Optimal selection of parameters for nonuniform embedding of chaotic time series using ant colony optimization

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)790-802
Journal / PublicationIEEE Transactions on Cybernetics
Volume43
Issue number2
Publication statusPublished - Apr 2013

Abstract

The optimal selection of parameters for time-delay embedding is crucial to the analysis and the forecasting of chaotic time series. Although various parameter selection techniques have been developed for conventional uniform embedding methods, the study of parameter selection for nonuniform embedding is progressed at a slow pace. In nonuniform embedding, which enables different dimensions to have different time delays, the selection of time delays for different dimensions presents a difficult optimization problem with combinatorial explosion. To solve this problem efficiently, this paper proposes an ant colony optimization (ACO) approach. Taking advantage of the characteristic of incremental solution construction of the ACO, the proposed ACO for nonuniform embedding (ACO-NE) divides the solution construction procedure into two phases, i.e., selection of embedding dimension and selection of time delays. In this way, both the embedding dimension and the time delays can be optimized, along with the search process of the algorithm. To accelerate search speed, we extract useful information from the original time series to define heuristics to guide the search direction of ants. Three geometry-or model-based criteria are used to test the performance of the algorithm. The optimal embeddings found by the algorithm are also applied in time-series forecasting. Experimental results show that the ACO-NE is able to yield good embedding solutions from both the viewpoints of optimization performance and prediction accuracy.

Research Area(s)

  • Ant colony optimization (ACO), Attractor embedding, Nonuniform embedding, Phase space reconstruction, Time series

Citation Format(s)

Optimal selection of parameters for nonuniform embedding of chaotic time series using ant colony optimization. / Shen, Meie; Chen, Wei-Neng; Zhang, Jun et al.
In: IEEE Transactions on Cybernetics, Vol. 43, No. 2, 04.2013, p. 790-802.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review