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Prediction and dynamical reconstruction of non-stationary data with delay-coordinates embedding and support vector machine regression

The paper presents a new effective approach for the construction of local Support Vector Machine (SVM) regression models for the prediction of non-stationary data. We illustrate that an analysis in the framework of dynamical systems theory can provide critically useful parameters for the effective training of the SVM predictors. 
 
A correlation dimension parameter is approximated and is used in order to obtain an appropriate dimensionality for the input space of the predictive SVM. The presented prediction framework can be utilized both for continuous signals and for the case where the observable variable is a discrete symbol, a circumstance very common in data mining problems. Using the information extracted from the correlation dimension computation, local Support Vector Machine models are trained and they are used only for local predictions. 
 
We apply this methodology to the difficult problem of evaluating the predictability of DNA sequences. The results support the importance of the estimation of the proper dimensionality of the embedding space by means of the correlation dimension. Additionally, they demonstrate the effectiveness of the presented SVM based prediction approach that is formulated under a dynamical systems reconstruction framework.