A Greedy Graph Search Algorithm Based on Changepoint Analysis for Automatic QRS Complex Detection
AA Greedy Graph Search Algorithm Based on ChangepointAnalysis for Automatic QRS Complex Detection
Atiyeh Fotoohinasab , Toby Hocking , and Fatemeh Afghah School of Informatics, Computing and Cyber Systems at Northern Arizona University * Corresponding author: Atiyeh Fotoohinasab, [email protected] a r X i v : . [ ee ss . SP ] F e b bstract The electrocardiogram (ECG) signal is the most widely used non-invasive tool for the investigation ofcardiovascular diseases. Automatic delineation of ECG fiducial points, in particular the R-peak, serves as the basisfor ECG processing and analysis. This study proposes a new method of ECG signal analysis by introducing a newclass of graphical models based on optimal changepoint detection models, named the graph-constrained changepointdetection (GCCD) model. The GCCD model treats fiducial points delineation in the non-stationary ECG signal as achangepoint detection problem. The proposed model exploits the sparsity of changepoints to detect abrupt changeswithin the ECG signal; thereby, the R-peak detection task can be relaxed from any preprocessing step. In this novelapproach, prior biological knowledge about the expected sequence of changes is incorporated into the model usingthe constraint graph, which can be defined manually or automatically. First, we define the constraint graph manually;then, we present a graph learning algorithm that can search for an optimal graph in a greedy scheme. Finally, wecompare the manually defined graphs and learned graphs in terms of graph structure and detection accuracy. Weevaluate the performance of the algorithm using the MIT-BIH Arrhythmia Database. The proposed model achievesan overall sensitivity of 99.64%, positive predictivity of 99.71%, and detection error rate of 0.19 for the manuallydefined constraint graph and overall sensitivity of 99.76%, positive predictivity of 99.68%, and detection error rateof 0.55 for the automatic learning constraint graph.
Index Terms
ECG segmentation, R-peak detection, Changepoint detection, Graph learning . INTRODUCTIONThe electrocardiogram (ECG) is a quasi-periodicbiomedical signal that provides information about car-diac muscle electrical activities. One cardiac cycle ina typical ECG signal is delineated by arrangementsof P, the QRS complex, T waves, and PQ and STsegments. Correct R-peak detection is the first and mostcritical step in almost all ECG analysis methods. TheR-peak is the highest and only positive peak within theQRS complex, reflecting the ventricular depolarizationof the heart’s electrical activity. Precise detection ofthe R-peak location plays a critical role in obtainingthe morphology of the QRS complex and revealingthe location of other ECG fiducial points. Furthermore,R-peak localization serves as the basis for automateddetermination of the heart rate, which is a significant cri-terion for heart arrhythmia diagnoses such as prematureatrial contraction, tachycardia, and bradycardia. Manyother diseases can also be diagnosed in a non-invasiveway using R-peak detection due to the relationshipbetween heart rate variability and several physiologicalsystems (e.g., vasomotor, respiratory, central nervous,and thermoregulatory).Various approaches have been proposed in the lit-erature for detecting R-peaks in an ECG signal [1].Typically, these methods consist of two main steps: pre-processing and detection. In the pre-processing step, thealgorithm attempts to eliminate the noise and artifactsand to highlight the relevant sections of the ECG [2,3]. In the second step, various methods are used tolocate R-peaks based on the result of the pre-processingstep, and then other waves are detected by defining aset of heuristic rules [4]. However, these approachessuffer from some critical drawbacks that limit their performance in practical applications. First, in real-timedata processing and ambulatory care settings, wherethe collected data are highly noisy, preprocessing-basedalgorithms are less effective. Second, these algorithmscan fail to detect R-peaks in some determinant morpho-logical patterns resulting from certain life-threateningheart arrhythmias due to the time-varying morphologyof the QRS complex. Incorrect detection of R-peaks canaffect the correct identification of subsequent waves.The R-peak detection step can be generally accom-plished either by implementing a threshold-based tech-nique or by employing an independent threshold tech-nique. The amplitude of the peak and time durationbetween two consecutive R peaks (i.e., the RR interval)are typically used to determine a suitable threshold [5].A constant threshold is only efficient for detecting R-peaks within records with normal morphological pat-terns. Therefore, recent studies have employed adaptivethresholds, for which there is no need to determinethe threshold experimentally. In [6] and [7], the Hilberttransform with an adaptive thresholding technique wasutilized to detect R-peaks. Some threshold-based tech-niques with other criteria have also been used to specifythe threshold. In [4], an adaptive threshold concerningthe geometric angle between two consecutive samplesof the ECG signal was defined. The performance of thethreshold-based technique is highly dependent on theselection of initial parameters; hence, it can lead to asignificantly higher number of false beats. Therefore,independent threshold techniques are more desirablethan the threshold-based technique.Most of the state-of-the-art methods for R-peak detec-tion are based on wavelet transform [8–10], simple math-ematical operations [6, 11, 12], hidden Markov models,nd machine learning. Wavelet transform is a suitableapproach for considering the non-stationary behavior ofthe ECG signal. However, considering the various shapesof the QRS complex, it is difficult to select the optimalmother wavelet or find the required threshold in the de-tection step of the wavelet transform. Additionally, dis-crete wavelet transform fails to provide reliable resultsin a short-recording duration. Mathematical operation-based algorithms have a low computational cost, whichis more appropriate for real-time applications and largedataset analysis. However, achieving high performancewhen the signal-to-noise ratio is high remains challeng-ing for these algorithms. Hidden Markov models arealso widely used in ECG segmentation because they arepowerful tools for considering the temporal dependencyamong the waveforms [13–15]. The majority of thestudies on machine learning-based methods have utilizedsparse signal processing to represent an approximationof the nonlinear ECG signal using sparsity constraints[16–21]. Some studies have also applied deep learningtechniques to detect the ECG waveforms consideringits high performance in various classification tasks [22,23]. However, the caveat with deep learning-based ap-proaches is that they need large-scale datasets for thetraining phase and often suffer from the imbalanced classproblem [24, 25].In this paper, we propose a new class of graphicalmodels based on optimal changepoint detection mod-els, named the graph-constrained changepoint detection(GCCD) model, to locate R-peaks in the ECG signal. Achangepoint detection model identifies abrupt changesin data when a property of the time series changes.In the non-stationary ECG signal, ECG waves can alsobe considered as abrupt up or down changes over time during the heart cycle. We exploit the model introducedby Hocking et al. [26, 27], in which a graph-based opti-mal changepoint detection model was used for detectingabrupt changes in the genomics data. In their work, theypropose a new class of functional pruning algorithmswith log-linear time complexity in the amount of data,which is capable of handling the large datasets that arecommon to ECG analysis.Only a few studies in the literature have appliedchangepoint detection models for cardiac analysis. Goldet al. [28] adopted a changepoint detection method basedon Bayesian inference to extract the onset of the QRScomplex over a small time window containing just oneQRS complex. In [29], a changepoint detection approachbased on the Haar wavelet and Kolmogorov-Smirnovstatistic was applied to find normal and abnormal ECGsegments within the assembled ECG samples from dif-ferent ECG datasets. Sinn et al. [30] analyzed heartrate changes in ECG recordings by detecting abruptchanges in the ordinal pattern distributions, which areused to represent the order structure of a time series.Some studies have also applied changepoint detectionmodels to investigate sleep problems by analyzing heartrate variability in the ECG signal during sleep [31, 32].To the best of our knowledge, this is the first studyin which changepoint detection models have been pro-posed to detect ECG fiducial points in long records ofECG signals. In this novel framework, prior biologicalknowledge about the expected sequence of changes canbe specified in a constraint graph. Then, functionalpruning dynamic programming algorithms can computethe globally optimal model (mean, changes, and hiddenstates) in fast log-linear time. We furthermore proposea new algorithm for learning the graph structure usingabeled ECG data. Therefore, the main contributions ofthis study are: • A new class of graphical models based on optimalchangepoint detection models to detect R-peak po-sitions in the ECG signal. The proposed methoddoes not require any noise removal preprocessingstep as it uses the sparsity of changepoints to detectabrupt changes. • A new algorithm to learn the graph structure andparameters using labeled ECG data. Thus, themodel’s performance is no longer dependent on anexpert to encode prior knowledge into the constraintgraph. • Comparison of the learned graphs with the manu-ally constructed graphs in terms of graph structureand detection accuracy. Results demonstrate thatthere can exist different optimum graph structuresfor one subject, and the proposed graph learningalgorithm can find global optima depending on theinitial graph structure.The rest of the paper is organized as follows. Inthe next section, we describe the proposed model forR-peak detection in the ECG signal. We explain theGCCD model in Section II-A and the constraint graph inSection II-B. Section II-B also defines the manual graphand the proposed graph learning algorithm. Section IIIprovides a description of the dataset used in this studyand a discussion of the results as well as a comparisonbetween the performance of the manually defined graphsand learned graphs. Finally, Section IV summarizes thisresearch work and its contributions.II. M
ETHODOLOGY
The proposed method treats ECG wave detection as achangepoint detection problem for a non-stationary ECG signal. It extracts the R-peaks in the raw ECG signal byrepresenting the periodic non-stationary ECG signal asa piecewise locally stationary time series with constantmean values (i.e., each piece is the mean of one segmentof datapoints). The model takes a raw ECG signal and aconstraint graph as inputs and computes the onset/offsetand the mean of desired segments (i.e., hidden states).Then, the center of each state is associated with thelocation of a peak. The constraint graph allows theincorporation of prior knowledge into the model andregularizes the model. Figure 1 illustrates an overviewof the proposed algorithm in the detection of R-peakpositions in the ECG signal. It is worth re-emphasizingthat the model takes the raw ECG signal as the input,without applying any preprocessing step, as it leveragesthe sparsity of changepoints to denoise the signal and todetect abrupt changes.The constraint graph, which encodes the expectedsequence of changes in the ECG signal, can be definedmanually by an expert or automatically from the data. Inthe following sections, we describe the details of variousparts of the proposed model.
A. Graph-Constrained Changepoint Detection Model
ECG fiducial points detection can be defined as theproblem of finding abrupt changes over one cardiaccycle caused by changes in statistical characteristics.From this point of view, a proper changepoint detectionalgorithm can be employed to detect ECG waves in afast and effective way. We applied the optimal change-point detection model introduced in [26] to localizeR-peak positions in the ECG signal. In this model,prior biological knowledge about the expected sequenceof changes is incorporated into the model as a graphconstraint. Then, a dynamic programming algorithm aw ECG SignalManually Defined Constraint GraphGraph Learning
Algorithm
Changepoint
Detection
Model R-Peak
Positions
Fig. 1:
An overview of the GCCD model. The GCCD model takes a constraint graph and a raw ECG signal as inputs and thendetects segments corresponding to the nodes of the constraint graph at the output. using functional pruning computes the globally optimalmodel (mean, changes, and hidden states) in fast log-linear O ( N log N ) time.We assumed a directed graph G = ( V, E ) as theconstraint graph, where the vertex set V ∈ { , . . . , | V |} represents the hidden states/segments (not necessarily awaveform), and the edge set E ∈ { , . . . , | E |} repre-sents the expected changes between the states/segments.Each edge e ∈ E incorporates the following associ-ated prior knowledge about the expected sequences ofchanges: • The source v e ∈ V and target v e ∈ V arevertices/states for a changepoint e from v e to v e . • A non-negative penalty constant λ e ∈ R + is thecost of changepoint e . • A constraint function g e : R × R → R defines thepossible mean values before and after each change-point e . If m i is the mean before the changepointand m i +1 is the mean after the changepoint, thenthe constraint is g e ( m i , m i +1 ) ≤ . These functionscan be used to constrain the direction (up or down)and/or the magnitude of the change (greater/less than a certain amount).Mathematically, given the input signal Y = { y , . . . , y n } and the directed graph G = ( V, E ) , theproblem of finding changepoints c , segment means m ,and hidden states s can be solved using the followingoptimization problem: minimize m ∈ R N , s ∈ V N c ∈{ , ,..., | E |} N − N (cid:88) i =1 (cid:96) ( m i , z i ) + N − (cid:88) i =1 λ c i (1)s. t. no change: c i = 0 ⇒ m i = m i +1 & s i = s i +1 (2)change: c i (cid:54) = 0 ⇒ g c i ( m i , m i +1 ) ≤ s i , s i +1 ) = ( v c i , v c i ) . (3)The changepoints c i can be assigned to any of the pre-defined edges ( c i ∈ { , . . . , | E |} ). Consequently, c i = 0 indicates no change with zero cost, λ = 0 . Function(1) consists of a data-fitting term (cid:96) and a model com-plexity term λ c i [33, 34]. (cid:96) represents the negative log-likelihood of each datapoint, and λ c i is a non-negativepenalty on each changepoint. In other words, λ regu-larizes the number of predicted changepoints/segmentsy the model so that a larger λ reduces the number ofchangepoints by estimating a more sparse changepointvector. The constraint function g e also encodes theexpected up/down change and the least amplitude gapbetween the mean of two states. When there is no change c i = 0 , Constraint (2) forces the model to stay inthe current state s i = s i +1 with no change in mean m i = m i +1 . However, when there is a change c i (cid:54) = 0 ,Constraint (3) imposes a change in the mean implied bythe constraint function g c i ( m i , m i +1 ) ≤ as well as achange in the state ( s i , s i +1 ) = ( v c i , v c i ) . An open-source implementation of the Generalized FunctionalPrunining Optimal Partitioning (GFPOP) algorithm isavailable in C++ code inside an R package namedGFPOP on GitHub [35]. B. Constraint Graph
The constraint graph G = ( V, E ) in the optimizationproblem of Equation (1) encodes prior biological knowl-edge about the expected sequences of changes withinone cardiac cycle. It can be designed manually by anexpert or be learned from the data by the model. Thetwo following subsections detail both the manual andlearning-based designs.
1) Manual Graph Definition:
To manually define theconstraint graph G , we took into account the possiblemorphological categories for the ECG waves (i.e., P,QRS, and T waves) and the overall morphologicalproperties of the signal in each record [36]. An expectedhidden state/segment in the signal is characterized as anode in the constraint graph, and the required conditionsfor transition between states are encoded in the edges.The required conditions are determined based on the ex-pected minimum amplitude difference of two successivestates and the polarity of each transition (i.e., up/down). The caveat with the manual definition of the constraintgraph is that it can be inefficient for ECG signal anal-ysis considering the various morphological patterns foreach waveform. Furthermore, the model’s performancedepends on the expert knowledge encoded into theconstraint graph. In the next subsection, we explainthe proposed graph learning algorithm for learning theconstraint graph using the R-peak labels provided by thegold standard.
2) Constraint Graph Learning:
To automate the R-peak detection task, we modified the previous modelby learning the constraint graph from the data (seethe dashed part in Figure 1). In this new framework,the proposed model takes the raw signal and an initialgraph structure as inputs and yields the desired outputs,including the onset/offset and the mean of segmentsspecified in the nodes of the learned constraint graph[37]. Here, the model architecture is comprised of twostages: training and detection. The training step tries toheuristically find an optimum graph structure by whichthe label errors in the training set are minimized (theblock named “Graph Learning Algorithm” in Figure 1).The detection step then extracts the R-peaks in the rawECG record constrained to the graph learned in theprevious step (the block named “Changepoint DetectionModel” in Figure 1).The novelty of this new structure lies in the trainingstep, which is comparable to the previous model inSection II-B.1. The main idea of the training step isto automatically discover the desired topology of theconstraint graph G and the information about the edgesfrom the data. As described in Section II-A, each edgecontains the following information: (1) the expectedup/down change in the segment means, (2) the leastmplitude gap between the means of two states, and (3)a non-negative penalty imposed by the edge transition.Suppose that the initial graph for each record is denotedas G = ( V , E ) , where V and E are the correspond-ing graph node and edge sets, respectively. Each node inthe V set represents initial hidden states in the model.Each edge in the E set represents a transition betweentwo consecutive hidden states (i.e., a changepoint e from the source v e to the target v e in section II-A)and also contains initial values for parameters of t , g , and λ , which are the initial type, the initial gapbetween two states, and the initial penalty, respectively.Figure 2a shows the simple initial graph used for theoptimization process. It should be noted that the initialedge information was chosen based on the overall resultsobtained from the manual definition of the constraintgraph.A sketch of the proposed graph learning algorithm issummarised as Algorithm 1. The greedy graph searchalgorithm starts with the initial graph G and iterativelyoptimizes the graph structure and edge parameters tofind a graph that maximizes the accuracy regardingthe provided labels. At the t -th iteration, the function F ind Graph Candidates () finds the graph candidateset G ct using the editing candidates for each edge ofthe output graph from the previous iteration G t − . Inthis study, the algorithm considers 11 editing candidatesper edge to optimize the graph topology and the threeedge parameters. For example, in the iteration t , ifthe parent graph (i.e., G t − ) has two edges, the graphcandidate set G ct will have no more than 22 members | G ct | ≤ . These editing candidates include three typesof adding a node, two types of deleting a node, one typeof adding two nodes, changing the type of the abrupt change, and increasing or decreasing the penalty and gapcorresponding to an edge. We believe all morphologicalpatterns of the ECG waves can be constructed usingthese editing candidates. Figure 2 illustrates the graphediting candidates related to the edge ( V i , V j ) with anup change. C. Computational Complexity
As can be seen in Algorithm 1, the time complexityof the GCCD algorithm is theoretically proportional tothe number of graph candidates at each iteration (Line9) and the number of required iterations to achieve anoptimum graph with minimum label errors (Line 4).There are three main aspects that characterize the timecomplexity of the algorithm: • Given a record with n data samples and a graphcandidate ˆ G with V vertices and E edges, the timecomplexity to detect R-peaks (Lines 10–14) is S = O ( En ) in the worst case (pathological simulateddata) and S = O ( En log n ) in the average case(typical in real data). Also note that since we con-sider only graphs with a single circular path, E = O ( V ) , and the time complexity is further reducedto O ( V n log n ) (for average case/non-pathologicaldata). • Considering C graph edit candidates in the iteration t , the time complexity to compute all the models ˆ G ∈ { , , . . . , | G ct | = C } is O ( SC ) (where S isthe time complexity of solving for optimal modelparameters given a single graph). It should be notedthat the number of graph candidates in the iteration t depends on G t − , which is the graph from theprevious iteration (Line 9). The time complexity tocompute the label error given L labels is O ( CL ) ,which can be effectively ignored from the overallime complexity as this task is fast. • Finally, iterating over T iterations to obtain thegraph with the minimum label error (Line 4) causesthe overall time complexity of the algorithm tobe O ( SCT ) , where S is the time to solve for asingle graph, and C is the number of edit candidatesconsidered in each iteration. Algorithm 1
Greedy Graph Learning
Input: data, labels, initial graph structure G t ← Best Cost ← inf ˆ E t ← label error ( G t ) while ˆ E t < Best Cost do Best Cost ← ˆ E t t ← t + 1 G ct ← F ind Graph Candidates ( G t − ) ,Based on F igure ˆ E t ← Best Cost for each ˆ G in G ct do ˆ E ← label error ( ˆ G ) if ˆ E < ˆ E t then ˆ G t ← ˆ G ˆ E t ← ˆ E end if end for end whileOutput: constraint graph G t III. E
XPERIMENTAL S TUDIES
A. Dataset
We applied the well-known MIT-BIH Arrhythmia(MIT-BIH-AR) database to evaluate the GCCD model.This database contains 48 ECG recordings taken from47 subjects. Each record’s duration is 30 min, and eachrecording is sampled at 360 Hz with a resolution of 200samples over a 10 mV range [38, 39]. Each recordingconsists of two ambulatory ECG channels from themodified lead II (MLII) and one of the leads V1, V2, V4,or V5. In this study, all 48 records with one MLII or V5 RA 𝝀 = 𝝀 , 𝑔 = 𝑔 , 𝑔 = 𝑔 𝝀 = 𝝀 (a) Initial Graph 𝑽 𝒏 𝑽 𝒊 ൗ𝝀 2 𝑽 𝒋 ൗ𝝀 2↑, ൗ𝑔 2 ↑, ൗ𝑔 2𝑽 𝒋 𝑽 𝒊 𝝀↑,𝑔 𝑽 𝒏 𝑽 𝒊 ൗ𝝀 2 𝑽 𝒋 ൗ𝝀 2↓,𝑔 = 0 ↑,𝑔𝑽 𝒏 𝑽 𝒊 ൗ𝝀 2 𝑽 𝒋 ൗ𝝀 2↑,𝑔 ↓,𝑔 = 0 (b) Add One Node 𝑽 𝒋 𝑽 𝒊 𝝀↑,𝑔 ൗ𝝀 3 ൗ𝝀 3↑,𝑔 ↓ ,𝑔 = 0 ൗ𝝀 3↑,𝑔 = 0𝑽 𝒊 𝑽 𝒋 𝑽 𝒏 𝑽 𝒏 (c) Add Two Nodes 𝑽 𝒋 𝑽 𝒊 𝜆 𝑽 𝒔 𝜆 ↑,𝑔 ↓,𝑔 𝑽 𝒔 𝑽 𝒊 𝜆 + 𝜆 ↑,𝑔 𝑽 𝒔 𝑽 𝒊 𝜆 + 𝜆 ↓,𝑔 (d) Delete One Node 𝑽 𝒋 𝑽 𝒊 𝝀↑,𝑔 𝑽 𝒋 𝑽 𝒊 𝝀↑,2𝑔 (f) Increase/Decrease Gap 𝑽 𝒋 𝑽 𝒊 𝝀↑,𝑔 𝑽 𝒋 𝑽 𝒊 (g) Increase/Decrease Penalty 𝑽 𝒋 𝑽 𝒊 𝝀↑,𝑔 𝑽 𝒋 𝑽 𝒊 𝝀↓,𝑔 (e) Change Type RA 𝝀 = 𝝀 , 𝑔 = 𝑔 , 𝑔 = 𝑔 𝝀 = 𝝀 𝑽 𝒋 𝑽 𝒊 𝝀↑,𝑔 ൗ𝝀 3 ൗ𝝀 3↑,𝑔 ↓ ,𝑔 = 0 ൗ𝝀 3↑,𝑔 = 0𝑽 𝒊 𝑽 𝒋 𝑽 𝒏 𝑽 𝒏 Fig. 2: (a:)
The initial constraint graph structure with twonodes labeled as A and R , representing an alternative segmentand the R-peak segment, respectively, in a cycle. (b–g:) Someof the applied graph editing candidates related to the edge ( V i , V j ) with an up change. lead were used to evaluate the algorithm. The databasehas been annotated with both RR intervals and heartbeatclass information by two or more expert cardiologistsndependently. B. Results and Discussion
This section presents a comprehensive discussionof the results obtained by the proposed model anda detailed comparison between the manually definedgraphs and the learned graphs. We also provide somesuggestions for the future development of the GCCDmodel.Figure 3 illustrates an example of the model’s per-formance with a manually defined constraint graph inthe R-peak detection task for a window of Record 230of the MIT-BIH-AR dataset. However, as mentionedin Section II-B.1, the performance of the model usingmanually defined graphs depends on an expert withprior knowledge. Furthermore, manual annotation by anexpert is time consuming and expensive. To address thisissue, we proposed a new graph learning algorithm thatsearches for a locally optimal constraint graph using agreedy scheme on the labeled ECG data. Regarding thevarious morphological patterns for the ECG signal, theproposed graph learning algorithm can relax the modelfrom the manual definition of the constraint graph foreach record.We adopted the intra-patient paradigm to train theconstraint graph to address the intra-patient variation inECG morphologies. Thus, the training and testing setswere generated by randomly splitting the intra-samplesfor each record with an approximate ratio of . Weused a k -fold cross-validation approach to evaluate themodel performance with a k size of . More specifically,we divided the intra-sample data into k = 5 folds so thateach trial used four folds to train the model and one foldfor validation.Figures 4 and 5 show representative examples of the Fig. 3:
Demonstration of R-peak detection using the proposedmodel on Record 230 of the MIT-BIH-AR dataset. (Top:)
Theproposed model represents Record 230 as piece-wise locallystationary segments (blue lines). Extracted R-peak positionsare marked with a red “R.” (Bottom:)
The graph structure forthe proposed model. The constraint graph has a vertex for eachstate including state “R” for the R-wave. Below each edge e we show the penalty λ e , which is either a constant λ > or ; above we show the constants δ, γ in the constraint function g e ( m i , m i +1 ) = δ ( m i − m i +1 ) + γ ≤ , where δ = 1 fora non-decreasing change (shown with ↑ ), δ = − for a non-increasing change (shown with ↓ ), and γ ≥ is the minimummagnitude of change. R-peak detection task performed by the model integratedwith the graph learning algorithm for two records fromthe MIT-BIH-AR database. These figures illustrate howthe proposed graph learning algorithm iteratively editsthe graph structure to yield a model with maximum ac-curacy in detecting R-peaks. We initialized the constraintgraphs using the graph structure in Figure 2a with theinitial values of g = 100 and λ = 5 × for Record107 and g = 100 and λ = 10 for Record 219. Itshould be noted that the initial edge information wasassigned based on the overall results derived from themanually defined graphs in all experiments. However,graph candidates 2f and 2g can adjust the parameters g and λ for the optimum values. For these two examples,we chose the initial edge information so that all thetraining steps could be completely displayed. Labelerrors are omitted from Figures 5a–5c to reduce clutter 𝝀 = , 𝑔 =100 , 𝑔 =100 𝝀 =
25 ∗ 10 R 1 , 𝑔 =0 𝝀 =
25 ∗ 10 , 𝑔 =100 𝝀 =
25 ∗ 10 R 1 , 𝑔 =100 𝝀 ≅ 16 ∗ 10 A 2 3 , 𝑔 =0 𝝀 ≅ 16 ∗ 10 , 𝑔 =0 𝝀 ≅ 16 ∗ 10 , 𝑔 =0 𝝀 =
25 ∗ 10 , 𝑔 =200 𝝀 =
25 ∗ 10 R 1 , 𝑔 =100 𝝀 ≅ 16 ∗ 10 A 2 3 , 𝑔 =0 𝝀 ≅ 16 ∗ 10 , 𝑔 =0 𝝀 ≅ 16 ∗ 10 , 𝑔 =0 𝝀 =
25 ∗ 10 , 𝑔 =400 𝝀 =
25 ∗ 10 R 1 , 𝑔 =100 𝝀 ≅ 16 ∗ 10 A 2 3 , 𝑔 =0 𝝀 ≅ 16 ∗ 10 , 𝑔 =0 𝝀 ≅ 16 ∗ 10 , 𝑔 =0 𝝀 =
25 ∗ 10 , 𝑔 =400 𝝀 =
25 ∗ 10 R 1 , 𝑔 =100 𝝀 ≅ 16 ∗ 10 A 2 3 , 𝑔 =0 𝝀 ≅ 16 ∗ 10 , 𝑔 =0 𝝀 ≅ 16 ∗ 10 , 𝑔 =0 𝝀 =
25 ∗ 10 , 𝑔 =400 𝝀 =
25 ∗ 10 R 1 , 𝑔 =100 𝝀 ≅ 16 ∗ 10 A 2 3 , 𝑔 =0 𝝀 ≅ 16 ∗ 10 , 𝑔 =0 𝝀 ≅ 16 ∗ 10 , 𝑔 =0 𝝀 =
25 ∗ 10 (a) (b)(c) (d)(e) (f) Fig. 4:
Demonstration of constraint graph optimization using the proposed graph learning algorithm for Record 107 of theMIT-BIH-AR dataset. (a–e, top:)
Extracted R-peak positions given the learned constraint graph in each learning iteration. Thered and orange coverage bands show the used labels in the training procedure, including training and validation sets. The bluelines represent separate states at the model output over the raw ECG signal (gray points). (a–e, bottom:)
The learned constraintgraph in each learning iteration. For each edge, λ is the penalty, g is the gap (the minimum magnitude of change), and theup/down arrow shows the type of change. The part of the graph that is modified from the previous iteration is shown in red. (f:) Testing results for the final learned constraint graph using a new window of data. The pink coverage bands show the labelsin the testing set. a) (b) A 𝝀 = , 𝑔 =100 , 𝑔 =100 𝝀 = R 1 , 𝑔 =0 𝝀 = (c) , 𝑔 =100 𝝀 = R 1 , 𝑔 =50 𝝀 = 5∗10 A 2 , 𝑔 =50 𝝀 =5∗10 , 𝑔 =0 𝝀 = (d) , 𝑔 =100 𝝀 = R 1 , 𝑔 =50 𝝀 = 5∗10 A 2 , 𝑔 =50 𝝀 =5∗10 , 𝑔 =0 𝝀 = (e) (f) , 𝑔 =50 𝝀 = , 𝑔 =50 A 2 R , 𝑔 =50 , 𝑔 =50 𝝀 =25∗10 , 𝑔 =0 𝝀 = 𝝀 = 5∗10 𝝀 =5∗10 (g) , 𝑔 =50 𝝀 = , 𝑔 =50 A 2 R , 𝑔 =50 , 𝑔 =50 𝝀 =25∗10 , 𝑔 =0 𝝀 = 𝝀 = 5∗10 𝝀 =5∗10 (h) , 𝑔 =50 𝝀 = , 𝑔 =50 A 2 R , 𝑔 =50 , 𝑔 =50 𝝀 =25∗10 , 𝑔 =0 𝝀 = 𝝀 = 5∗10 𝝀 =5∗10 𝝀 = , 𝑔 =100 , 𝑔 =100 RA 𝝀 = 𝝀 = , 𝑔 =100 , 𝑔 =100 RA 𝝀 = Fig. 5:
Detection of R-peak positions for Record 219 of the MIT-BIH-AR dataset using the proposed graph learning algorithm. (a–h, top:)
Extracted R-peaks given the constraint graph structure learned in each iteration. The orange and red coverage bandspresent training and validation labels, respectively. The blue line demonstrates locally stationary segments at the model output,and the gray points also show the raw ECG signal at the model input. (a–h, bottom:)
The constraint graph learned in eachiteration. The red part of the constraint graph represents the selected graph editing candidate in each iteration. a) (b)
Fig. 6:
Test result for Record 219 for two different windows of time. The pink coverage bands represent the labels in the testingset, and the blue lines demonstrate model output. in the figures. The red part of the graph structure in eachiteration presents the chosen editing candidate in thecurrent iteration over the graph in the previous iteration.More interestingly, Figure 5 demonstrates the model’scapability to detect R-peaks in the presence of a baselinewandering artifact, which is a typical artifact in the ECGsignal. Baseline wandering can change the shape of theQRS complex and thereby causes incorrect detection ofthe R-peak. The performance of the Pan and Tompkins[11] algorithm, algorithms derived from the ECG signalslope [40], and methods based on wavelet transform arehighly dependent on the removal of this artifact. Figure6 shows the test result for this record over two differenttime windows of data. Figure 7 illustrates the trainingprogress for these two records, where the Y-axis showsthe sum of false negative and false positive error rates.Indeed, the training progress curve reflects the numberof label errors produced by the model in each iterationgiven the provided labels for the training and validationsets. It is worth mentioning that the proposed graphlearning algorithm avoids possible overfitting issues asit tries to extract the morphology of the ECG signal thatcontains multiple various morphological patterns.The proposed graph learning algorithm employs a (a)(b)
Fig. 7:
Training progress for (a)
Record 107 and (b)
Record219 of the MIT-BIH-AR dataset. greedy search scheme to select the best performinggraph in terms of detection accuracy (see Section II-B.2).Therefore, the performance of the algorithm depends ig. 8:
Comparison of the training progress initialized withtwo simple and complex initial graph structures for the record106 in the MIT-BIH-AR dataset. heavily on the initial graph structure and will likely leadto local optima. Figure 8 compares the training progressfor Record 106 of the MIT-BIH-AR database initializedwith the two simple (see Fig. 2a) and complex graphstructures (i.e., a graph with eight nodes representingthe morphology of a normal ECG signal). Figure 9also presents a comparison of the final selected graphsand their performances for a window of this record.As these figures show, the model initialized with thecomplex graph structure can achieve higher accuracy(i.e., a lower number of label errors) in a lower numberof iterations than the model initialized with the simplegraph structure.The investigation of the experimental results showsthat the greedy graph search algorithm can achieveoptimal performance for the model trained with themanually defined graphs, although its performance isaffected by the initial graph. We noticed that for most ofthe records from the MIT-BIH-AR database, the learnedgraphs could reach the performance of the manuallydefined graphs but with different graph structures. Thismeans that the GCCD model can obtain global optimausing various initialization structures, which will likelylead to different final graph structures. Figure 10 com- , 𝑔 =0 𝝀 =10 R 1 2 , 𝑔 =0 𝝀 = 10 , 𝑔 =0 A 𝝀 = 10 , 𝑔 =0 𝝀 =5∗10 , 𝑔 =0 𝝀 =10 , 𝑔 =0, 𝑔 =0 𝝀 =10 , 𝑔 =0 𝝀 =10 , 𝑔 =100, 𝑔 =200 𝝀 = 2∗10 𝝀 =5∗10 𝝀 =5∗10 , 𝑔 =0 𝝀 = 0 , 𝑔 =0 𝝀 = 0 , 𝑔 =0 𝝀 =0 𝝀 = 0 , 𝑔 =150 , 𝑔 =0 𝝀 = 0 , 𝑔 =0 , 𝑔 =0 𝝀 = 0 𝝀 = 0 , 𝑔 =0 𝝀 = 10 R , 𝑔 =0 𝝀 =0 𝝀 = 0 , 𝑔 =0 (a)(b) Fig. 9:
Comparison of the trained models for Record 106 ofthe MIT-BIH-AR dataset inititalized with (a) a simple graphstructure and (b) a complex graph structure. pares the constraint graph structures defined manuallyvs. those learned automatically using the initial graphstructure in Figure 2a for Record 100 of the MIT-BIH-AR dataset. As shown in this figure, the manuallydefined graph and the learned graph both achieved theoptimal performance but with different graph structures.We also noticed that for some records from the MIT-BIH-AR database, the graph learning algorithm chosethe same structure as the manually defined graph struc-ture. Figure 11 shows the model performance usingthe graph learning algorithm for Record 232 from theMIT-BIH-AR dataset, for which the manually definedconstraint graph and the learned graph had the samestructures. a)(b) , 𝑔 =0 𝝀 = , 𝑔 =50 𝝀 =5∗10 , 𝑔 =100 𝝀 = 25∗10 , 𝑔 =0 𝝀 = 25∗10 , 𝑔 =50 𝝀 = , 𝑔 =200 𝝀 =10 , 𝑔 =0 𝝀 = 0 , 𝑔 =0 R 𝝀 = 0 , 𝑔 =0 𝝀 =0 , 𝑔 =0, 𝑔 =0, 𝑔 =150 𝝀 = 0 𝝀 =0𝝀 =0 𝝀 = 0 , 𝑔 =0, 𝑔 =0 𝝀 = 0 , 𝑔 =0 𝝀 =10 R 1 2 , 𝑔 =0 𝝀 = 10 , 𝑔 =0 A 𝝀 = 10 , 𝑔 =0 𝝀 =5∗10 , 𝑔 =0 𝝀 =10 , 𝑔 =0, 𝑔 =0 𝝀 =10 , 𝑔 =0 𝝀 =10 , 𝑔 =100, 𝑔 =200 𝝀 = 2∗10 𝝀 =5∗10 𝝀 =5∗10 Fig. 10:
Comparison of the constraint graph structures (a) defined manually and (b) learned using the proposed graphlearning algorithm for Record 100 of the MIT-BIH-AR dataset.
Different metrics were adopted to evaluate the perfor-mance of the proposed model with both the manual andlearning-based graph designs. These metrics includedsensitivity (
Sen ), positive predictivity rate (
P P R ), anddetection error rate (
DER ), which are calculated by:
Sen (%) =
T PT P + F N × (4) PPR (%) =
T PT P + F P × (5) DER (%) =
F N + F PT P + F N × (6)where T P is true positives,
F P is false positives,
F N is false negatives, and
T N is true negatives. Table I (a)(b)(c) , 𝑔 =0 𝝀 =0 , 𝑔 =50 𝝀 = 3 ∗ 10 , 𝑔 =100 𝝀 = 0 , 𝑔 =0 𝝀 = 0 , 𝑔 =0 𝝀 =0 , 𝑔 =0 𝝀 =0 Fig. 11:
The model’s performance for Record 230 of the MIT-BIH-AR dataset. (a)
The training progress, (b) extracted R-peaks for a window of this record, and (c) the constraint graphstructure. presents the performance of the proposed model re-garding both the manually defined and learning graphsagainst other state-of-the-art methods for R-peak detec-tion (QRS complex). As shown in the table, the proposedalgorithm achieved
Sen = %99.76,
PPR = %99.68, and
DER = 0.55 for the manual definition of the constraintgraph and
Sen = %99.64,
PPR = %99.71, and
DER =0.19 for the learning constraint graph using the MIT-BIH-AR database. Note that the model constrained to themanually defined graphs outperformed the model com-bined with the graph learning algorithm because in thelatter, the model’s performance was largely dependentn the initial graph structure.
TABLE I:
Comparison of the performance of several R-peakdetection methods using the MIT-BIH-AR database
Method
Sen (%)
PPR (%)
DER (%) P ark et al. [8] 99.93 99.91 0.163 F arashi [41] 99.75 99.85 0.40 S harma and Sunkaria [3] 99.50 99.56 0.93 C astells-Rufas and Carrabina [2] 99.43 99.67 0.88 GCCD Model with Manual Definition of the Constraint Graph 99.76 99.68 0.55GCCD Model with Learning of the Constraint Graph 99.64 99.71 0.19
ECG recordings in the MIT-BIH-AR database werechosen to challenge the R-peak detection task becausethey represent a wide variety of QRS morphologies withreal-world variability. Our proposed model yielded out-standing results when detecting R-peaks in these trickyrecords. Records 103, 104, 105, 108, 111, 112, 116,200, 201, 203, 205, 208, 210, 217, 219, 222, and 228are comprised of abrupt changes in ECG morphology,and they are severely affected by noise and artifacts.Figure 5 shows the capability of the model to detectR-peaks in the presence of baseline wandering noise.We re-emphasize that these comparable results wereobtained without applying any preprocessing operations,as opposed to other methods in the literature. Records108, 113, 117, 201, 202, 203, 213, 219, 222, 223, 231,and 232 contain many peaks with unusual amplitudes.Small-amplitude R-peaks or high-amplitude P- and T-peaks embedded in high-amplitude QRS complexes canlead to high FN and FP errors in the R-peak detectiontask. As a representative example, Figure 4 illustratesthe efficiency of the GCCD model in R-peak detectionfor Record 117, which contains many beats with high-amplitude T-peaks.The experimental results obtained using the proposedmodel justify changepoint detection models as a po-tential approach to extract ECG fiducial points. In thisstudy, we demonstrated the capability of the GCCDmodel in locating R-peaks within various morphological patterns of ECG. The proposed greedy graph searchalgorithm can potentially detect ECG waves other thanthe R wave (i.e., P, Q, S, and T waves) by consideringcorresponding prior knowledge of the graph editingcandidates. We noticed that in Records 114, 200, 203,207, and 210, the
Sen and
PPR values were less than99%. These records contain multiple different morpho-logical patterns, including negative QRS complexes, andRecords 200 and 203 have several QRS complexes withventricular arrhythmias. The constraint graph for theserecords involves learning a graph with more than oneoptimum graph path. Learning a multi-path constraintgraph is also required to detect all ECG waves dueto the various morphological patterns of each waveincorporated into the graph. The other point that shouldbe considered here is that the GCCD model estimatesthe ECG signal using a Gaussian function. A modifiedmodel with a multi-Gaussian fitting method can dras-tically improve the ECG-related changepoint detectiontask.Future work should focus on developing the proposedmodel with a multi-Gaussian fitting and a multi-pathgraph learning algorithm. Incorporating these modifica-tions into the proposed model could provide a promisingplatform for evolving new graph-based tools to detectand classify heart arrhythmias. A multi-path graph learn-ing algorithm could reveal the morphology of the ECGsignal (time duration, amplitude, and direction of eachwave) in each cardiac cycle. Subsequently, new graph-based features could be extracted from the constraintgraph path for an ECG cycle to classify heartbeats.IV. C
ONCLUSION
The accurate delineation of R-peaks in the ECG signalplays a crucial role in most automated ECG analysisools. This paper proposed a novel graphical modelbased on changepoint detection techniques for detectingR-peaks within a non-stationary ECG signal. The pro-posed model was highly successful at detecting R-peaksin noisy ECG data without applying any preprocessingsteps. To our knowledge, this is the first time thata changepoint detection model has been applied forECG fiducial points detection. In this new framework,prior biological knowledge about the expected sequencesof changes was incorporated into the model using agraph. We defined the constraint graph manually andautomatically using a proposed greedy graph searchalgorithm. Using the proposed graph learning algorithm,the initial graph structure can develop into a structurecontaining edge parameters with maximum detectionaccuracy for a record. The experimental results providedin this paper demonstrate that the GCCD model canbe a promising approach for detecting ECG wavesand developing new graph-based tools for further ECGanalysis. The proposed graphical model approach can beadvanced by learning a multi-path constraint graph andfitting a multi-Gaussian curve model to the ECG signal,which should be considered in future studies.ACKNOWLEDGMENTThis material is based on work supported by theNational Science Foundation under Grant Number1657260. Research reported in this publication was sup-ported by the National Institute on Minority Health andHealth Disparities of the National Institutes of Healthunder Award Number U54MD012388.R
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