Oguz Akbilgic^{1,2*}, John A. Howe^{3,4} and Robert L. Davis^{1}

*Correspondence: Oguz Akbilgic oakbilg1@uthsc.edu

1. UTHSC-ORNL Center for Biomedical Informatics, Memphis, TN, USA.

2. Department of Preventive Medicine, University of Tennessee Health Science Center, USA.

3. King Abdullah Petroleum Studies and Research Center, Riyadh, Saudi Arabia.

4. Risk Dynamics Consultancy, Istanbul, Turkey.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this research article, we apply clustering within the Symbolic Pattern Recognition (SPR) framework to problems related to classifying different clinical categories of atrial fibrillation by modeling the changes in electrical activity of the heart. SPR characterizes a sequential dataset by modeling the transition behavior exhibited by patterns of symbols; clearly, this technique requires continuous data to be discretized into a set of defined symbols. With SPR, we were able to find hidden patterns in electrocardiograms (ECG) recorded during normal sinus rhythm that allowed us to classify patients as having paroxysmal atrial fibrillation (PAF) vs. those that did not. Even without extensive tuning of the model, our correct classification rate of 80% is inline with other published models. Additionally, we were able to identify normal sinus rhythm ECGs of PAF patients when a PAF episode was imminent. Finally, we used SPR clustering to distinguish between episodes of atrial fibrillation which would end within one minute (spontaneously-terminating) vs. those which needed intervention to stabilize (sustained). These are very important considerations for clinical practitioners for several reasons. The ability to screen for, and diagnose, PAF even with no known history or ongoing episode would be invaluable. This is especially true as related to elderly patients whom are at greater risk from atrial fibrillation, many of whom undergo regular ECG screenings anyway. Secondly, early warning that a PAF episode is imminent can give caregivers the chance to prepare an appropriate intervention in advance. For certain patients, this could mean the difference between life and death. Lastly, it is recognized that intervention to stabilize atrial fibrillation is not always in the best interest in the patient. One consideration is how long the episode is expected to last; in many cases, it may be better to allow an episode to spontaneously terminate.

**Keywords**: Symbolic Pattern Recognition, clustering of sequential data, ECG, atrial fibrillation,
paroxysmal atrial fibrillation, cardiac arrhythmia, time series modeling

For the human heart to pump blood efficiently, the muscular layer (the myocardium) must be electrically stimulated and respond in a manner conducive to a rhythmic pattern of activation and deactivation; this is called normal sinus rhythm. However, there are many conditions that can disrupt normal cardiac rhythm. The general term for abnormal pumping speed and/or rhythm is cardiac arrhythmia, and there are many types and causes of arrhythmia. A necessary condition for the optimal rhythmic pumping is that the electrical signals need to propagate from the sinoatrial node throughout the myocardium in a periodic, systematic fashion.

One irregular pattern and/or rate of signal propagation and myocardium stimulation is called atrial fibrillation (AF). Atrial fibrillation is, in fact, the most prevalent abnormal heart rhythm condition with serious consequences [14]. In 2013, atrial fibrillation and atrial flutter together resulted in over 110,000 confirmed deaths [9]. As of 2014, about 2%-3% of the population were afflicted with AF [24].

While many people exhibit no symptoms from atrial fibrillation, it is a potentially serious condition; it can increase the risk of stroke, and even lead to heart failure, dementia, and death [15,18].

There are two broad approaches to treating atrial fibrillation: slowing the heart rate to normal (rate control) or correcting the rhythm to a normal sinus rhythm (rhythm control) [7]. Of course, there are often side effects and unwanted consequences of any medical intervention. Hence, one problem related to AF is accurately distinguishing between AF that will stop by itself shortly, called spontaneously-terminating AF, and sustained AF. In many cases of the former, medical intervention may not be necessary, or indeed may be harmful. Atrial fibrillation can be further classified into four types based on duration and frequency [6]:

- First Detected: first diagnosed episode
- Paroxysmal: recurrent episodes which cease without intervention before 7 days
- Persistent: recurrent episodes which last longer than 7 days
- Permanent: on-going episode

Neglecting newly detected AF, among patients with paroxysmal, persistent or permanent, about half of patients who experience atrial fibrillation end up being classified as permanent. The remaining patients are classified evenly between the persistent class, and as paroxysmal atrial fibrillation (PAF) [24]. Relatively longer episodes of PAF are associated with increasing risk of ischemic stroke [1,20,21]. Approximately 18% of PAF cases evolve into permanent AF within 4 years [4]. Unfortunately, accurate diagnosis of PAF can be difficult-especially when it occurs with short periods of time. Therefore, it is important to develop methods that can help identify PAF during normal sinus rhythm.

Quantitative diagnostic evaluation of atrial fibrillation can
use several techniques, including surface electrocardiogram
(ECG), transthoracic ECG, transesophageal ECG, exercise stress
test, and correlation of heart rate response to exercise. The
arrhythmia can be easy to visually identify in an ECG recording.
During normal sinus rhythm, the P wave, *QRS complex* (the triplet of deflections in the spike), and T wave should be
clearly visible, as seen in the bottom of Figure 1.

Figure 1 **:** **ECG During Atrial Fibrillation (Top) and Normal
Sinus Rhythm (Bottom).**

In 2001, a challenge was issued jointly by PhysioNet and Computers in Cardiology on the subject of applying data mining to the problem of predicting PAF. There were two events described in this challenge. In event 1, called PAF screening, the challenge was to correctly classify subjects into PAF and non- PAF groups. Separately, in event 2, called PAF prediction, the challenge was to determine for which ECG sets of PAF subjects a PAF episode was imminent of PAF. A detailed description of the challenge and summary of entrants and their classification/prediction performances can be found in [13]. The team of Schreier, Kastner, and Marko [19] obtained the best results for the first event, correctly classifying 82% of patients, and predicting 41/50 of the PAF episodes. In the second event, their performance was 71% and 20/28, respectively. Their technique used standard preprocessing techniques and statistical hypothesis testing procedures. More recently, in his thesis [10], Gilani used various feature selection/extraction/engineering and supervised classification techniques to develop models to classify atrial fibrillation and screen for PAF.

Several authors have analyzed the time interval between successive R-R peaks in the QRS complex in order to model AF. Krstacic et al. [12] used inductive machine learning by logic minimization to identify ratios of the interval which tended to precede onset of AF. Sun and Wang [23] applied a multilayer perceptron neural network and fuzzy support vector machine to several engineered features of the R-R interval data to distinguish between sustained and spontaneouslyterminating AF, with an accuracy rate over 90%. This work was an extension of their previous work, which used other structural characteristics of the QRS complex [22]. Alcaraz and Rieta [5] and Nilsson et al. [16] both analyzed the organization properties of the main atrial wave from ECGs to classify atrial fibrillation as sustained vs. spontaneously-terminating; both efforts resulted in approximately 90% correct classification of known cases in their respective testing sets, which came from the 2004 PhysioNet/Computers in Cardiology challenge [8,11].

**Objectives**

In this work, we implement a novel method called Symbolic
Pattern Recognition (SPR) [2] to identify underlying patterns
and signals of AF in normal sinus rhythm ECG recordings. The
SPR method is designed to model the pattern transition behaviour
of symbolic series. Therefore, in using SPR for clustering
of raw ECG data, we begin by applying a symbolic discretization
to the continuous ECG series into an alphabet of discrete
symbols. The discretized series is then composed into pattern
transition matrices that define the predicted behavior of the
series, given the observed patterns. SPR defines a procedure
whereas unsupervised clustering of series can be performed,
based on a similarity measure of these transition matrices.

In this research, we first apply Symbolic Pattern Recognition to cluster normal sinus rhythm ECG data and distinguish between people with and without PAF. Secondly, we use SPR clustering of R-R interval data to classify PAF episodes as sustained vs spontaneously-terminating, as well as to identify normal sinus rhythm ECGs for which an episode of PAF is imminent. The first example was originally presented as a poster at the Southern Regional Council of Statistics Summer Research Conference [3].

The Symbolic Pattern Recognition (SPR) framework of [2] is based on learning pattern transition behaviors in sequential data. Based on these probabilistic transition behaviors, the researcher can characterize and cluster series. For completeness, we've repeated some of [2] in this section.

**Learning pattern transition behaviour**

SPR aims to learn and model the pattern transition behavior
in a discrete series represented with *ns* unique symbols. To
do this, SPR looks for joint occurrences of observed patterns
of length *n _{p}* followed by a single symbol. For example, a
two-symbols pattern ba followed by

By observing the frequency with which these patterns
and transitions occur, we can infer the transition probabilities
governing how the series evolves. As an example, consider a
sample series *S={aabcabccbabcabcbaabc}*, defined over the
alphabet *{a, b, c}*. We see the pattern ab occurring five times,
always followed by a *c: {a|abc|abc|cb|abc|abc|ba|abc|}*. Table 1
shows the i-symbols pattern transition frequencies (*PTF _{i}*) and
probabilities (

Table 1
**: PTF _{2} and PTP_{2} for S.**

For a given series of length *n*, there are up to *n _{p}* pattern transition
matrices calculated, with

Table 2
**: Sparity Indices SI_{i} for S.**

In the SPR algorithm, we sequentially compute *PTP _{i}* and

1) set *i=1*

2) compute *PTP _{i}* and

3) if

Using the sparsity indices for *S* in Table 2, we set *n _{p}=2* when
the threshold is 0.5, but if

**Clustering with SPR**

By using the SPR framework to model pattern transition behavior,
we are essentially reducing a discrete series into a matrix of
pattern transition probabilities. Therefore, series with similar pattern transition behavior should exhibit similar *PTPs*. The
framework specifies a pattern transition similarity (*PTS*)
measure as a function of distance between a pair of PTPs. We
would like two identical series to have *PTS=0*, indicating perfect
similarity. To simplify the calculations, the *PTPs* should be the
same size with any missing pattern transition probabilities
zero-filled. After this zero-fill, we compute the *PTS* of two series
*D _{i}*and

For the *k ^{th}* pair of

Where *Npk* indicates the number of patterns in the kth *PTP*
matrices, and *Ns* is the length of the longest alphabet. The
distance *dist* *(PTP _{ik}* and

A logical extension of simple comparison, we can leverage the
PTS scores to perform unsupervised clustering of *m* discretized
series by computing and comparing *PTSs* for all pairs of series
under consideration. This results in an *m*x*m* symmetric matrix
with *PTS _{i,j}* being the distance between the

We return to our series *S* once again to demonstrate measuring
similarity and dissimilarity. We want to compare *S* to two series simulated
by SPR (see [2, Section3.3]): *S*=abcbaabcabccbabcabcb*
and *S**=bcbabcbaababcbababcc*. We simulated *S** using np=6,
while *S*** was simulated using *n _{p}=2*. Logically,

S | S* | S** | ||

PTS= | S | 0.00 | 0.43 | 4.08 |

S* | 0.43 | 0.00 | 3.99 | |

S** | 4.08 | 3.99 | 0.00 |

Visual inspection of the PTS matrix, and/or a visual representation
of it can guide researchers in developing clusters.
In addition to visual inspection, we can identify meaningful
patterns with statistical analysis of the *PTS* matrix.

In this section, we apply SPR clustering to two symbolically discretized ECG datasets. The first is from the 2001 Physio Net/Computers in Cardiology challenge and the second is from their 2004 challenge.

**Searching for finger prints of paroxysmal atrial fibrillation**

The data for this example is the training set of the PAF prediction database from the 2001 PhysioNet/Computers in Cardiology
challenge [11,17]. It consists of excerpts of two-channel
long-term Holter monitor ECG recordings, measured at a
frequency of 128Hz, from 75 individuals. Fifty of the patients,
whose 30-minute ECGs we'll annotate as NN, have not been
diagnosed with PAF; they are considered to be the control
group. ECG excerpts from the remaining 25 patients are categorized
into sets of three series:

**PAF _{E}**5-minute ECG recording during an episode of PAF

PAF_{P} and PAF_{N}ECGs were recorded during normal sinus rhythm.
The database is more thoroughly described in the challenge
summary [13].

To apply Symbolic Pattern Recognition, we first discretized each continuous ECG recording using an alphabet of five symbols. Because of the skewed nature of the data, we applied an equal-frequency discretization, rather than equal-width. Cutoff points for a sample ECG recording is shown in Table 3, and demonstrated visually on one second of a normal sinus rhythm ECG in Figure 2, showing the entire QRS complex.

Table 3
**: Equal-Frequency Discretization Rules for Sample
PAF ECG Recording.**

Figure 2 **:** **Equal-Frequency Discretization for Sample PAF
ECG Recording.**

After each ECG recording was individually discretized, we
computed pattern transition matrices for each series up to
PTP_{7}, and used this to build the partial pattern transition
similarity matrix comparing the NN and PAF_{N} series to PAF_{E}.
Overall computation time from loading data to creating the
similarity matrix took 20 minutes on a machine with a 2.8
GHz Intel quad core i7 processor and 16 GB 1600 MHz DDR3
memory using 4 workers on Matlab 2015b parallel computing.

This 75x25 matrix is too big to show here, but we show part
of it in Table 4. Average distances across all 25 PAF_{E} series are
shown in the last column of Table 4, and plotted in Figure 4.

Table 4
**: Partial Transition Similarity Matrix Comparing Normal
Sinus Rhythm ECGs to PAF ECGs.**

Figure 4 **:** **Average PTP Distances Showing the Decision Rule.**

We began our analysis by testing for the equality of the mean
of the NN and PAF_{N} average distances. The standard parametric
t-test rejected the null hypothesis with a p-value <0.001. Furthermore,
the nonparametric Mann-Whitney U test rejected
the null hypothesis that the observations come from the same
population with the same low p-value. We thus conclude that
the discretization and SPR clustering results in the two being
statistically different series with the ROC curve given in Figure 3.

Figure 3 **:** **ROC curve for classification of ECGs into Normal and PAF.**

By using a subjectively chosen cutoff point of 3.02, we can classify patients as either normal or with PAF. Applying the decision rule,

$$class=\{\begin{array}{c}Avg\left(dist\right)\ge 3.02Normal\\ Avg\left(dist\right)<3.02PAF\end{array}$$results in a classification accuracy of 80%, which is comparable to the best results from the PhysioNet challenge. The confusion matrix in Table 5 shows that most of the misclassified observations are false positives, with only 5 (6.67%) false negatives.

Table 5
**: Confusion Matrix Using the Decision Rule.**

We would have preferred to use the PhysioNet testing dataset mentioned in the challenge summary [11] to evaluate our decision rule. However, the autoscorer webpage is no longer available.

Nevertheless, our analysis with this small dataset suggests
that clustering with SPR can create a decision rule to detect
the underlying fingerprints of PAF even in ECGs recorded
during normal sinus rhythm. In fact, recall that our SPR similarity
matrix only included the PAF_{E}, PAF_{N}, and NN ECGs- the
PAF_{P} data from immediately preceding a PAF episode was
not used. This suggests the model is picking up on a subtle
long-term difference in the patterns of electrical stimulation
of the myocardium, implying success as a model to diagnose
PAF would not rely on an imminent episode.

In addition to the need to diagnose PAF from a normal
sinus rhythm ECG, it's important to be able to detect when a
PAF episode is imminent. In terms of this dataset, that means
distinguishing between PAF_{P} and PAF_{N}. However, when we
computed the pattern transition similarities between NN, PAF_{N},
and PAF_{P}, we were unable to distinguish between PAFP and
PAF_{N}. Visual inspection of Figure 5 shows that the mean of the
average distances are very similar, and there is a tremendous
amount of overlap in their 95% intervals.

Figure 5 **:** **Box Plots for Average PTP Distances Showing
the Decision Rule, Comparing NN, PAF _{N}, and PAF_{P}.**

In the next example, which focuses on a slightly different diagnostic problem, we see that we can distinguish between these two types of ECGs by applying a data transformation before a substantially different symbolic discretization.

**Differentiating between sustained and spontaneouslyterminating
atrial fibrillation**

The data for this example is from the PhysioNet/Computers
in Cardiology 2004 challenge [8,11]. It is composed of 1-minute
excerpts from ECGs-recorded at 128 Hz - of 30 patients
during AF episodes.

They are divided into three equally-sized groups:

**AF**_{Non}T AF that was not observed to have terminated for
the duration of the long-term recording, for at least an hour
following the excerpt

**AF**_{T1min} AF that terminated within one minute after the end
of the recording

**AF**_{T1sec} AF that terminated within one second after the end
of the recording

The data from PhysioNet included QRS annotations from an automatic detector, which we used to compute the R-R intervals. We then discretized the interval data using an alphabet of eight symbols according to the cutoff points in Table 6. Since R-R intervals associated with normal sinus rhythm typically vary between 0.6 and 1.2, we simply generated symmetric intervals around and within this range.

Table 6
**: Discretization Rules for AF R-R Interval Data.**

The same transformation and discretization was also applied
to the PAF and NN data from the previous example, using only
the final minute of each to be consistent with the AF data.
Again, we computed the SPR pattern transition matrices up to
PTP_{8}, then built a pattern transition similarity matrix comparing
the PAF_{N}, PAF_{P}, AF_{NonT}, AFT_{1min}, and AFT_{1sec} data (rows) to
the NN series (columns). Averaging the similarities for each
series across all 50 patients in the control group resulted in
the box plots shown in Figure 6.

Figure 6 **:** **Box Plots for Average PTP Distances, Comparing NN, PAF _{N}, PAF_{P}, PAF_{E}, AF_{NonT}, AFT_{1min}, and AFT_{1sec}.**

The right-most three box plots are from the 30 ECGs related to AF termination. As compared to the pattern transition behavior
in the control group, we see a clear difference between
the PAF and AF data, in that AF ECGs are less similar to normal
sinus rhythm ECGs. For all pairs of series, we computed the
Mann-Whitney U nonparametric test for the null hypothesis
of equal populations, with results shown in Table 7. We also
applied the parametric t-test for equal means; the results are
similar, so not shown here. We see that SPR clustering of the
discretized R-R intervals separates all abnormal ECGs from
the sinus rhythm ECGs. Additionally, we see that the PAF_{P}
and PAF_{N} data are significantly different; this is also visible in Figure 6. Thus, we conclude that we can detect in normal
sinus rhythm ECGs when a PAF episode is imminent, using
the R-R intervals.

Table 7
**: Mann-Whitney U-test for Equality of Populations for all
Series.**

The mean of the average distances for the sustained AF
records is approximately 9.57, while the averages for the
spontaneously-terminating AF are 9.29 and 9.22 for the 1-minute
and 1-second data, respectively. Merging the AFT_{1min} and
AFT_{1sec} data, we then performed a *t-*test to evaluate the null hypothesis that the sustained and spontaneously-terminating
AF series have the same underlying population mean; the
p-value of 0.001 forces us to reject the null hypothesis. The
Mann-Whitney U test for equal populations also rejected the
null hypothesis, with a p-value of 0.017. We conclude that
SPR clustering of the R-R interval data is able to distinguish
between sustained and spontaneously terminating AF.

In this research article, we have detailed how clustering within the Symbolic Pattern Recognition framework can classify and distinguish among different clinical categories of atrial fibrillation. In the first case, we analyzed the pattern transition behavior underlying discretized ECG recordings from patients during normal sinus rhythm, as well as during PAF episodes. Analysis with SPR was able to identify some underlying characteristics of PAF even in ECGs recorded during normal sinus rhythm that were only present in PAF patients. The pattern transitions during normal sinus rhythm were significantly more similar to those during PAF for patients that had been diagnosed with paroxysmal atrial fibrillation. We used the similarities to develop a simple classification rule that correctly classified 80% of patients in our dataset.

In the second case, we computed the sequence of intervals between R peaks in the QRS complex for the same data, plus another dataset composed of sustained vs. spontaneouslyterminating atrial fibrillation. After symbolic discretization and analysis of the pattern transition behaviors, we were able to distinguish between patients not diagnosed with any form of AF, patients experiencing sustained AF vs spontaneously-terminating AF, and PAF patients about to experience an episode of PAF. A critical next step in our work is to validate the per-formance of our method on a larger dataset.

One key learning from this study is that, while SPR is a powerful method for analyzing sequential data series, selecting the right symbolic discretization is the key to successful application of SPR. This is likely especially true in the health sciences; expert opinions from the field on discretization of continuous data may improve the accuracy of SPR-based analysis. We believe that the SPR framework has potential for quantitative analysis in healthcare and the clinical environment. For the specific types of atrial fibrillation modeled here, our models can be used for screening and diagnosis, guiding intervention decisions, and early warning during monitoring.

In predictive modeling, predictive variables may be continuous, binary, categorical, or sequential data. It is easy to incorporate the first three (age, gender, income level etc...) into models because they are represented by a unique value> for each subject. Conversely, representation of sequential data predictors (for example, systolic blood pressure records during surgery) as a unique value in predictive modeling is not a trivial task. Using simple descriptive statistics (average, standard deviation, quantiles, etc...) loses a substantial amount of information. Moreover, two series with same average values (and even variances) may be significantly different than each other in terms of the associated response outcomes. Instead of using basic descriptive statistics, we suggest that metrics from SPR - which incorporate pattern transition behavior of arbitrary length - could instead be integrated into these predictive models, and reduce information loss. In our examples, we obtained high classification accuracies, despite the fact that we did not use any patient characteristics (demographics, genetic risk factors, co-morbidities, etc...). We expect that the addition of such information into an AF classification model based on SPR would substantially increase the accuracy of our results.

Finally, the resulting predictive models could be embedded into wearable devices currently used to collect physiological data, such as a Holter monitor. An obvious benefit being that a real-time monitor could provide early warnings of the onset of adverse events, rather than simply recording them.

The authors declare that they have no competing interests.

Authors' contributions |
OA |
JAH |
RLD |

Research concept and design | √ | -- | -- |

Collection and/or assembly of data | √ | -- | -- |

Data analysis and interpretation | √ | √ | -- |

Writing the article | √ | √ | -- |

Critical revision of the article | √ | √ | √ |

Final approval of article | √ | √ | √ |

Statistical analysis | √ | √ | -- |

Editor: Feng Gao, Washington University School of Medicine, USA.

Received: 18-Oct-2016 Final Revised: 28-Nov-2016

Accepted: 16-Dec-2016 Published: 26-Dec-2016

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Volume 4

Akbilgic O, Howe JA and Davis RL. **Categorizing atrial fibrillation via Symbolic Pattern Recognition**. *J Med Stat Inform*. 2016; **4**:8. http://dx.doi.org/10.7243/2053-7662-4-8

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