Delay Vector Variance MATLAB Toolbox
The Delay vector variance (DVV) method uses predictability of the signal in phase space to characterize the time series. Using the surrogate data methodology, so called DVV plots and DVV scatter diagrams can be generated using the DVV method, as a test statistic, to examine the determinism/stochastisity and linearity/nonlinearity within a signal simultaneously. In DVV scatter diagram, the target variance values of the original signal is plotted against the averaged variance values, calculated over a number of iAAFT surrogates. As a result, for linear signals, the scatter diagram coincides with the bisector line and conversely for nonlinear signals, the scatter diagram deviates from bisector lineas shown in the attached document. The DVV method has been successfully applied to analyse the nature of biometric signals (EEG and fMRI).
The DVV Toolbox
A DVV toolbox for MATLAB is provided, which can be downloaded as a zip archive. The code is provided under the GNU General Public License (GPL).
Further Reading + References
- T. Gautama, D.P. Mandic, and M. M. Van Hulle, "The delay vector variance method for detecting determinism and nonlinearity in time series," Physica D, vol. 190, no. 3-4, pp. 167-176, 2004. [pdf]
- T. Gautama, D.P. Mandic, and M.M. Van Hulle, "Indications of nonlinear structures in brain electrical activity," Phys. Rev. E, vol. 67, 2003. [pdf]
- T. Gautama, D.P. Mandic, and M.M. Van Hulle, "Signal nonlinearity in fMRI: A comparison between BOLD and MION," IEEE Transactions in Medical Imaging, vol. 22, 2003. [pdf]
- D.P. Mandic, M. Chen, T. Gautama, M.M. Van Hulle, and A. Constantinides, "On the characterization of the deterministic/stochastic and linear/nonlinear nature of time series," Proceedings of Royal Society, vol. 464, 2008. [pdf]
- M. Chen, T. Gautama, and D. P. Mandic, "An assessment of qualitative performance of machine learning architectures: Modular feedback networks," IEEE Transactions on Neural Networks, vol. 19, pp. 183-189, 2008.
- D.P. Mandic, M. Golz, A. Kuh, D. Obradovic, and T. Tanaka, Eds., Signal Processing Techniques for Knowledge Extraction and Information Fusion, Springer, 2008. [Amazon]
- Y. Yuan, Y. Li, and D. P. Mandic, "Comparison Analysis of Embedding Dimension between Normal and Epileptic EEG Time Series," Journal of Physiological Sciences, vol. 58, no. 4, pp. 239-247, 2008. [pdf]
- D.P. Mandic and J. A. Chambers, Recurrent Neural Networks for Prediction , Wiley, 2001. [Amazon]