Coarse-graining time series data: Recurrence plot of recurrence plots and its application for music

We propose a nonlinear time series method for characterizing two layers of regularity simultaneously. The key of the method is using the recurrence plots hierarchically, which allows us to preserve the underlying regularities behind the original time series. We demonstrate the proposed method with musical data. The proposed method enables us to visualize both the local and the global musical regularities or two different features at the same time. Furthermore, the determinism scores imply that the proposed method may be useful for analyzing emotional response to the music.