title: Complex correlation measure: a novel descriptor for Poincaré plot.
abstract: BACKGROUND
  Poincaré plot is one of the important techniques used for visually representing the heart rate variability. It is valuable due to its ability to display nonlinear aspects of the data sequence. However, the problem lies in capturing temporal information of the plot quantitatively. The standard descriptors used in quantifying the Poincaré plot (SD1, SD2) measure the gross variability of the time series data. Determination of advanced methods for capturing temporal properties pose a significant challenge. In this paper, we propose a novel descriptor "Complex Correlation Measure (CCM)" to quantify the temporal aspect of the Poincaré plot. In contrast to SD1 and SD2, the CCM incorporates point-to-point variation of the signal.
  
  
  METHODS
  First, we have derived expressions for CCM. Then the sensitivity of descriptors has been shown by measuring all descriptors before and after surrogation of the signal. For each case study, lag-1 Poincaré plots were constructed for three groups of subjects (Arrhythmia, Congestive Heart Failure (CHF) and those with Normal Sinus Rhythm (NSR)), and the new measure CCM was computed along with SD1 and SD2. ANOVA analysis distribution was used to define the level of significance of mean and variance of SD1, SD2 and CCM for different groups of subjects.
  
  
  RESULTS
  CCM is defined based on the autocorrelation at different lags of the time series, hence giving an in depth measurement of the correlation structure of the Poincaré plot. A surrogate analysis was performed, and the sensitivity of the proposed descriptor was found to be higher as compared to the standard descriptors. Two case studies were conducted for recognizing arrhythmia and congestive heart failure (CHF) subjects from those with NSR, using the Physionet database and demonstrated the usefulness of the proposed descriptors in biomedical applications. CCM was found to be a more significant (p = 6.28E-18) parameter than SD1 and SD2 in discriminating arrhythmia from NSR subjects. In case of assessing CHF subjects also against NSR, CCM was again found to be the most significant (p = 9.07E-14).
  
  
  CONCLUSIONS
  Hence, CCM can be used as an additional Poincaré plot descriptor to detect pathology.
authors.affiliation: Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne, VIC 3010, Australia. c.karmakar@ee.unimelb.edu.au
authors.forename: Chandan K
authors.initials: CK
authors.lastname: Karmakar
authors.forename: Ahsan H
authors.initials: AH
authors.lastname: Khandoker
authors.forename: Jayavardhana
authors.initials: J
authors.lastname: Gubbi
authors.forename: Marimuthu
authors.initials: M
authors.lastname: Palaniswami
mesh_terms: D000368:Aged; D000465:Algorithms; D001145:Arrhythmias, Cardiac / Q000175:diagnosis* / Q000503:physiopathology*; D003627:Data Interpretation, Statistical; D003936:Diagnosis, Computer-Assisted / Q000379:methods*; D006339:Heart Rate; D006801:Humans; D066298:In Vitro Techniques; D008875:Middle Aged; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013223:Statistics as Topic
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