Quality estimation of the electrocardiogram using crosscorrelation among leads
 Eduardo Morgado^{1},
 Felipe AlonsoAtienza^{1},
 Ricardo SantiagoMozos^{1},
 Óscar BarqueroPérez^{1},
 Ikaro Silva^{2},
 Javier Ramos^{1}Email author and
 Roger Mark^{2}
https://doi.org/10.1186/s1293801500531
© Morgado et al. 2015
Received: 16 February 2015
Accepted: 28 May 2015
Published: 20 June 2015
Abstract
Background
Fast and accurate quality estimation of the electrocardiogram (ECG) signal is a relevant research topic that has attracted considerable interest in the scientific community, particularly due to its impact on telemedicine monitoring systems, where the ECG is collected by untrained technicians. In recent years, a number of studies have addressed this topic, showing poor performance in discriminating between clinically acceptable and unacceptable ECG records.
Methods
This paper presents a novel, simple and accurate algorithm to estimate the quality of the 12lead ECG by exploiting the structure of the crosscovariance matrix among different leads. Ideally, ECG signals from different leads should be highly correlated since they capture the same electrical activation process of the heart. However, in the presence of noise or artifacts the covariance among these signals will be affected. Eigenvalues of the ECG signals covariance matrix are fed into three different supervised binary classifiers.
Results and conclusion
The performance of these classifiers were evaluated using PhysioNet/CinC Challenge 2011 data. Our best quality classifier achieved an accuracy of 0.898 in the test set, while having a complexity well below the results of contestants who participated in the Challenge, thus making it suitable for implementation in current cellular devices.
Keywords
Background
The electrocardiogram (ECG) signal is a standard clinical tool for diagnosis and monitoring of cardioelectrical function. The ECG measures the electrical activity of the heart using different electrode lead configurations, placed on the body surface of the patient. Clinical interpretation of the ECG requires waveform data of high quality. However, ECG signals are commonly distorted by artifacts, both physiological (muscular activity, patient motion) and nonphysiological (electromagnetic interference, cable and electrode malfunction) in nature [1]. Thus, automatic estimation of ECG quality is of paramount importance, particularly in telemonitoring applications where the ECG is commonly collected by untrained or inexperienced technicians; or even selfmonitoring applications, where the patient collects his ECG following some basic instructions. TeleECG applications will make a difference in developing countries lacking adequate primary care capacity. In such scenarios, automatic realtime assessment of ECG quality is required in order to alert the technician about the need to repeat the ECG while the patient is still present. This task could be performed by current cellular terminals (smartphones) able to capture and to instantaneously estimate the quality of the ECG [2].
Performance comparison of ECG signal quality algorithms
E1  E2  E3  

Physionet/CinC Challenge (accuracy scores)  
Xia et al. [3]^{a}  0.932  0.914  0.845 
Clifford et al. [4]  0.926  \(\)  \(\) 
Tat et al. [7]  0.920  \(\)  \(\) 
0.916  0.834  0.873  
Kalkstein et al. [5]  0.912  \(\)  \(\) 
0.908  \(\)  \(\)  
Zausender et al. [6]  0.904  \(\)  \(\) 
Noponen et al. [10]  0.900  \(\)  \(\) 
Moody [11]  0.896  0.896  0.802 
0.880  0.880  0.791  
Langley et al. [12]  0.868  0.868  0.814 
Chudacek et al. [14]  0.828  0.833  0.872 
Other studies (accuracy score in the test set^{b})  
Clifford et al. [16]  0.970  
Xia et al. [1]^{c}  0.951  
Langley et al. [19]  0.914 
Rulebased methods also provided remarkable results [1, 3, 7, 8, 10–14, 17, 19, 20], being the set of computed ECG parameters the main difference among these studies. Xia et al. [1, 3] reached the highest score of the competition, 0.932 in event 1. They combined different features, such us flat baseline detection, missing lead identification, and auto and cross correlation among ECG signal leads. Tat et al. [7] scored 0.92 in event 1 by combining QRS parameters, flat line detection, noise detection and ECG amplitude distribution measurements. Hayn et al. [8, 17] used basic signal properties (amplitude, saturation and flat baseline), number of crossing points between leads, and QRS quality metrics. Hayn et al. scored 0.916 in event 1 and 0.873 (1st place) in event 3. Jekova et al. [9, 18] proposed an algorithm based on scoring the noise level by analyzing the ECG amplitude and slopes in different frequency bands. They attained a score of 0.908 in event 1. Noponen et al. [10] estimated each lead signal as a linear combination of any other three leads, and the prediction residuals were used to assess the quality of the ECG. In addition to the residuals, they also included information about the amplitude variation of the ECG, achieving an accuracy of 0.90 in event 1. Moody [11] defined three simple heuristic rules based on ECG amplitude criteria. This algorithm attained a score of 0.896 in event 1. Johannesen et al. [13, 20] proposed a threshold detector based on ECG amplitude metrics (saturation, flat baseline) and the quantification of the noise content of the ECG which scored 0.88 in event 1. Langley et al. [12] used basic ECG amplitude metrics to develop an algorithm yielding an score of 0.868 in event 1. This work was later improved [19] by including QRS quality metrics and noise characterization achieving an accuracy of 0.914. Chudacek et al. [14] used five simple rules based on common ECG measurements (flat baseline, amplitude, baseline drift). They scored 0.828 in event 1 and a remarkable 0.872 in event 3 (2nd place).
Although the crosscorrelation among leads has been used as a single metric to classify the quality of the ECG, the structure of the covariance matrix of the ECG signal leads has not been explored in the scientific literature. The 12lead ECG signals are different projections of the same electrical activation process of the heart, and consequently the covariance matrix of the leads should have a particular structure. Crosscovariance of signals has been widely used in other signal processing applications, such as spectral estimation, antenna beamforming, equalization or pattern recognition, among many others. Also, it has been successfully used in ECG signal processing [24, 25], including data compression and filtering [26], STT segment analysis [27], and ventricular repolarization analysis [28].
The objective of this work is to provide a novel technique to classify the quality of the ECG signal based on the covariance matrix of the leads using a simple and computationally lowcost algorithm. Eigenvalues of the covariance matrix are fed into three different supervised binary classifiers: two tree inducers, namely CART [29], and C4.5 [30], and a propositional rule learner, namely RIPPER [31]. These algorithms are simple and provide useful interpretable models for the classification process, thus allowing us to gain better understanding about the relationship between data and the classification outcomes. To analyze the performance of the proposed methodology, we used the PhysioNet/CinC Challenge 2011 data [2], so the presented results can be compared to the work of challenge participants (Table 1) using the same database.
Methods
ECG collection
We used the PhysioNet/CinC Challenge 2011 data [2], which comprise a collection of standard 12lead ECG recordings (leads I, II, III, aVR, aVL, aVF, V1, V2, V3, V4, V5, and V6) with full diagnostic bandwidth (0.05 through 100 Hz). The recordings were collected using conventional ECG machines, instead of using the equipment originally planned, which was intended to replicate the conditions to record and transmit ECG from rural patients for their remote analysis [32]. The leads are recorded simultaneously for 10 seconds; each lead is sampled at 500 Hz with 16bit resolution. These signals were manually annotated by a group of 23 volunteers, giving each ECG a reference quality classification of Acceptable (AC) or Unacceptable (UN). ECGs signals are publicly available for download at Physionet database [32].
Note that ECG quality classification is not based on an objective quality metric, such as the SignaltoNoiseRatio, the percentage of detectable QRS waves, or the dynamic range among other possibilities. Instead, the annotated ECG quality classification was the result of a combination of subjective criteria that somehow tried to estimate the usability for clinical purposes of a given ECG. Volunteer annotators, having different levels of clinical knowledge, graded each ECG on a five letter scale: A (an outstanding recording with no visible noise or artifact; B (a good recording with transient artifact or low level noise that does not interfere with interpretation; all leads recorded well); C (an adequate recording that can be interpreted with confidence despite visible and obvious flaws, but no missing signals); D (a poor recording that may be interpretable with difficulty, or an otherwise good recording with one or more missing signals); or F (an unacceptably poor recording that cannot be interpreted with confidence because of significant technical flaws). Letter grades were mapped to numerical values (A = 0.95, B = 0.85, C = 0.75, D = 0.6, and F = 0), and scores from different annotators were averaged to a final value. An ECG was classified as AC if two or more grades were available, the average grade larger than 0.7, and no more than one grade was F. ECGs having an average lower than 0.7, were labeled UN.
Each of the ECGs available for the Challenge was randomly assigned to one of three groups: the training set A (Dataset A) containing 998 ECGs; the test set B (Dataset B) containing 500 ECGs used in events 1 and 2 of the Challenge [2], for which classification labels were withheld; and set C (Dataset C) containing 500 ECGs used in event 3 but not available to challenge participants.
ECG signal model
Lead signals in a standard 12lead ECG are computed in ECG equipment by linear combination of 9 signals captured by electrodes, so the rank of any data structure built from the 12 leads cannot be larger than 9. Moreover, the bipolar lead signals are constructed by using as reference a specific lead signal (for limb leads) or a combination of them (for precordial leads). Thus, the bipolar configuration of lead signals imposes the rank of the data structure defined on (2) to be equal or lower than 8. Consequently we have considered \(L=8\). We checked (simulations not shown) that the inclusion of the signals from leads III, aVR, aVL and aVF did not add any useful information to ECG quality estimation, but just added low level quantification noise generated internally by the ECG equipment.
Lead covariance
 1.
Form the XLead ECG data matrix, \(\mathbf X\), by stacking up the 8 rows containing K timesamples of the 8 leads.
 2.
Estimate the sample covariance matrix \(\hat{\mathbf {R}}_x= {1 \over K} \mathbf X \mathbf X^T\).
 3.
Compute the eigenvalues, \(\lambda _i\) from \(\hat{\mathbf {R}}_x\), for \(i=1, 2,\ldots , 8\).
During these computations and for the classification process, neither signals nor eigenvalues were scaled or normalized.
Machine learning algorithm
Given a training dataset \(\mathcal {D}=\{(\mathbf {x}_i,y_i)\}_{i=1}^M\), where \(\mathbf {x}_i=[\lambda _{1}^i,\ldots , \lambda _8^i]^T \in \mathbb {R}^8\) are the predictors of the ith record and \(y_i \in \{AC, UN\}\) denote its label, supervised binary classification [40] considers the selection of a model f in a space \(\mathcal {H}\) that minimizes a criterion (usually the classification error) on \(\mathcal {D}\) and provides good generalization (i.e., good performance on unseen data). Among the available methods to design classifiers, exploratorydataanalysis classification procedures were selected to give both an insight in data structure and to provide easytointerpret models. Namely, we selected two tree inducers, CART [29] and C4.5 [30], and a propositional rule learner, RIPPER [31]. While simple, these algorithms provide useful interpretable models for the classification process, allowing us to better understand the goodness and limitations of our approach regarding the available data. We have also included a SVM [41] classifier with a radial basis function kernel with the aim of comparing the above methods with a stateoftheart classifier.
Best machine learning practices were followed. Dataset A was divided into training and test blocks, where the test block was used once to provide an estimate of the accuracy. Model selection was done only on the training block. As data is scarce, 10fold crossvalidation was performed to estimate on Dataset A the accuracy, sensitivity (proportion of UN records classified as UN), specificity (proportion of AC records classified as AC) and the area under the receiver operating characteristics curve (AUC) for each classifier. Then, the best model was trained on the complete Dataset A and evaluated on Dataset B. Labels of Dataset B were not available and its predicted labels were sent to the Challenge organizers to get their classification accuracy.
Results
The behavior of the proposed classifiers has been analyzed by using the Dataset A, since this is the only data that provide both the ECG signals and their corresponding labels (AC, UN). First, we have carried out an exploratory analysis using the Dataset A. Then, we have estimated the performance of the proposed classifiers through crossvalidation using the Dataset A. Finally, we have tested our best classifier on the Dataset B (whose labels are withheld by PhysioNet/CinC Challenge 2011 organisers).
Exploratory analysis: analysis of eigenvalues and classification
Classifiers were induced with the WEKA [42] package using Dataset A. Note that no filtering of ECG signals was performed (except for mean subtraction) to compute the eigenvalues. A number of preprocessing algorithms (noise filtering) were evaluated [1, 10], showing no improvement in the classification performance.
CART classifier
C4.5 classifier
RIPPER classifier
Classification performance

Crossvalidation on Dataset A: 10fold crossvalidation results on Dataset A are shown in Table 3. AUC was obtained with the predictions on each testfold. If we consider accuracy, RIPPER performs the best in this dataset, if we consider AUC, C4.5 is the best and CART provides the most balanced result considering specificity and sensitivity. There is therefore no clear cut ranking for these classifiers as they were induced to maximize accuracy.

Testing on Dataset B: Considering the RIPPER our best classifier (in terms of accuracy), the predicted labels obtained by this classifier in Dataset B were sent to the organizer of the PhysioNet/CinC Challenge 2011 and obtained an accuracy of 0.898 (449 out of 500).
The complexity of the algorithm is the sum of the complexities of the calculation of the covariance matrix (\(8*L*K^2\) operations, see BLAS dgemm routine), the calculation of the eigenvalues of the covariance matrix (O(\(L^3\)) operations, see LAPACK dsyev routine) and the complexity of the classifier, which in the case of the above RIPPER classifier is only 5 comparisons and 2 logical operations, which is extremely fast [43, 44].
Conclusions
This paper presents a classification approach that combines linear signal subspace analysis (the eigenvalues of the covariance matrix) with interpretable machine learning. One of the strengths of the proposed approach is the interpretability of the results, which provide further insight into the ECG quality estimation problem and the shortcomings of our proposal.
The analysis of the eigenvalues of the Dataset A, shown in Figure 1, revealed that UN records have either simpler or richer signal spaces than the AC ones. That is, eigenvalues for UN records showed a bimodal distribution, having either small (\(\log _{10}(\lambda _i)\le  2\)) or large (\(\log _{10}(\lambda _i)\ge 2\)) eigenvalues, while for AC records the distribution of eigenvalues were more concentrated around their mean. The simpler signal space can be attributed to poorly connected or disconnected leads while the richer signal space is probably caused by external noise sources and artifacts. Given these differences in the eigenvalue distribution for UN and AC records, we also evaluated the condition number, \(\kappa =\frac{\lambda _1}{\lambda _8}\), of the sample covariance as a possible feature for classification. However, its introduction provided no improvement in performance over the set of eigenvalues because our classifiers looked for the best thresholds for each feature, which is equivalent to look for the best threshold on a quotient of two of the eigenvalues.
The classifiers decision rules and their errors also revealed new details of the classification problem and how our proposed methodology addressed it. The CART classifier (Figure 2) demonstrated a high accuracy, deciding on its first rule on the lowest eigenvalue (\(\lambda _8\)). This provides evidence suggesting that when a nonfullrank covariance matrix (\(\lambda _8 < T_1\)) is obtained there might have been some problems with the lead connections. In fact, the 6 AC ECGs that were wrongly classified as UN by this rule had one of the precordial leads to zero or to a constant value. The second CART rule decided on \(\lambda _1\), that for most AC cases is in the range \(3\le \log _{10}(\lambda _1)\le 5\). Many UN cases had larger \(\lambda _1\) values, which can be attributed to: (i) high noise or high power artifacts present on the record; and (ii) \(\lambda _1\) captures most energy, meaning that record is not rich enough or that the same noise/artifact is present in several leads (specially if it has high power). Figure 8a–c show three AC records classified as UN by this rule. Figure 8a represents one example of two high power artifacts in two leads. These artifacts dominate the energy of the signals and they contribute most to the first two eigenvalues. Figure 8b shows a common artifact that affects all but one lead, therefore the first eigenvalue is high as this single artifact dominates the energy of the ECG. However, classification error in Figure 8b may be an example of a mistake in the challenge database annotations, since only one lead contains usable information. Figure 8c shows a case with high frequency noise affecting several leads. This noise mainly affects the second eigenvalue. Also in this record, some of the leads have 5 times higher voltage than other leads, which is likely the cause of misclassification. Besides this, the CART classifier also presents other limitations: high energy artifacts and/or wandering baseline in some leads can make the classifier to wrongly reject a record classified as AC. Nevertheless, these limitations can be overcome, in part, by baseline removal and clipping, at the expense of more computational processing requirements.
With respect to CART, the C4.5 classifier produced a refinement for cases with large \(\lambda _1\). Figure 5a–c show some UN records wrongly classified as AC by C4.5. Whether noise or artifacts made the record labeled as AC or UN is unclear to the authors (the reader can compare the ECGs presented in Figures 5, 6, 7 and 8). On the other hand, the rule \(\lambda _1 \le T_2'\) showed another limitation of the proposed algorithm. Some UN records with low power noise were not easy to separate from AC records by just considering the power distribution of the different components of the signal space (see Figure 5c). The last rule for C4.5 relied on \(\lambda _6\). The rationale behind this last rule is again related to dimensional spaces. In a “perfectly clean” ECG, three eigenvalues are expected to be high (the ones related with the main components of the heartbeat), while the rest of the eigenvalues should be smaller. Therefore, if \(\lambda _6\) is above a threshold, this represents that there is too much energy out of the three main eigenvalues, which indicates several unexpected sources of noise. The sixth eigenvalue is selected for the last decision because the classifier learned from the training Dataset A the amount of perturbation (other signal/noise/interference sources) that is allowed to classify a record as AC. The limitations of the C4.5 classifier, e.g. UN records with several noise contributions that have similar signal spaces that AC records or records without a clear QRS pattern, could be alleviated with more processing by rhythmanalysis.
RIPPER ruleset, where \(\log _{10}(T_1^*) = 0.0863\), \(\log _{10}(T_2^*) = 4.85\), \(\log _{10}(T_3^*) = 4.06\), \(\log _{10}(T_4^*) = 5.09\) and \(\log _{10}(T_5^*) = 3.75\)
1  (\(\lambda _8 \le T_1^*\)) \(\Rightarrow\) Label = UN (143/6) 
2  (\(\lambda _1 \ge T_2^*\)) \(\wedge\) (\(\lambda _3 \ge T_3^*\)) \(\Rightarrow\) Label = UN (30/4) 
3  (\(\lambda _1 \ge T_4^*\)) \(\wedge\) (\(\lambda _2 \ge T_5^*\)) \(\Rightarrow\) Label = UN (47/19) 
4  Label = AC (778/34) 
Performance comparison of classifiers on Dataset A using 10fold crossvalidation. Alg., Acc., Sens., Spec. and AUC stand for algorithm, accuracy, sensitivity, specificity, and area under the ROC curve, respectively
Alg.  Acc. (%)  Sens. (%)  Spec. (%)  AUC 

CART  92.1  84.4  94.3  0.913 
C4.5  91.7  77.8  95.7  0.925 
RIPPER  92.7  83.1  95.5  0.910 
SVM  92.5  70.7  99.0  0.902 
As previously stated, most of the above mentioned shortcomings of the proposed classifiers could be mitigated in part by introducing additional steps to conveniently process the ECG signals. This, however would increase the computational cost of the algorithm. Moreover, labeling of some of the ECGs of Challenge database are borderline or errors. When analyzed in detail the errors of classifiers proposed herein, particularly those shown in Figures 5, 6, 7 and 8, it seems that our classifiers fail precisely in those borderline cases or those that are clear labeling errors. Also, our approach works on multilead recordings, while other studies developed methods suitable for singlelead recordings [4, 8, 16, 17].
Here, we present a simple, fast and reliable approach for ECG quality estimation that combines linear signal subspace analysis with machine learning. On the one hand, linear subspace analysis estimates the energy of the different ECG components; on the other hand, interpretable machine learning discovers how experts classify and provides simple and easy to understand decision rules. The understanding gained with the proposed approach, on how ECG quality is estimated by cardiologists, could be useful to design different algorithms. The result is a new ECG quality classifier with extremely low computational burden and, if we had submitted this classifier to the open source PhysioNet/CinC Challenge 2011, this classifier would have ranked second best (event 2, Table 1). Therefore, the proposed approach is particularly suitable for inexpensive portable ECG monitoring systems. A Java code implementing this approach can be found at https://github.com/obarquero/ECG_quality.
Declarations
Author’s contributions
EM analyzed the ECG data. FAA prepared the manuscript. RSM implemented the machine learning methods. OBP wrote the java software and helped to the ECG analysis. IS revised the manuscript and evaluated the algorithms using the Physionet/CinC Challenge data. JR and RM pro posed the theoretical quality estimation model. All authors read and approved the final manuscript.
Acknowledgements
This work has been partially supported by Research Grants TEC201346067R, TEC201348439C41R ,and TEC201019263 of the Spanish Government, and PRIN13_IYA12 of Universidad Rey Juan Carlos. R. SantiagoMozos is supported by the Juan de la Cierva Program (JCI201111150) of the Ministerio de Ciencia e Innovación of Spain. O. Barquero has the support of a FPU Grant (AP20091726) from the Ministerio de Educación of Spain. Roger Mark and Ikaro Silva were supported in part by NIH/NIGMS Grant R01GM104987.
Compliance with ethical guidelines
Competing interests The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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