Fifth International Symposium on Signal Processing and its Applications, ISSPA ‘99, Brisbane, Australia, 22-25 August, 1999 Organised by the Signal Processing Research Centre, QUT, Brisbane, Australia RECURRENCE PLOT FEATURES: AN EXAMPLE USING ECG David T. Mewett, Karen J. Reynolds, Homer Nazeran School of Informatics and Engineering, minders University of South Australia GPO Box 2100 Adelaide SA, Australia, 5001 (email: david.mewett@flinders.edu.au) ABSTRACT Electrocardiogram (ECG) signals are analysed using the nonlinear method of recurrence plots, which reveals subtle time correlations in time-domain signals. Large-scale features in the recurrence plots, which consist entirely of single dots, line segments of different orientations and white spaces, are directly related to time-domain features in the original signals. The relationship between recurrence plot features and time-domain features is easy to see for these ECG signals, and can be used to infer time-domain features of other signals (such as other bioelectric signals) that are more difficult to interpret due to their complexity. 1. INTRODUCTION The aim of this study was to demonstrate how features that can be clearly observed in a time-domain signal give rise to particular features in recurrence plots of the data. Originally proposed in the physics literature, recurrence plots are a nonlinear dynamical analysis method describing subtle time correlation information about a signal [l]. They have since been applied to a diverse range of biomedical data, including bioelectric signals [2]-[5], interval analysis [4], [6] and motion analysis [7]. However, little attention has been paid to the way in which large scale features of recurrence plots relate to specific features of the analysed signals. In this study, recurrence plot analysis was applied to electrocardiogram (ECG) signals which have clear time- domain features. 2. RECURRENCE PLOTS 2.1 Formal Definition Fundamental to the definition of recurrence plots is the idea that any scalar time series s(n) can be considered as the projection of a multivariate signal x(n) onto the single dimension that we observe. Consider, for example, the ECG which originates in 3 dimensions, yet each lead is only a 1- dimensional signal. Not all variables represented by x(n) are necessarily observable. By use of Takens and Maiib’s Embedding Theorem, we can create d-dimensional vectors y(n) from the original time series s(n) so that the evolution in time of y(n) follows that of x(n), even though the dimensions of x(n) and y(n) may differ [SI. The form of these vectors is: Lag Tis chosen as the value that gives the first minimum of the average mutual information (AMI) between s(n) and s(n + r) [9]. Embedding dimension d is the smallest dimension that gives no ‘global false nearest neighbours’; that is, the distance between y(n) and its nearest neighbour in dimension d is not increased too much by extending both vectors into dimension (d + 1) [8]. Two forms of recurrence plots, which we refer to as direct and relative forms, appear in the literature. Suppose that we have constructed N vectors y(n) from a given scalar time series. Then a direct form recurrence plot is a scatter plot of dots in an N x N square, where a dot at (id] indicates that y(i) is close to yo’) in d-dimensional space [ 13. Direct form recurrence plots contain a line of identity, since y(i) must be close to yo] if i =j. The test for whether two vectors are ‘close’ has been defined variously in terms of a required number of neighbours for each vector [l], or in terms of a threshold for the distance between vectors [3], [4] where the distance may be defined by different norms [6], [lo]. If a fixed threshold is used, then a direct form recurrence plot is symmetrical about its line of identity. A relative form recurrence plot is a modified form where a dot at (ij) indicates that y(i) is close to y(i +j) [3], [6]. In these plots, the vertical time index J is relative to the horizontal index I. Before interpreting any recurrence plot, care must be taken to ascertain whether it is in direct or relative form. 2.2 Alternative Interpretation While recurrence plots are strictly defined as above, they can also be understood based on more traditional signal processing concepts. The axes of the plot can be thought of as the time indices of two sliding windows I and J, similar to the time index for short-time Fourier transforms. For direct form recurrence plots, each dot (ij) indicates that windows I and J are similar, where the measure of similarity is whether vectors formed from the time-ordered windowed data are ‘close’. If I is considered the current window, then above the line of identity, J represents future windows; below, it represents past windows. In relative form plots, J only represents future windows. The data may be oversampled for the purposes of generating a recurrence plot; that is, the mutual information between successive samples may be too high. This can be remedied by downsampling the data within each window by a factor T, where T is a lag value corresponding to the first minimum of the average mutual information between s(n) and s(n + T) [9]. A global false nearest neighbours test [SI is then used to 175