# Singular-value decomposition in attractor reconstruction: pitfalls and precautions

@article{Pal1992SingularvalueDI, title={Singular-value decomposition in attractor reconstruction: pitfalls and precautions}, author={Milan Pal and Ivan Dvor̂ak}, journal={Physica D: Nonlinear Phenomena}, year={1992}, volume={55}, pages={221-234} }

## 105 Citations

Local Analysis of dissipative Dynamical Systems

- PhysicsInt. J. Bifurc. Chaos
- 2005

In this tutorial review, the local dispersion along with the surrogate testing is suggested to discriminate nonlinear correlations arising in deterministic and non-deterministic settings.

On reconstruction of strange attractors using their noise related directional properties

- PhysicsSignal Process.
- 2002

Estimating the correlation dimension of an attractor from noisy and small datasets based on re-embedding

- Computer Science
- 1993

Symplectic geometry spectrum analysis of nonlinear time series

- Computer ScienceProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2014

The effectiveness of SGSA in reconstructing and predicting two noisy benchmark nonlinear dynamic systems: the Lorenz and Mackey-Glass attractors are demonstrated and the applicability of the SGSA method in real-life applications is demonstrated.

Nonlinear Time-Series Analysis

- Computer Science
- 1998

An overview of the achievements and some present research activities in the field of state space based methods for nonlinear time-series analysis and a new approach for modeling data from spatio-temporal systems is presented.

Symplectic Principal Component Analysis: A New Method for Time Series Analysis

- Computer Science
- 2011

A novel principal component analysis (PCA) method based on symplectic geometry, called symplectic PCA (SPCA), to study nonlinear time series, and it is shown to be able to better represent nonlinear data, especially chaotic data, than PCA.

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