Recurrence plots of experimental data: To embed or not to embed?

A recurrence plot is a visualization tool for analyzing experimental data. These plots often reveal correlations in the data that are not easily detected in the original time series. Existing recurrence plot analysis techniques, which are primarily application oriented and completely quantitative, require that the time-series data first be embedded in a high-dimensional space, where the embedding dimension $d_E$ is dictated by the dimension $d$ of the data set, with $d_E\text{⩾2d+1.}$ One such set of recurrence plot analysis tools, recurrence quantification analysis, is particularly useful in finding locations in the data where the underlying dynamics change. We have found that for certain low-dimensional systems the same results can be obtained with no embedding.