This document presents a method to classify cardiac data using multifractal feature extraction and symbolic representation. Multifractal Detrended Fluctuation Analysis (MFDFA) is used to analyze RR interval time series data and determine Holder exponents. Symbolic representation then assigns letters to exponent values to create word vectors of varying lengths. The frequency of words is analyzed using classification models to distinguish normal sinus rhythm from cardiac arrhythmias. Results found that using a 6-letter alphabet and word lengths of 3-6 letters achieved average classification accuracies of 89.7-94.6%, demonstrating the potential of this method for alternative cardiac diagnosis and risk assessment. Future work involves classifying multiple types of arrhythmias.

1. • To develop a classification method used to
distinguish cardiac arrhythmias from normal sinus
rhythm.
• Fractal properties of IBI can be used to classify
cardiac data and aid in diagnosing heart conditions.
Multifractal Detrended Fluctuation Analysis (MFDFA)
• RR interval time series is segmented
into a moving window at different time scales to
create n partitions.
• Time- and scale-dependent root-mean-square
(RMS) values are found using a linear fit applied at
each window and partition.
• Local scaling exponents (Holder exponents) were
determined by finding the slope of a log-log plot
of the RMS values and scale at each time point.
Symbolic Representation (Bag-Of-Words)
• From the newly acquired Holder time series, each
point is assigned to a letter defined by its location
on the series’ probability density function. [5]
• Frequency of occurrence is recorded for each
permutation of letter vectors (words) of specified
lengths.
• It has been shown that signal complexity
can be used as an indicator for
disease and aging. [1]
• Cardiac inter-beat interval fluctuations (IBI)
signal loses its complexity when the heart is in a
diseased state, such as cardiac arrhythmias. [2]
• One measure of complexity is through
fractal properties.
• Fractals are patterns that exhibit self similarity
over different time scales.
• Simple fractal signals can be described by a single
scaling exponent (monofractal). Complex signals
exhibit a spectrum of exponents (multifractal).
[1] A. Goldberger, L. Amaral, J. Hausdorff, P. Ivanov, C. Peng and H. Stanley, "Fractal dynamics in physiology: Alterations with disease
and aging“, Proceedings of the National Academy of Sciences, vol. 99, no. 1, pp. 2466-2472, 2002.
[2] M. Saeed, "Fractals Analysis of Cardiac Arrhythmias", The Scientific World JOURNAL, vol. 5, pp. 691-701, 2005.
[3] A. Goldberger, "Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside", The Lancet, vol. 347,
no. 9011, pp. 1312-1314, 1996.
[4] E. A. F. Ilhen, "Introduction to Muiltifractal Detrended Fluctuation Analysis in Matlab“, Frontiers in Physiology, vol. 3, 2012.
[5] J. Lin and Y. Li, "Finding Structural Similarity in Time Series Using Bag-of-Patterns Representation," Springer-Verlag, Berlin, 2009.
Classification of Cardiac Data based on
Multifractal Feature Extraction
Prateek Mathur1,2, Hamidreza Saghir MSc1,3, Tom Chau, PhD, P. Eng1,3,4
1Bloorview Research Institute, Holland Bloorview Kids Rehabilitation Hospital; 2Department of Electrical and Computer Engineering, McMaster University;
3Institute of Biomaterials and Biomedical Engineering, University of Toronto; 4Toronto Rehabilitation Institute
• Special thanks to the Ward Family Summer Student Research
Program, University of Toronto IBBME USRP, and NSERC USRA
for funding and facilitating this summer’s research.
• Thanks to Dr. Tom Chau, Hamidreza Saghir, Ka Lun Tam, and
the rest of the PRISM Lab for their insight and advice.
Background
References
• Results show MFDFA combined with symbolic
representation is a viable method to classify
cardiac data.
• These techniques have potential as alternative
diagnosis methods for cardiac conditions, and can
be used to assess a patient’s risk of cardiac event.
• Next steps involve developing classification
methods for multiple types of arrhythmias and
other cardiac conditions, allowing for more
targeted treatment.
Conclusions/Future Work
Methods
Objectives
• ECG recordings of 48 patients from MIT-BIH
Arrhythmia database and 18 patients from
MIT-BIH Normal Sinus Rhythm database.
[3]
d
c
b
a
• 3-6 letter alphabets were tested and classified
for word lengths of 2-6 letters.
• For each word length tested, a table of word
occurrences of each permutation is fed into a
binary linear classifier.
• Using 10-fold cross validation and word counts as
features, signals are classified as either normal
sinus rhythm or arrhythmia.
• Highest average classification accuracy was
obtained with a 6-letter alphabet (91.5%).
Classification/Results
6-Letter Alphabet
Word Length Accuracy Sensitivity Specificity
2 88.6 % 89.7 % 86.1 %
3 94.6 % 95.8 % 89.2 %
4 92.0 % 95.4 % 86.7 %
5 92.7 % 94.9 % 86.7 %
6 89.7 % 91.1 % 87.0 %
[4]
[4]
Dataset
Hypothesis
Acknowledgements
RR Interval
ECG Time Series
RR Interval RR Interval
Mike Borello / Wikimedia Commons / CC BY-SA 3.0 Retrieved from http://edumps.deviantart.com / CC BY-SA 3.0 User: Chris73 / Wikimedia Commons / CC BY-SA 3.0 BodyParts3D/Anatomography / Wikimedia Commons / CC BY_SA 2.1 jpUser: Prokofiev / Wikimedia Commons / CC BY-SA 3.0