler models than some previous methods.Keywords
This publication has 21 references indexed in Scilit:
- Multivariate phase space reconstruction by nearest neighbor embedding with different time delaysPhysical Review E, 2005
- Nearest neighbor embedding with different time delaysPhysical Review E, 2005
- Comparative study of embedding methodsPhysical Review E, 2003
- The Construction of Smooth Models using Irregular Embeddings Determined by a Gamma Test AnalysisNeural Computing & Applications, 2002
- Reconstructing embedding spaces of coupled dynamical systems from multivariate dataPhysical Review E, 2002
- MDL denoisingIEEE Transactions on Information Theory, 2000
- Takens embedding theorems for forced and stochastic systemsNonlinear Analysis, 1997
- Determining embedding dimension for phase-space reconstruction using a geometrical constructionPhysical Review A, 1992
- EmbedologyJournal of Statistical Physics, 1991
- Geometry from a Time SeriesPhysical Review Letters, 1980