Extracting Qualitative States from Nonlinear Time Series Using Integration of Fuzzy c-Means and Hierarchical Clustering

A novel method combined fuzzy c-means (FCM) and hierarchical agglomerative clustering (HAC) is presented to extract the qualitative states from reconstructed phase space by considering the dynamical relations of underlying nonlinear system. The qualitative state, in which all points have similar properties, is characterized by three measures, linear density, temporal reachability, and stable degree, which are defined as the criteria of merging subclasses. The time series sampled from a classic nonlinear system, Lorenz system, and electroencephalogram (EEG) signals are used to test this method. The results show that the qualitative states can be efficiently distinguished from these time series by the proposed method.