Solving nonstationary classification problems with coupled support vector machines.

Many learning problems may vary slowly over time: in particular, some critical real-world applications. When facing this problem, it is desirable that the learning method could find the correct input-output function and also detect the change in the concept and adapt to it. We introduce the time-adaptive support vector machine (TA-SVM), which is a new method for generating adaptive classifiers, capable of learning concepts that change with time.

Overembedding method for modeling nonstationary systems.

We propose a general overembedding method for modeling and prediction of nonstationary systems. It basically enlarges the standard time-delay-embedding space by inclusion of the (unknown) slow driving signal, which is estimated simultaneously with the intrinsic stationary dynamics. Our method can be implemented with any modeling tool.

Artificial neural network learning of nonstationary behavior in time series.

We refine and complement a previously-proposed artificial neural network method for learning hidden signals forcing nonstationary behavior in time series. The method adds an extra input unit to the network and feeds it with the proposed profile for the unknown perturbing signal. The correct time evolution of this new input parameter is learned simultaneously with the intrinsic stationary dynamics underlying the series, which is accomplished by minimizing a suitably-defined error function for the training process.

Learning persistent dynamics with neural networks.

Persistence is one of the most common characteristics of real-world time series. In this work we investigate the process of learning persistent dynamics by neural networks. We show that for chaotic times series the network can get stuck for long training periods in a trivial minimum of the error function related to the long-term autocorrelation in the series.

Nonstationary time-series analysis: accurate reconstruction of driving forces.

We propose a simple method for the accurate reconstruction of slowly changing external forces acting on nonlinear dynamical systems. The method traces the evolution of the external force by locally linearizing the map dependency with the shifting parameter. Application of our algorithm to synthetic data corresponding to discrete models of evolving ecosystems shows an accuracy that outperforms those of previous methods in the literature.