Title :
A Second-Order Mapping PCA Based Intrinsic Dimension Estimate for Nonlinear Time Series
Author :
Huang, Xiaolin ; Ning, Xinbao
Author_Institution :
Key Lab. of Modern Acoust., Nanjing Univ., Nanjing
Abstract :
The delay vectors of nonlinear time series are mapped into a second-order space and the intrinsic dimension of the underlying dynamics is estimated by the saturation of the nonvanishing eigenvalues of the covariant matrix as the embedding dimension increases. This method needs less data and has certain noise resistant degree.
Keywords :
covariance matrices; delays; eigenvalues and eigenfunctions; nonlinear dynamical systems; nonlinear estimation; time series; covariant matrix; delay vector; intrinsic dimension estimation; noise resistant degree; nonlinear time series; nonvanishing eigenvalue; primary component analysis; second-order mapping; Algorithm design and analysis; Covariance matrix; Delay effects; Delay estimation; Eigenvalues and eigenfunctions; Matrix decomposition; Phase estimation; Predictive models; Principal component analysis; Time series analysis; ECG; Nonlinear time series; delay embedding; intrinsic dimension; saturating embedding dimension; second-order mapping PCA;
Conference_Titel :
Natural Computation, 2008. ICNC '08. Fourth International Conference on
Conference_Location :
Jinan
Print_ISBN :
978-0-7695-3304-9
DOI :
10.1109/ICNC.2008.119
