ORIGINAL ARTICLE Robust automated cardiac arrhythmia detection in ECG beat signals Victor Hugo C. de Albuquerque1 • Thiago M. Nunes2 • Danillo R. Pereira3 • Eduardo José da S. Luz4 • David Menotti5 • João P. Papa3 • João Manuel R. S. Tavares6 Received: 16 December 2015 / Accepted: 6 July 2016 / Published online: 19 July 2016 � The Natural Computing Applications Forum 2016 Abstract Nowadays, millions of people are affected by heart diseases worldwide, whereas a considerable amount of them could be aided through an electrocardiogram (ECG) trace analysis, which involves the study of arrhythmia impacts on electrocardiogram patterns. In this work, we carried out the task of automatic arrhythmia detection in ECG patterns by means of supervised machine learning techniques, being the main contribution of this paper to introduce the optimum-path forest (OPF) classifier to this context. We compared six distance metrics, six feature extraction algorithms and three classifiers in two variations of the same dataset, being the performance of the techniques compared in terms of effectiveness and effi- ciency. Although OPF revealed a higher skill on general- izing data, the support vector machines (SVM)-based classifier presented the highest accuracy. However, OPF shown to be more efficient than SVM in terms of the computational time for both training and test phases. Keywords ECG heart beats � Electrophysiological signals � Cardiac dysrhythmia classification � Feature extraction � Pattern recognition � Optimum-path forest 1 Introduction The automatic detection and classification of arrhythmias in electrocardiography-based signals (ECG) has been widely studied in the last years in order to aid the diagnose of heart diseases. One way to perform this type of test is to conduct a long-time recording of the cardiac activity of an individual in his/her normal routine in order to obtain a & João Manuel R. S. Tavares tavares@fe.up.pt Victor Hugo C. de Albuquerque victor.albuquerque@unifor.br Thiago M. Nunes tmnun@hotmail.com Danillo R. Pereira dpereira@ic.unicamp.br Eduardo José da S. Luz eduluz@gmail.com David Menotti menotti@inf.ufpr.br João P. Papa papa@fc.unesp.br 1 Laboratório de Bioinformática, Programa de Pós-Graduação em Informática Aplicada, Universidade de Fortaleza, Fortaleza, CE, Brazil 2 Centro de Ciências Tecnológicas Universidade de Fortaleza, Fortaleza, CE, Brazil 3 Departamento de Ciência da Computação, Universidade Estadual Paulista, Bauru, São Paulo, Brazil 4 Departamento de Computação, Universidade Federal de Ouro Preto, Ouro Prêto, MG, Brazil 5 Departamento de Informática, Universidade Federal do Paraná, Curitiba, PR, Brazil 6 Instituto de Ciência e Inovação em Engenharia Mecânica e Engenharia Industrial, Departamento de Engenharia Mecânica, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal 123 Neural Comput & Applic (2018) 29:679–693 https://doi.org/10.1007/s00521-016-2472-8 http://orcid.org/0000-0001-7603-6526 http://crossmark.crossref.org/dialog/?doi=10.1007/s00521-016-2472-8&domain=pdf http://crossmark.crossref.org/dialog/?doi=10.1007/s00521-016-2472-8&domain=pdf https://doi.org/10.1007/s00521-016-2472-8 reasonable amount of information about the individual’s heartbeats. However, the posterior task of analyzing such data may be tiresome and more prone to errors when interpreted by human beings, since there is a huge amount of information to be processed. In order to cope with such problem, several works have been carried out arrhythmia classification in EEG signals by means of machine learning-oriented techniques [1, 5, 14, 15, 18]. However, regardless of the classification algorithm used, some processing steps are crucial to design a reasonable approach to detect arrhythmia. The quality of classification when dealing with ECG signals is directly dependent on the preprocessing phase, which aims at filter- ing noise frequencies that might interfere with ECG signal [21]. After preprocessing, it is required to detect and segment each heartbeat of the ECG signal. In order to perform this task, an important step is the detection of the QRS complex (three deflections from ECG signal), specifically theR wave, since most part of the techniques for the detection and seg- mentation of heartbeats are based on the location of such deflection. Because of the steep angular coefficient and amplitude of the R wave, the QRS complex becomes more obvious than any other part of the ECG signal, being easier to be detected for later segmentation. The final step is the classification of ECG signals, which is usually accomplished in a supervised fashion. Support vector machines (SVMs) [1, 7–9, 13, 27, 29, 31] and artificial neural networks (ANNs) [6, 10, 12, 14, 20, 23, 28, 30, 32, 33] are among the most used machine learning techniques for this purpose. Other approaches such as linear discriminant analysis [5] and a hybridization of support vector machines and artificial neural networks [11] are also applied for heartbeat classification. However, one of the main short- comings related to the aforementioned pattern recognition techniques concern with their parameters, which need to be fine-tuned prior to their application over the unseen samples (test set). SVMs are known due to their good skills on gen- eralizing over test samples, but with the cost of having a high computational burden when learning the statistics of the training data, since each different kernel has its own parameters to be set up. ANNs are usually very fast for classifying samples, but its training step may be trapped in local optima, as well as it is not straightforward to choose a proper neural architecture. Based on such assumptions, Papa et al. [25, 26] pro- posed the optimum-path forest (OPF) classifier, which is a framework for designing classifiers based on graph parti- tions, being the samples (feature vectors) encoded by graph nodes and connected to each other by means of a prede- fined adjacency relation. A set of key nodes (prototypes) competes among themselves in order to conquer the remaining nodes offering to them optimum-path costs. This competition process generates a set of optimum-path trees rooted at each prototype node, meaning that a sample of a given tree is more strongly connected to its root than to any other in the forest. The OPF classifier has gained considerable attention in the last years, since it has some advantages over traditional clas- sifiers: (1) it is free of hard-to-calibrate control parameters; (2) it does not assume any shape/separability of the feature space; (3) it runs the training phase usuallymuch faster; and (4) it can take decisions based on global criteria. However, to the best of our knowledge, theOPF classifier has never been employed to aid the diagnosis of arrhythmias in heart rate bymeans ofECG signals so far. Therefore, themain contribution of this paper is to evaluate OPF effectiveness in ECG-based arrhythmia classification, being its results compared against some state- of-the-art pattern recognition techniques in terms of accuracy, computational time, sensitivity and specificity. Finally, another contribution of this work is to assess the performance of six different feature extraction methods in the aforemen- tioned context, mainly: the approaches proposed by Chazal et al. [5], Güler and Übeyli [10], Song et al. [29], Yu and Chen [32], You and Chou [33], and Ye et al. [31]. 2 Methodology In this section, we describe the methodology employed in this work. Initially, the MIT-BIH (Massachusetts Institute of Technology—Beth Israel Hospital Boston) arrhythmia database [19] is described addressing considerations of ANSI/AAMI standard EC57 [3], which standardizes the evaluation of computational tools for the classification of cardiac arrhythmia datasets. After that, the feature extrac- tion techniques used to generate the feature vectors are then described, followed by the description of the statistical parameters used to evaluate the performance of the clas- sifiers under comparison. 2.1 MIT-BIH arrhythmia database The MIT-BIH arrhythmia database is composed of signals from electrocardiography exams, being widely used to evaluate the performance of algorithms concerning the task of detecting arrhythmias [22]. The data consist of 48 records, 30 min long, taken from 24 h of ECG acquisition, being the samples obtained from two different channels. The signals were acquired from 47 patients between 1975 and 1979 at the laboratory of Arrhythmia Boston’s Beth Israel Hospital, which are aged between 23 and 89 years of which 22 females and 25males. The analog recordswere digitized according to a sampling rate of 360 Hz, and the heartbeats marked and manually classified by experts in 15 classes regarding the type of arrhythmia. The types of arrhythmia identified in the database are indicated in Table 1. 680 Neural Comput & Applic (2018) 29:679–693 123 Since the detection and segmentation of beats in ECG signals is not the main goal of this work, we have employed precomputed annotations of R waves provided by the database in order to accomplish the signal seg- mentation. In addition, 4 records derived from patients that make use of pacemakers that were discarded, following the recommendation of ANSI/AAMI standard EC57 [3], which also recommends to group the 15 classes reported in the database’s annotations into 5 classes (Table 1). Figure 1 depicts some ECG signals for each class, being class Q represented by 10 signals, and the remaining ones rep- resented by 100 signals. The signals were randomly picked up from the database. 2.2 Training and test set The database was partitioned into two sets of records in order to separate the patients in training and testing groups. The composition of both sets was based on the study of Chazal et al. [5], which proposed to separate the patients by balancing each heartbeat class, as presented in Table 2. Besides the division of heartbeats into 5 classes as defined in [3], it was also considered the classification of heartbeats proposed by Llamedo and Martı́nez [15], which divided the 5 classes proposed in [3] into three main classes: N, S and V. Classes F and Q, which are less significant, were added to class V. Table 1 Types of heartbeats presented in the MIT-BIH database grouped according to AAMI Standard AAMI class MIT-BIH original class Type of beat Normal (N) N Normal beat L Left bundle branch block beat R Right bundle branch block beat e Atrial escape beat j Nodal (junctional) escape beat Supraventricular ectopic beat (S) A Atrial premature beat a Aberrated atrial premature beat J Nodal (junctional) premature beat S Supraventricular premature beat Ventricular ectopic beat (V) V Premature ventricular contraction E Ventricular escape beat Fusion beat (F) F Fusion of ventricular and normal beat Unknown beat (Q) / Paced beat f Fusion of paced and normal beat Q Unclassifiable beat Fig. 1 MIT-BIH heartbeat signals grouped according to [3] Neural Comput & Applic (2018) 29:679–693 681 123 2.3 Feature extraction Six feature extraction approaches (associated with Dataset A–F) were chosen based on the work of Luz and Menotti [16], which performed a comparison among some of the most used approaches for such purpose, mainly: Discrete Wavelet Transform (DWT), Independent Component Analysis (ICA), Principal Component Analysis (PCA), as well as information about RR range/interspace, which is the distance between peaks of two successive R waves in an ECG signal. For each dataset, the following methods were considered in this work: • Dataset A—morphology of the signal and RR range [5]; • Dataset B—DWT [10]; • Dataset C—DWT [29]; • Dataset D—DWT, RR range and signal energy [32]; • Dataset E—DWT, ICA and RR range [33] and • Dataset F—DWT, ICA, PCA and RR range [31]. The distribution of heartbeats by class and feature extrac- tion approach considering the division of classes proposed by [3] is shown in Table 3, while Table 4 displays the same information considering the distribution into 3 classes proposed by [15]. In this Table Tb and nf stand for the number of heartbeats of the set and the number of features extracted by each technique, respectively. One can noticed the variation in the number of beats among the methods concerns with the feature extraction techniques that usually do not allow using the entire database. Samples located at the extremities of the signal, for instance, do not contain enough neighboring samples/segments to perform the proper feature extraction. Table 2 Composition of the training and test sets according to Chazal et al. [5] Set Records Training 101, 106, 108, 109, 112, 114, 115, 116, 118, 119, 122, 124, 201, 203, 205, 207, 208, 209, 215, 220, 223 e 230 Test 100, 103, 105, 11, 113, 117, 121, 123, 200, 202, 210, 212, 213, 214, 219, 221, 222, 228, 231, 232, 233 e 234 Table 3 Description of the experimental datasets according to AAMI classes [3] Dataset Feature extraction nf Hearbeat class Tb N S V F Q Training A [5] 155 45,747 940 3777 415 8 50,887 B [10] 19 45,845 943 3788 415 8 50,999 C [29] 21 45,825 943 3788 414 8 50,978 D [32] 13 45,844 943 3788 415 8 50,998 E [33] 31 45,511 929 3770 412 8 50,630 F [31] 100 45,844 943 3788 415 8 50,998 Test A [5] 155 44,181 1786 3218 388 7 49580 B [10] 19 44,238 1836 3221 388 7 49690 C [29] 21 44,218 1836 3219 388 7 49,668 D [32] 13 44,238 1836 3221 388 7 49,690 E [33] 31 43,905 1823 3197 388 7 49,320 F [31] 100 44238 1836 3221 388 7 49,690 Table 4 Description of the experimental datasets according to [15] Dataset Method Heartbeat class Tb nf N SVEB VEB Train A [5] 155 45,747 940 4200 50,887 B [10] 19 45,845 943 4211 50,999 C [29] 21 45,825 943 4210 50,978 D [32] 13 45,844 943 4211 50,998 E [33] 31 45,511 929 4190 50,630 F [31] 100 45,844 943 4211 50,998 Test A [5] 155 44,181 1786 3613 49580 B [10] 19 44,238 1836 3616 49,690 C [29] 21 4,4218 1836 3614 49,668 D [32] 13 44,238 1836 3616 49,690 E [33] 31 43,905 1823 3592 49,320 F [31] 100 44,238 1836 3616 49,690 682 Neural Comput & Applic (2018) 29:679–693 123 2.4 Optimum-path forest classifier Let D ¼ D1 [ D2 be a k-labeled dataset, where D1 and D2 denote the training and test sets, respectively. Let S � D1 be a set of prototypes of all classes (i.e., the key samples that best represent each samples class). The complete graph ðD1;AÞ is composed of nodes that represent samples in D1, and any pair of samples defines an edge in A ¼ D1 �D1 (Fig. 2a). 1 Additionally, let ps ¼ \s1; s2; . . .; sn; s[ be a path with terminus at node s 2 D1. Roughly speaking, the OPF classifier contains two dis- tinct phases, being the first one employed for training purposes, and the latter used to assess the robustness of the classifier designed in the previous phase. The training phase aims at building the optimum-path forest, and the test step classifies each test node individually, i.e. ,they are added to the training set for classification purposes only, and further removed. 2.4.1 Training step S� is an optimum set of prototypes when the OPF algorithm minimizes the classification errors for every s 2 D1. Such set S� can be found by the theoretical association between the minimum spanning tree (MST) and the optimum-path tree for fmax [2]. Briefly, the training is the process of finding the S� and an OPF classifier rooted at S�. The MST in the com- plete graph ðD1;AÞ (Fig. 2b) is represented by a connected acyclic graph whose nodes are all samples of D1, and the edges are undirected and weighted by the distances d between two adjacent samples. Every pair of samples is connected by a single path, which is minimum according to fmax. Hence, the minimum spanning tree contains one opti- mum-path tree for any selected root node. The optimum prototypes are the closest nodes of the MST with different labels in D1 (i.e., samples that fall in the frontier of the classes, as highlighted in Fig. 2b). Removing the edges between different classes, their adja- cent nodes become prototypes in S�. The OPF algorithm can define an optimum-path forest with minimum classi- fication errors in D1 (Fig. 2c). Soon after finding prototypes, the OPF algorithm is used, which essentially aims at minimizing the cost of every training sample. Such cost is computed using the fmax path-cost function, given by: fmaxðhsiÞ ¼ 0 if s 2 S þ1 otherwise; � fmaxðps � hs; tiÞ ¼ maxffmaxðpsÞ; dðs; tÞg; ð1Þ where hsi is a trivial path, hs; ti is the arc between the adjacent nodes s and t such that s; t 2 D1, d(s, t) denotes the distance between nodes s and t, and ps � hs; ti, is the 0.5 0.4 1.9 1.9 2.1 2.7 0.3 0.7 2.1 1.7 0.5 0.4 0.3 0.7 0.0 0.0 0.4 0.7 0.5 (c)(b)(a) 0.0 0.0 0.4 0.5 0.7 0.6 0.7 1.7 1.8 0.3 0.0 0.0 0.4 0.5 0.7 0.6 (e)(d) Fig. 2 a In the training step the training set is modeled as a complete graph, b a minimum spanning tree over the training set is computed (prototypes are highlighted), c optimum-path forest over the training set, d classification process of a test sample (in green), and e test sample classification (color figure online) 1 The edges are weighted by the distance between their correspond- ing samples/nodes. Neural Comput & Applic (2018) 29:679–693 683 123 concatenation of path ps with the arc hs; ti. One can note that fmaxðpsÞ computes the maximum distance between adjacent samples in ps when ps is not a trivial path. Roughly speaking, the OPF algorithm aims at minimizing fmaxðptÞ; 8 t 2 D1. 2.4.2 Classification step For any node t 2 D2, we consider all edges connecting t with samples s 2 D1, as though t were part of the training graph (Fig. 2d). Considering all possible paths from S� to t, OPF finds the optimum path P�ðtÞ from S� and labels t with the class kðRðtÞÞ of its most strongly connected prototype RðtÞ 2 S� (Fig. 2e). This path can be identified incremen- tally evaluating the optimum cost C(t): CðtÞ ¼ minfmaxfCðsÞ; dðs; tÞgg; 8s 2 D1: ð2Þ Let the node s� 2 D1 be the one that satisfies Eq. (2) (i.e., the P(t) in the optimum path P�ðtÞ). Given that Lðs�Þ ¼ kðRðtÞÞ, the classification simply assigns Lðs�Þ as the class of t. An error occurs when Lðs�Þ 6¼ kðtÞ. 3 Results and discussion In this section, we present the experimental results con- cerning the effectiveness and efficiency of each pair clas- sifier/feature extraction technique employed in this work. First of all, the OPF classifier is evaluated considering six distance metrics: Euclidean, Chi-square, Manhattan, Chi- squared and squared Bray–Curtis. After that, a comparison among OPF with the best metrics, support vector machines with radial basis function (SVM-RBF) and a Bayesian classifier (BC), is then presented. 3.1 Experimental analysis of optimum-path forest In this section, we evaluate the performance and the computational time of the OPF classifier using six distance metrics.2 The evaluation is performed considering the classification according to five [3] and three classes [15]. 3.1.1 Five-class problem Here, we present the results considering the experimental dataset divided into five classes. Table 5 displays the recog- nition rates obtained byOPFusing eachdistancemetric3 in the datasets defined by each feature extraction approach. We can observe that OPF with Manhattan distance obtained the best recognition rate with dataset D (91.21 %), and that is approximately 0.35 % higher than the second best result obtained with the Canberra distance metric (90.88 %), as well as 0.5 % higher than the result obtained with the squared Chi-squared metric (90.75 %). Additionally, the results using dataset D were the best for all employed distances, suggesting that the method pro- posed by Yu and Chen [32] might be a good feature extractor to be used together with OPF. In addition to the recognition rate, we also computed the sensitivity (Se) and specificity (Sp), as well as the harmonic mean (H) of these two parameters (Table 6). The best values of H considering class N were obtained using Canberra (0.78) and squared Chi-squared (0.78) distances and feature extractor C. The combination of squared Chi-squared metric and extractor C resulted in the best value of H for class S (0.60). In regard to classes V and F, Euclidean distance has provided the best results with feature extractor F. As to class Q, OPF did not classify any sample properly due to the following main factors: the non- concentrated distribution of samples from that class and the low representation of samples in the training and test sets (� 0.00015 % of the total number of samples). However, a high recognition rate not always reflects a satisfactory performance in terms of classes separation, once that only class N (patient without cardiac arrhythmia) represents � 90 % of all dataset. For instance, let us con- sider the case of Chi-square metric, which presented the best accuracy rates for feature extractor B (Table 5). The Table 5 OPF accuracy considering 5 classes Dataset Distance metric Euclidean (%) Chi-square (%) Manhattan (%) A 80.68 83.26 77.57 B 79.63 88.80 79.43 C 81.25 87.60 84.46 D 90.70 89.12 91.21 E 86.54 89.05 86.47 F 89.12 85.28 90.39 Dataset Distance metric Canberra (%) Squared Chi-squared (%) Bray–Curtis (%) A 77.93 76.14 79.81 B 80.51 80.61 87.69 C 84.90 82.63 76.55 D 90.88 90.75 88.90 E 86.53 86.62 81.79 F 86.60 85.70 78.41 The most accurate result is indicated in bold 2 For such purpose, we used the LibOPF library [24]. 3 The recognition rates were computed using the standard formula, i.e., the ratio of the number of correct classifications by the number of database samples and H the harmonic mean between sensitivity and specificity. 684 Neural Comput & Applic (2018) 29:679–693 123 good results of such metric did not lead us to a satisfactory performance in terms of classes separation, since it pre- sented low values for sensitivity and specificity for all classes, except for class N. This is due to the misclassifi- cation of most samples of classes S, V, F and Q, as belonging to class N, leading to a low harmonic mean (2 %). In order to clarify this, the confusion matrix related to feature extractor B and squared Chi-square metric was built, Table 7. From the data obtained, one can verify that the dataset is dominated by class N, which clearly influ- Table 6 Specificity, sensitivity and their harmonic mean considering the OPF classifier and the AAMI five-class categorization Metrics Dataset Heartbeat classes N S V F Q H—Se—Sp H—Se—Sp H—Se — Sp H—Se—Sp H—Se—Sp Euclidean A 066—085—054 002—001—097 084—078—091 055—038—097 000—000—100 B 050—086—035 005—002—097 056—041—090 001—001—098 000—000—100 C 074—085—066 031—018—095 084—078—091 014—007—097 000—000—100 D 073—096—059 030—018—099 084—075—097 007—004—099 000—000—100 E 065—092—050 006—003—098 076—062—097 029—017—097 000—000—100 F 074—093—062 022—012—099 091—086—097 031—018—097 000—000—100 Chi-square A 017—093—009 003—001—099 015—008—095 005—002—099 000—000—100 B 002—100—001 000—000—100 000—000—100 001—001—100 000—000—100 C 015—098—008 002—001—100 017—009—098 000—000—100 000—000—100 D 004—100—002 000—000—100 004—002—100 000—000—100 000—000—100 E 004—100—002 000—000—100 004—002—100 000—000—100 000—000—100 F 012—095—006 002—001—099 011—006—097 001—001—100 000—000—100 Manhattan A 066—081—056 003—002—095 086—082—090 051—035—096 000—000—100 B 046—087—031 006—003—097 051—035—090 001—000—099 000—000—100 C 076—088—066 031—018—097 085—078—093 013—007—098 000—000—100 D 071—096—056 023—013—099 085—075—098 008—004—099 000—000—100 E 064—092—048 006—003—098 075—061—097 023—013—097 000—000—100 F 072—095—058 010—006—099 090—083—098 034—021—098 000—000—100 Canberra A 071—081—063 047—031—098 080—073—087 025—015—096 000—000—100 B 042—088—028 005—003—098 045—029—091 002—001—099 000—000—100 C 078—088—071 056—039—096 084—077—093 016—009—099 000—000—100 D 071—096—057 026—015—099 085—075—098 011—006—099 000—000—100 E 064—092—049 007—004—098 076—062—097 024—014—097 000—000—100 F 064—092—049 007—004—099 083—071—098 009—005—095 000—000—100 Squared Chi-square A 065—080—056 006—003—097 081—076—086 037—023—097 000—000—100 B 048—088—033 004—002—098 053—037—091 001—001—098 000—000—100 C 078—085—072 060—044—095 085—078—093 022—012—097 000—000—100 D 073—096—060 032—019—099 085—075—097 009—005—099 000—000—100 E 065—092—050 006—003—098 076—062—097 027—016—097 000—000—100 F 069—090—056 020—011—099 087—079—098 008—004—093 000—000—100 Bray–Curtis A 051—086—036 018—010—098 057—041—090 016—009—098 000—000—100 B 005—098—002 000—000—100 000—000—098 000—000—100 000—000—100 C 055—083—041 008—004—096 057—043—088 001—000—099 000—000—100 D 002—100—001 001—000—100 000—000—100 000—000—100 000—000—100 E 036—090—022 005—003—098 044—028—096 006—003—096 000—000—100 F 053—085—039 003—002—096 054—038—091 021—012—098 000—000—100 The best values for the harmonic mean are indicated in bold. Notice the H, Se and Sp values are not divided by 100 due to the lack of space Neural Comput & Applic (2018) 29:679–693 685 123 enced all other classes. This can be confirmed by analyzing the results obtained for classes S, V, F and Q that had the majority of the samples misclassified as being from class N (first column of Table 7). Also, it is important to stress that the accuracy calculated in this work do consider unbalanced datasets [25]. 3.1.2 Three-class problem We have also evaluated OPF considering the three-class dataset division proposed by Llamedo and Matı́nez [15], where classes F and Q are merged into class V. Table 8 presents the accuracy results obtained considering the three-class problem. Once again, the best result was obtained with Manhattan distance and feature extractor D (91.42 %), as happened in the five-class problem (Table 5). Although some classes have been merged, we still have an unbalanced dataset. The aggregation of classes F and Q into class V has smoothed such problem, but class C still concentrates approximately 90 % of the samples. Table 9 presents the results obtained in terms of sensitivity, specificity and harmonic mean. Considering class N, Canberra and squared Chi-squared distances together with the feature extractor C presented the best values for the harmonic mean (H) (0.78). Addi- tionally, squared Chi-squared and the same feature extractor achieved the best result over class S. This may indicate that aggregation into 3 classes does not influence the measure H for classes N and S, the same values where obtained in the five-class problem (Table 6). In regard to class V, the best value ðH ¼ 0:88Þ was obtained with Euclidean and Manhattan distances over the feature extractor F. Therefore, the aggregation into three classes seemed to improve the results for the classes V, F and Q, which are now clustered into class V. Table 10 presents the OPF computational time (in sec- onds) for the training and test phases, being the fastest approaches the ones using Bray–Curtis and Manhattan metrics, since they are simpler to compute. It is important to highlight that these results are accompanied by a satisfactory classification performance, since OPF with Manhattan distance obtained generally very good classifi- cation results. 3.1.3 Comparative analysis of the classifiers considering the five-class problem In order to compare the performance of OPF over tradi- tional classifiers (SVM-RBF4 and Bayesian classifier), we considered only the two best distance metrics found in the previous section, i.e., Manhattan and squared Chi-squared distances. Therefore, we can summarize the techniques to be compared as follows: • OPF-L1: OPF with Manhattan distance; • OPF-SCS: OPF with squared Chi-squared distance; • SVM-RBF: support vector machines using RBF kernel;5 • BC: Bayesian Classifier. Table 11 shows the accuracy obtained for each feature extractor and classifier considering five classes of heart- beats. The most accurate technique was SVM-RBF with 94.09 % of classification accuracy, followed by OPF-L1, BC and OPF-SCS, which obtained 91.21, 90.95 and 90.75 % of classification accuracies, respectively, Table 7 Confusion matrix obtained for Chi-square and feature extractor B True class N S V F Q Predicted class N 44,115 1834 3209 350 7 S 27 0 2 4 0 V 76 0 7 32 0 F 19 2 3 2 0 Q 1 0 0 0 0 Table 8 OPF accuracy considering three classes Dataset Distance metric Euclidean (%) Chi-square (%) Manhattan (%) A 81.00 83.41 77.82 B 80.43 88.89 80.18 C 81.41 87.68 84.61 D 90.92 89.13 91.42 E 86.81 89.08 86.80 F 89.46 85.35 90.78 Dataset Distance metric Canberra (%) Squared Chi-squared (%) Bray–Curtis (%) A 78.29 76.43 80.20 B 81.21 81.46 88.48 C 85.18 82.84 76.88 D 91.07 90.94 88.92 E 86.84 86.90 82.11 F 86.87 85.94 78.73 The most accurate result is indicated in bold 4 SVM parameters were optimized through cross-validation procedure. 5 SVM implementation used was based on LIBSVM [4]. 686 Neural Comput & Applic (2018) 29:679–693 123 considering the feature extractor D. Additionally, Table 12 presents the sensitivity, specificity and harmonic mean results. From Table 12, one can realize that the best results in terms of harmonic mean were obtained for class N with SVM-RBF and feature extractor D (80.00 %). This result is about 2 % higher than the second best result obtained by OPF-SCS with feature extractor C (78.00 %). In regard to class S, the best classifier was OPF-SCS using feature extractor C, followed by SVM-RBF with 51 % of classi- fication accuracy, which achieved the best recognition rates for classes V and F. Table 9 Specificity, sensitivity and their harmonic mean considering the OPF classifier and the three-class categorization Metric Dataset Heartbeat class N S V H—Se—Sp H—Se—Sp H—Se—Sp Euclidean A 066—085—054 002—001—097 082—077—088 B 050—086—035 005—002—097 062—047—090 C 074—085—066 031—018—095 080—072—089 D 073—096—059 030—018—099 081—070—096 E 065—092—050 006—003—098 074—060—094 F 074—093—062 022—012—099 088 —082—094 Chi-square A 016—093—009 003—001—099 016—009—094 B 002—100—001 000—000—100 002—001—100 C 015—098—008 002—001—100 016—009—098 D 004—100—002 000—000—100 004—002—100 E 004—100—002 000—000—100 004—002—100 F 012—095—006 002—001—099 011—006—097 Manhattan A 066—081—056 003—002—095 083—080—086 B 046—087—031 006—003—097 056—041—090 C 076—088—066 031—018—097 081—072—091 D 071—096—056 023—013—099 081—070—097 E 064—092—048 006—003—098 073—060—094 F 072—095—058 011—006—099 088 —081—096 Canberra A 071—081—063 047—031—098 077—072—083 B 042—088—028 005—003—098 051—035—091 C 078—088—071 056—039—096 081—073—092 D 071—096—057 026—015—099 081—070—097 E 064—092—049 007—004—098 074—061—094 F 064—092—049 007—004—099 078—068—093 Squared Chi-square A 066—080—056 006—003—097 078—074—083 B 048—088—033 004—002—098 059—044—090 C 078—085—072 060—044—095 081—074—090 D 074—096—060 032—019—099 081—070—096 E 065—093—050 006—003—098 074—061—094 F 069—090—056 020—011—099 082—074—091 Bray–Curtis A 051—086—036 018—010—098 057—042—088 B 001—099—001 000—000—100 001—000—099 C 055—083—041 008—004—096 057—042—087 D 002—100—001 001—000—100 000—000—100 E 035—090—022 005—003—098 045—030—092 F 053—085—039 003—002—096 055—039—089 The best values for the harmonic mean are indicated in bold Neural Comput & Applic (2018) 29:679–693 687 123 Table 13 displays the mean execution times considering the training, testing and total time (training ? testing) required by each classifier.6 The fastest classifier in the training phase was the BC in all datasets, followed by OPF- L1. The OPF-SCS was faster than SVM-RBF in all datasets as well, except for dataset F, where SVM-RBF had the third best time. The excessive times of SVM-RBF were due to the grid search that is necessary to fine-tune its parameters. In the test phase, the best computational time was obtained by SVM-RBF (6.7 s), being almost 8 times faster than OPF-L1 (53.3 s), both with feature extractor D. The third fastest technique was OPF-SCS (131.3 s), while BC, despite being the fastest in the training phase, took 173 s to classify the samples. In resume, SVM-RBF was the fastest in the classification phase, followed by OPF-L1, OPF-SCS and BC. Usually, SVM is fast for classifying samples, since it only considers the support vectors for such purpose, while OPF may need to evaluate a considerable number of training samples for that. However, if we consider the total time, OPF-L1 was the most efficient technique, which may lead us to consider it as a very suitable classifier concerning the trade-off between low computational time and high recognition rate. Table 14 presents the confusion matrix related to SVM-RBF classifier in the five-class problem for the Dataset A [5]. It can be noted a confusion of class SVEB with class N, where only 37 (2 %) samples were clas- sified correctly for class SVEB. However, using the OPF-SCS classifier with Dataset C [29], the amount of samples correctly classified in the same class was around 43 %. Thus, to detect Cardiac arrhythmia, also known as cardiac dysrhythmia or irregular heartbeat, the accuracy over class SVEB is usually considered most important. As such, the OPF-SCS accuracy obtained for this class, which is much higher than the one of SVM-RBF, is of greater clinical relevance. 3.1.4 Comparative analysis of the classifiers considering the three-class problem In this section, we analyze the performance and computa- tional time of all classifiers considering the three-class Table 10 OPF computational time (in s) considering the three- class problem Distance metrics Euclidean Chi-square Manhattan Training Test Total Training Test Total Training Test Total A 445.18 682.89 1128.07 3230.23 1987.14 5217.37 335.07 584.79 919.86 B 145.53 173.48 319.01 416.65 6.57 423.21 54.50 94.53 149.03 C 142.70 177.63 320.34 464.50 102.25 566.74 55.19 97.24 152.43 D 128.90 132.96 261.86 299.52 2.74 302.26 40.09 53.07 93.15 E 172.76 181.13 353.89 650.34 14.66 665.00 80.58 108.42 189.00 F 317.86 444.96 762.82 2103.07 818.28 2921.35 219.07 360.48 579.55 Distance metrics Canberra Squared Chi-squared Bray–Curtis Training Test Total Training Test Total Training Test Total A 1479.33 1588.78 3068.11 1478.00 1588.67 3066.67 1143.30 1168.50 2311.81 B 187.74 161.54 349.28 189.63 183.48 373.11 43.35 0.06 43.41 C 203.89 225.74 429.63 204.11 230.33 434.44 104.88 118.07 222.96 D 130.45 142.55 273.00 132.00 136.51 268.52 35.22 6.01 41.22 E 297.03 198.04 495.07 299.07 227.00 526.07 150.78 125.34 276.12 F 969.35 997.24 1966.59 9682.9 976.22 1944.50 431.96 519.69 951.66 Best values are indicated in bold Table 11 Accuracy rates obtained considering AAMI five classes Dataset Classifier OPF-L1 (%) OPF-SCS (%) SVM-RBF (%) BC (%) A 77.57 76.14 88.21 80.69 B 79.43 80.61 84.06 79.52 C 84.46 82.63 89.82 81.37 D 91.21 90.75 94.09 90.95 E 86.47 86.62 87.06 86.82 F 90.39 85.70 87.12 89.14 The best accuracy value is indicated in bold 6 We have executed all techniques 10 times for statistical purposes. 688 Neural Comput & Applic (2018) 29:679–693 123 division proposed by [15]. Table 15 presents the recogni- tion rates for each pair classifier/feature extractor method, being the sensitivity, specificity and harmonic mean results displayed in Table 16. In regard to class N, the SVM-RBF classifier has obtained the best harmonic mean value with feature extractor D; meanwhile, OPF-SCS was the most accurate technique for class S using feature extractor C. These results are consistent with those obtained considering five classes. With respect to class V, three classifiers obtained the best harmonic mean values: SVM-RBC with feature extractor A, and OPF-L1 and BC with feature extractor F. However, in all these three cases, the values are followed by low sensitivity values for class S. Table 17 presents the mean computational time in sec- onds concerning all techniques. Once again, the lowest computational time for training was achieved by BC and followed by OPF-L1 for all datasets. Except for feature extractors C and F, where OPF took longer to train, SVM- RBF classifier was the most costly technique for training the samples. Relatively to the five-class problem, similar computational times could be observed for BC and OPF- based classifiers, evidencing the robustness of these clas- sifiers when dealing with different number of classes. As expected, the SVM computational time decreased, since we have less classes to be analyzed during the pair-wise comparison against them.7 Last but not least, SVM-RBF was the fastest technique for the classification phase, while OPF-L1 obtained the lowest execution time considering both training and test phases. Also, based on a similar analysis to the one carried out with the data in Table 14, it could be confirmed that also in the three-class problem, OPF-SCS is the most appropriate to identify the pathological classes, i.e., the ones with greater clinical interest. Luz et al. [17] considered only the Euclidean metric and obtaining highest accuracy rates of 90.7 and 90.9 % in the 3- and 5-class problems, Table 12 Harmonic mean, specificity and sensitivity obtained considering five classes and all classifiers Metric Dataset Heartbeat class N S V F Q H—Se—Sp H—Se—Sp H—Se—Sp H—Se—Sp H—Se—Sp OPF-L1 A 066—081—056 003—002—095 086—082—090 051—035—096 000—000—100 B 046—087—031 006—003—097 051—035—090 001—000—099 000—000—100 C 076—088—066 031—018—097 085—078—093 013—007—098 000—000—100 D 071—096—056 023—013—099 085—075—098 008—004—099 000—000—100 E 064—092—048 006—003—098 075—061—097 023—013—097 000—000—100 F 072—095—058 010—006—099 090—083—098 034—021—098 000—000—100 OPF-SCS A 065—080—056 006—003—097 081—076—086 037—023—097 000—000—100 B 048—088—033 004—002—098 053—037—091 001—001—098 000—000—100 C 078—085—072 060—044—095 085—078—093 022—012—097 000—000—100 D 073—096—060 032—019—099 085—075—097 009—005—099 000—000—100 E 065—092—050 006—003—098 076—062—097 027—016—097 000—000—100 F 069—090—056 020—011—099 087—079—098 008—004—093 000—000—100 SVM-RBF A 074—092—063 006—003—099 093—091—096 082—072—097 000—000—100 B 049—091—033 001—000—100 061—045—093 000—000—098 008—005—100 C 070—094—056 015—008—098 089—083—097 003—002—100 000—000—100 D 080—098—067 051—035—099 090—082—099 004—002—100 000—000—100 E 070—092—057 012—007—099 089—082—098 001—001—094 000—000—100 F 074—091—063 026—015—099 093—089—096 030—018—096 000—000—100 BC A 066—084—054 002—001—097 084—078—091 055—038—097 000—000—100 B 050—086—035 005—002—097 056—041—090 001—001—099 000—000—100 C 074—085—066 031—018—095 084—078—091 013—007—097 000—000—100 D 073—096—059 029—017—099 085—076—097 007—004—099 000—000—100 E 064—093—049 005—003—098 076—062—097 027—016—097 000—000—100 F 074—093—062 021—012—099 091—086—097 031—018—097 000—000—100 The best values are indicated in bold 7 LIBSVM implements the one-against-one method for multi-class tasks. Neural Comput & Applic (2018) 29:679–693 689 123 respectively, considering in both cases the extraction method proposed by [33]. However, the present work could improve the accuracy of OPF with Manhattan distance, obtaining 91.42 and 91.21 % in the 3- and 5-class prob- lems, respectively, for the same dataset and with compu- tational time inferior to the one achieved by Luz et al. [17]. This considerable increase in accuracy directly leads to a more accurate detection of pathological classes. As such, it is possible to identify more precisely a cardiac arrhythmia with the Manhattan distance than with Euclidean one. Again, it should be stressed that the aforementioned classes are of great importance for clinical analysis, and that the SVM classifier could not detect accurately enough the samples of these classes. Table 13 Mean computational time (in s) required in the AAMI five-class problem Dataset Classifier OPF-L1 OPF-SCS Train Test Total Train Test Total A 337.0 (1.6) 584.2 (0.7) 921.2 (1.8) 1487.2 (10.8) 1604.7 (12.4) 3091.9 (22.3) B 54.8 (0.7) 102.9 (13.4) 157.7 (13.7) 191.9 (2.4) 181.2 (4.0) 373.1 (3.6) C 55.5 (0.4) 95.1 (4.0) 150.6 (3.9) 206.9 (2.0) 242.5 (7.9) 449.4 (9.9) D 40.3 (0.2) 53.3 (7.3) 93.6 (7.2) 132.4 (0.8) 131.3 (4.9) 263.7 (5.4) E 81.1 (0.8) 115.1 (3.5) 196.2 (3.2) 302.2 (3.7) 223.8 (4.9) 525.9 (6.9) F 220.4 (2.1) 380.3 (6.9) 600.8 (6.1) 974.9 (6.7) 990.0 (3.4) 1964.8 (9.9) Dataset Classifier SVM-RBF BC Train Test Total Train Test Total A 2668.4 (26.2) 32.2 (6.7) 2700.6 (31.3) 62.9 (0.3) 1622.2 (8.6) 1685.2 (8.9) B 576.0 (474.0) 12.6 (1.7) 588.6 (472.3) 11.1 (0.2) 236.0 (2.7) 247.1 (2.8) C 195.3 (8.6) 6.9 (2.1) 202.2 (10.5) 11.9 (0.0) 253.8 (3.0) 265.7 (2.9) D 170.7 (5.7) 6.7 (0.0) 177.4 (5.7) 8.7 (0.1) 173.0 (1.9) 181.7 (1.9) E 546.5 (48.2) 9.4 (0.7) 555.9 (47.5) 15.6 (0.1) 354.1 (4.1) 369.6 (4.0) F 608.7 (9.5) 15.3 (0.1) 624.0 (9.6) 42.0 (0.1) 1058.8 (9.2) 1100.8 (9.2) The standard deviation is also displayed. The lowest times are indicated in bold Table 14 Confusion matrices obtained for SVM-RBF and OPF-SCS classifiers True class N SVEB VEB F Q SVM-RBF—Dataset A [5] Classified as N 40099 1705 221 83 3 SVEB 361 37 3 0 0 VEB 2285 23 2933 15 4 F 1436 21 61 290 0 Q 0 0 0 0 0 OPF-SCS—Dataset C [29] Classified as N 37677 612 591 322 2 SVEB 2495 802 33 2 0 VEB 2798 412 2514 17 5 F 1245 9 81 47 0 Q 3 2 0 0 0 Table 15 Classification accuracy considering the three-class problem Dataset Classifier OPF-L1 OPF-SCS SVM-RBF BC A 77.82 76.43 80.01 80.98 B 80.18 81.46 84.29 80.31 C 84.61 82.84 90.01 81.53 D 91.42 90.94 93.72 91.17 E 86.80 86.90 88.45 87.07 F 90.78 85.94 83.66 89.47 The best accuracy value is indicated in bold 690 Neural Comput & Applic (2018) 29:679–693 123 4 Conclusions and future works In this paper, a detailed study about the performance and computational time of supervised classification algorithms regarding the task of arrhythmia detection in ECG signals was presented. The main contributions of this work are: (1) to evaluate the OPF classifier in the task of arrhythmia detection, (2) to evaluate six distances with OPF, among which the best accuracy rates were obtained by the Man- hattan metric, while better generalization (i.e., the accuracy achieved per class) was attained using squared Chi-square distance, (3) to test six feature extraction techniques and investigate which one leads to better recognition rates and generalization, (4) to compare OPF against support vector machines and a Bayesian classifier, being found that OPF was the less generalist, while the SVM classifier was the most accurate, and, finally, (5) to find that OPF achieved the best trade-off between computational load and recog- nition rate. OPF being less generalist with respect to classes V and S, which are of great clinical significance regarding class N, one can conclude that this classifier is more appropriate for the classification of arrhythmias in ECG signals than the SVM and Bayesian classifiers. Since we observed that OPF and SVM-RBF were the most accurate classifiers, our future works will be guided to explore the synergy between these classifiers in order to build an ensemble of classifiers aiming at increasing the Table 16 Harmonic mean, specificity and sensitivity considering three classes and all classifiers Metric Dataset Heartbeat class N S V H—Se—Sp H—Se—Sp H—Se—Sp OPF-L1 A 066—081—056 003—002—095 083—080—086 B 046—087—031 006—003—097 056—041—090 C 076—088—066 031—018—097 081—072—091 D 071—096—056 023—013—099 081—070—097 E 064—092—048 006—003—098 073—060—094 F 072—095—058 011—006—099 088—081—096 OPF-SCS A 066—080— 56 006—003—097 078—074—083 B 048—088—033 004—002—098 059—044—090 C 078—085—072 060—044—095 081—074—090 D 074—096—060 032—019—099 081—070—096 E 065—093—050 006—003—098 074—061—094 F 069—090—056 020—011—099 082—074—091 SVM-RBF A 072—082—065 007—004—098 088—092—084 B 053—090—038 001—000—100 069—056—091 C 070—095—056 012—007—099 083—074—095 D 080—098—067 052—035—099 084—074—098 E 071—093—057 012—006—099 086—080—093 F 072—087—062 023—013—099 086—085—088 BC A 066—085—054 002—001—097 082—077—088 B 050—086—035 005—002—097 062—047—089 C 074—085—066 031—018—095 080—072—089 D 073—096—059 029—017—099 082—071—096 E 065—093—049 005—003—098 074—060—094 F 074—093—062 021—012—099 088—083—094 The best values are indicated in bold Neural Comput & Applic (2018) 29:679–693 691 123 recognition rate of arrhythmia detection in ECG signals, as well as to evaluate other traditional and most recent feature extraction methods. Acknowledgments The first author thanks the Brazilian National Council for Research and Development (CNPq) for providing finan- cial support through Grants # 470501/2013-8 and # 301928/2014-2. The sixth author is grateful to CNPq Grants #306166/2014-3 and #470571/2013-6, as well as to São Paulo Research Foundation (FAPESP) Grant #2014/16250-9. The last author gratefully acknowledges the funding of Project NORTE-01-0145-FEDER-000022—SciTech—Science and Technol- ogy for Competitive and Sustainable Industries cofinanced by ‘‘Pro- grama Operacional Regional do Norte (NORTE2020)’’ through ‘‘Fundo Europeu de Desenvolvimento Regional (FEDER)’’. References 1. Abawajy JH, Kelarev AV, Chowdhury M (2013) Multistage approach for clustering and classification of ECG data. Comput Methods Progr Biomed 112:720–730 2. Allène C, Audibert JY, Couprie M, Keriven R (2010) Some links between extremum spanning forests, watersheds and min-cuts. Image Vis Comput 28(10):1460–1471 3. 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IEEE Trans Biomed Eng 58(3):616–625 Table 17 Mean computational time (in s) considering the three- class problem Dataset Classifier OPF-L1 OPF-SCS Train Test Total Train Test Total A 336.0 (1.7) 575.2 (11.5) 911.2 (9.9) 1486.1 (7.1) 1597.9 (8.1) 3084.1 (15.1) B 54.5 (0.2) 93.0 (2.8) 147.5 (3.0) 191.2 (1.7) 192.3 (7.8) 383.4 (9.4) C 55.5 (0.3) 92.3 (9.2) 147.7 (9.3) 206.2 (2.0) 233.5 (12.7) 439.7 (14.1) D 40.2 (0.2) 52.2 (5.2) 92.4 (5.4) 132.6 (0.5) 134.1 (3.8) 266.7 (3.5) E 81.0 (0.4) 105.9 (4.2) 186.9 (4.0) 301.6 (2.6) 224.8 (4.2) 526.4 (2.2) F 221.7 (2.7) 368.8 (11.6) 590.5 (14.1) 973.4 (4.7) 977.3 (2.8) 1950.7 (6.8) Dataset Classifier SVM-RBF BC Train Test Total Train Test Total A 2069.7 (23.7) 25.9 (5.4) 2095.6 (28.6) 62.5 (0.1) 971.2 (5.2) 1033.7 (5.3) B 280.5 (2.9) 11.6 (0.7) 292.2 (3.6) 11.0 (0.1) 141.5 (0.7) 152.5 (0.7) C 194.8 (2.7) 7.7 (0.0) 202.5 (2.7) 11.7 (0.1) 152.9 (0.3) 164.6 (0.4) D 165.9 (1.0) 6.0 (0.0) 171.9 (0.9) 8.7 (0.1) 105.4 (1.4) 114.1 (1.5) E 536.1 (58.9) 9.1 (0.8) 545.2 (58.1) 15.5 (0.1) 213.5 (2.2) 229.0 (2.3) F 553.3 (26.2) 17.0 (6.8) 570.3 (32.9) 41.6 (0.3) 638.5 (5.1) 680.1 (5.3) The standard deviation is also displayed. 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Expert Syst Appl 34(4):2841–2846 Neural Comput & Applic (2018) 29:679–693 693 123 http://www.ic.unicamp.br/%7eafalcao/LibOPF Robust automated cardiac arrhythmia detection in ECG beat signals Abstract Introduction Methodology MIT-BIH arrhythmia database Training and test set Feature extraction Optimum-path forest classifier Training step Classification step Results and discussion Experimental analysis of optimum-path forest Five-class problem Three-class problem Comparative analysis of the classifiers considering the five-class problem Comparative analysis of the classifiers considering the three-class problem Conclusions and future works Acknowledgments References