Abstract
Dynamical Systems Based Modeling (DSBM) is a method to decompose a multivariate signal leading to both a dimensionality reduction and parameter estimation describing the dynamics of the signal. We present this method and its application to EEG data sets of Petit-Mal epilepsies considering Shilnikov chaos as the underlying dynamic interaction. We demonstrate the power of this method compared to conventional decomposition methods like PCA and ICA. Since the fitting quality showed a strong correlation to the ictal phases of the signal, we performed a cross validation on seizure detection with a resulting specifity of 84% and sensitivity of 75%. By applying DSBM in a moving window setup we investigated the comparability of the obtained dynamic models and tested the hypothesis of Shilnikov chaos in terms of linear stability analysis for each of the investigated windows. Thereby we could corroborate the Shilnikov hypothesis for approx. 50% of the relevant windows.
Highlights
Dimensionality reduction of time-series data is often obtained by statistical methods, like principal component analysis (PCA) [1] or independent component analysis (ICA) [2]
Dynamical Systems Based Modeling is a methodology to simultaneously estimate the parameters of a system of ordinary differential equations from data and reduce the dimensionality of the data
As we propose the usage of Dynamical Systems Based Modeling (DSBM) instead of PCA [1] and ICA [2] for the dimensionality reduction of signals with strong deterministic parts, we present the projected trajectories of DSBM [with model assumption (10)], PCA and ICA as trajectories in phase space
Summary
Dimensionality reduction of time-series data is often obtained by statistical methods, like principal component analysis (PCA) [1] or independent component analysis (ICA) [2]. As these methods rely on statistical model assumptions, they are not optimal for settings, were deterministic dynamics govern the signal. Dynamical Systems Based Modeling (DSBM) [3] is a method integrating a deterministic model assumption into the dimensionality reduction process This approach is very useful in situations where one has higher-dimensional sensor data than modeling approaches, describing the underlying system, use. During absences the correlation dimension, an intrinsic measure for the dimensionality of the time-series data, drops to the value of three
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