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1 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO., NOVEMBER A Framework or Fuzzy Expert System Creation Application to Cardiovascular Diseases Markos G. Tsipouras, Student Member, IEEE, Costas Voglis, and Dimitrios I. Fotiadis*, Senior Member, IEEE Abstract A methodology or the automated development o uzzy expert systems is presented. The idea is to start with a crisp model described by crisp rules and then transorm them into a set o uzzy rules, thus creating a uzzy model. The adustment o the model s parameters is perormed via a stochastic global optimization procedure. The proposed methodology is tested by applying it to problems related to cardiovascular diseases, such as automated arrhythmic beat classiication and automated ischemic beat classiication, which, besides being well-known benchmarks, are o particular interest due to their obvious medical diagnostic importance. For both problems, the initial set o rules was detered by expert cardiologists, and the MIT-BIH arrhythmia database and the European ST-T database are used or optimizing the uzzy model s parameters and evaluating the uzzy expert system. In both cases, the results indicate an escalation o the perormance rom the simple initial crisp model to the more sophisticated uzzy models, proving the scientiic added value o the proposed ramework. Also, the ability to interpret the decisions o the created uzzy expert systems is a maor advantage compared to black box approaches, such as neural networks and other techniques. Index Terms Arrhythmic beat classiication, expert systems, uzzy modeling, ischemic beat classiication. I. INTRODUCTION MEDICAL expert systems are a challenging ield, requiring the synergy o dierent scientiic areas. The representation o medical knowledge and expertise, the decision making in the presence o uncertainty and imprecision, and the choice and adaptation o a suitable model are some issues that a medical expert system should take under consideration. Uncertainty is traditionally treated in a probabilistic manner recently, however, methods based on uzzy logic have gained ground [], [2]. The model s parameter adaptation (training) amounts to optimizing a properly constructed error unction. Manuscript received August 9, 2006 revised January 9, This work was supported by the program Heraklitos o the Operational Program or Education and Initial Vocational Training o the Hellenic Ministry o Education under the 3rd Community Support Framework. Asterisk indicates corresponding author. M. G. Tsipouras is with the Unit o Medical Technology and Intelligent Inormation Systems, Department o Computer Science, University o Ioannina, GR 450 Ioannina, Greece ( markos@cs.uoi.gr). C. Voglis is with the Department o Computer Science, University o Ioannina, GR 450 Ioannina, Greece ( voglis@cs.uoi.gr). *D. I. Fotiadis is with the Unit o Medical Technology and Intelligent Inormation Systems, Department o Computer Science, University o Ioannina, P.O. Box 86, GR 450 Ioannina, Greece ( otiadis@cs.uoi.gr). Digital Obect Identiier 0.09/TBME There is a variety o methods with diverse eatures that may be proper. Understanding the subtleties o the optimization procedures is a key to choosing an eective training approach. Expert systems are a branch o artiicial intelligence, which make extensive use o specialized knowledge to solve problems at the level o a human expert. This knowledge is represented in by a set o rules [3]. An expert system s review o applications is presented in [4]. An expert system is created by deining a crisp or uzzy model (set o rules) and then optimizing its parameters to it a given dataset. Several approaches have been proposed in the literature or the development o uzzy or crisp models. In most o them, the model is trained using a known optimization technique, i.e., uzzy rules with genetic algorithms [5], uzzy rules with simulated annealing [6], multicriteria decision analysis with genetic algorithms [7]. Neuro-uzzy algorithms have also been proposed, where, the uzzy rules are modeled by artiicial neural networks (ANNs) and popular training techniques are applied [8]. In this paper, a ramework or the automated generation o a uzzy expert system (FES) is proposed. The ramework is based on rules, which are initially represented using the crisp membership unction, org a crisp model. The rules are then transormed rom crisp to uzzy ones, using a uzzy membership unction and and, which are uzzy equivalence or the binary and OR operators, respectively []. Using dierent selections or the uzzy membership unction and dierent deinitions or the and, several uzzy models can be created. Then, the uzzy model is tuned so as to ind optimal parameters o the uzzy membership unctions, and, i necessary, parameters or the and the uzzy model combined with the optimal parameters comprises a FES. The proposed ramework is applied to two well-known cardiovascular domain problems, the arrhythmic beat classiication and the ischemic beat classiication rom electrocardiograms (ECGs). In the ollowing, initially some basics o the classiication problem and uzzy logic are briely described and then the ramework or the automated FES creation is presented in detail. Next, the two domains o application are described (arrhythmic beat classiication, ischemic beat classiication) along with the employed datasets or each one, the initial medical rules, the respective crisp models and the FESs, automatically generated rom the proposed methodology. Also, results rom the evaluation o the created FESs are presented. In the ollowing, the scientiic added value o the methodology along with its advantages and disadvantages are addressed. Also, the /$ IEEE Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

2 2090 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO., NOVEMBER 2007 generated FESs and their results are discussed. Finally, urther improvements o the automated methodology are discussed. number o simple rules used in and is the crisp membership unction (increasing or decreasing), deined as II. METHODOLOGY First, deinitions and related terology used in the classiication problems and uzzy logic, are introduced. Having the data,, where is a single pattern with eatures, is its class ( is the number o classes), and is the total number o patterns (the size o ), a classiication problem is deined as the deteration o a mapping model, where [9]. An alternative representation or the class is, where, i belongs to class, then. A common methodology to treat a classiication problem is to deine a mapping model and train it, using a subset o the data and a cost unction, which is imized. A tool that is used or the evaluation o a classiication model is the normalized conusion matrix, having dimension, deined as o patterns in class classiied to class total patterns in class where is the element o the conusion matrix. Crisp logic is the binary reasoning. Membership unctions are undamentals in set theory, measuring the certainty o an obect belonging to a set. The membership unction used in crisp logic, is a binary operator and its value is or 0, representing that does or does not belongs to, respectively. Fuzzy logic is a generalization o the classical set theory [], [2]. It has been used to represent and manage the vagueness, which arises in data or in expert s knowledge [0]. The uzzy logic is based on uzzy membership unctions, which are continuous approaches that have values in the interval, representing the relationship between the obect and the set. A. Crisp Model A crisp model consists o crisp rules, where is a vector containing all parameters (thresholds) used in the th rule and is the number o classes thus, one rule is deined or each class. Each consists o several simple rules, deined as (the th simple rule in the th rule), where is a unction o the data, is a parameter (the th parameter in the vector), is the () increasing or decreasing (2) Each rule can be expressed as a combination o simple rules, as ollows [see (3), shown at the bottom o the page] where,. A simple rule is a rule that contains only one inequality (e.g., ). Having several instances o an obect belonging to category, each row o the includes all simple rules, which are related to a single obect instance. Then, the combines all instances related to the same class. The inal decision (class) o the crisp model is made using the results rom all rules:, where is a vector containing all thresholds and is a unction that combines the outcomes o all crisp rules and results to one o the classes. Depending on the representation selected or, the inal decision is, where is the number o classes, or, where, i is classiied to class, then. A more general deinition o the unction could include an additional result, which states that the classiication process ailed (i.e., or a single case two or more rules were true). In this case the inal decision is or (but not necessary ). Each row o the rule (i.e., ) is a conunction (sequence o ) o one or more simple rules and the rule is a disunction (sequence o OR) o its rows. This orm is known as disunctive normal orm (DNF) and has been chosen because every logical expression (i.e., set o rules) can be written in DNF. B. Fuzzy Model The crisp model is transormed into a uzzy model using a uzzy membership unction instead o the crisp. In this case, is a vector containing all parameters used in the uzzy membership unction and its size depends on the selection o the uzzy membership unction. Table I presents some monotonic uzzy membership unctions along with the parameters needed or each one. Also, and are used Table II presents some common deinitions or the OR OR (3) Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

3 TSIPOURAS et al.: FRAMEWORK FOR FUZZY EXPERT SYSTEM CREATION 209 TABLE I MONOTONIC FUZZY MEMBERSHIP FUNCTIONS and. Depending on the deinition, the and might need parameters or not (also shown in Table II). A uzzy model consists o uzzy rules, where is a vector containing all parameters used in the th rule. Again, each consists o several simple rules,deined as (the th simple rule in the th rule):, where is the same unction o the data as in the crisp model and is a vector o parameters. Each rule is again ormed as a combination o simple rules, as ollows [see (4), shown at the bottom o the page], where,,, with each being a vector with parameters used in the membership unction o the th simple rule o the th rule, each being a parameter entering the o the th raw o the th rule (with being the total number o rows) and being a parameter (one or each rule) entering the. I the and does not need parameters, then,. The inal decision (class) o the uzzy model is made using the result o all rules:, where is a vector containing all parameters used in the rule and is a unction that combines the outcomes o all uzzy rules (deuzziier). Again, the deinition o the unction can include the unclassiied state. Depending on the representation selected or, the inal decision o the model could be or, where, i is classiied to class, then. Also, i unclassiied state is included, then the inal decision o the model could be or. The transormation o the crisp set o rules to the respective uzzy greatly depends on the selection o the uzzy membership unction, the and and the deuzziier i speciic combinations among these are selected then known solutions rom the literature can be used to express the explicit mathematical input-output o the uzzy model [2], []. C. Optimization The parameters entering a uzzy model can be optimally detered using an optimization procedure. Formulating the training process o a model as an optimization problem is a common practice in order to construct eicient expert systems. The eiciency o the system highly depends on the quality o the cost unction and the choice o a training dataset. Also, a robust optimization method increases the speed o training process and enhances the quality o the inal solution. The selection o the optimization method greatly depends on the equations describing the uzzy model and the selection o the cost unction i these are dierentiable then an optimization method making use o the irst derivatives inormation can be employed, else methods that do not require irst derivatives must be used (e.g., [47]). The optimization problem can be ormulated as: imize unction subect to, where and. It can be viewed as a decision problem which involves the computation o the best vector o the decision variables over all possible vectors in. This vector is called the imizer o over. Considering the optimization problem, two kinds o imizers can be distinguished, local and global imizers. A point is a local imizer o over i there exists such as or all and. A point is a global imizer o over i or all [2]. Finding global imizers is a challenging task and several techniques have been proposed: Branch and Bound techniques [3], simulated annealing [6], [4], genetic algorithms [5], [7], and stochastic methods. (4) Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

4 2092 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO., NOVEMBER 2007 TABLE II DEFINITIONS OF T S In the case o a uzzy model, a cost unction must be deined over a dataset,. The imization o this unction leads to an improved model, in terms o its classiication ability. A common cost unction is the mean square error (MSE) unction, which is deined as MSE (5) where thereore,. A second approach is to use the trace o the normalized conusion matrix [conusion matrix error (CME)] CME (6) where is a penalty term, which can be a unction o the unclassiied rates o each classiication category. In this case, and.i, then the normalized conusion matrix is deined as, and i the unclassiied ratio or each classiication category is deined as. In this case, the penalty term can be deined as. Fig. presents a lowchart o the above described methodology using a hypothetical initial set o crisp rules, the three stages o the methodology (crisp model, uzzy model, and optimization) are shown. III. APPLICATION TO CARDIOVASCULAR DISEASES The above described ramework was applied to two wellknown classiication problems rom the cardiovascular domain, the arrhythmic beat classiication and the ischemic beat classiication rom electrocardiograms (ECGs). For both cases, med- Fig.. Flowchart o the proposed methodology and its application on a hypothetical initial set o crisp rules. ical experts detered the initial set o rules, while well-known benchmark databases were used or the creation o the expert systems and their evaluation. A. Medical Background ) Arrhythmic Beat Classiication: Arrhythmia can be deined as any type o rhythm that deviates rom the normal sinus Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

5 TSIPOURAS et al.: FRAMEWORK FOR FUZZY EXPERT SYSTEM CREATION 2093 TABLE III DESCRIPTION OF DATASETS rhythm. An arrhythmia can be either a single or a group o heartbeats, and it can aect the heart rate causing slow, ast or irregular rhythms [5]. Arrhythmias can take place in a healthy heart and be o imal consequence but they may also indicate serious cardiac problems [6], [7]. Thereore, automatic arrhythmic beat detection and classiication, using the ECG and/or eatures extracted rom it, is a critical task in clinical cardiology, especially when perormed in real time. In the later, each beat is classiied into several dierent rhythm types. The techniques or beat classiication are based on artiicial neural networks [8], [9], mixture o experts approach [20], hermite unctions combined with sel-organizing maps [2], uzzy neural networks [22], AR models [23], artiicial neural networks and uzzy equivalence data [24], support vector machines [25], ECG morphology and linear discriates [26], time-requency analysis combined with knowledge-based systems [27], and rulebased systems [28]. 2) Ischemic Beat Classiication: Myocardial ischemia is the condition where oxygen deprivation to the heart muscle is accompanied by inadequate removal o metabolites due to reduced blood low or perusion. This reduced blood supply to the myocardium causes alterations in the ECG signal, such as deviations in the ST segment and changes in the T wave [29]. The accurate ischemic episode detection, where a sequence o cardiac beats is assessed [30], is based on the correct detection o ischemic beats [3] [33]. Several techniques that evaluate the ST segment changes and the T-wave alterations have been proposed or ischemic beat detection. More speciically, the use o approaches like parametric modeling [34], wavelet theory [35], set o rules [36], [37], artiicial neural networks [30], [38], multicriteria decision analysis and genetic algorithms [7] have been previously reported. B. Datasets ) Arrhythmia Dataset: All the records rom the MIT-BIH arrhythmia database [42] were used or the training and the evaluation o the arrhythmic beat classiication FES. Initially, the RR-interval signal was extracted rom the ECG recordings using QRS detection [43], [44], except in the case o VF episodes in record 207, where the actual beats rom the annotation o the database were used. Then, windows o three consecutive RR intervals, where is the th RR interval in the RR interval signal, were deined and both rhythm and beat annotations (deined in the database) were used to speciy the class o each window, as ollows: i the middle beat o the window belongs to 2 heart block episode (rhythm annotation BII in the database), ventricular lutter/ibrillation wave (beat annotations [,!, ], respectively, in the database) or it is annotated as premature ventricular contraction (beat annotation in the database) then or or, respectively. Everything else was considered as normal sinus rhythm. Thereore, the dataset was deined as:,, with being a single pattern with three eatures, its class with our dierent classes, and is the number o patterns (beats in the dataset). The class can be represented either as or, where, i belongs to class, then, i.e.,. The cardiac rhythm categories and the number o beats used in each cardiac rhythm category, are shown in Table III. 2) Ischemia Dataset: The European Society o Cardiology (ESC) ST-T database [45] was used or the training and the evaluation o the ischemic beat classiication FES h o two-channel ECG recordings were selected. Those, contain the irst hour o the e003, e005, e008, e03, e04, e047, e059, e062, and e0206 recordings and the whole e004 recording. These ten recordings were selected because their ischaemic ECG beats are characterized by signiicant waveorm variability. First, the preprocessing o the recorded ECG signal was perormed (or both channels) in order to eliate noise distortions (e.g., baseline wandering, A/C intererence and electromyographic contaation) [7] and locate the isoelectric line and the J point [46]. Then, the ollowing eatures were extracted rom each cardiac beat. i) The ST segment deviation, which is the amplitude deviation o the ST segment rom the isoelectric line. The ST segment changes were measured either 80 ms ater the J point (J80) (heart rate bpm), or 60 ms ater the J point (J60) (heart rate bpm). ii) The ST segment slope, which is the slope o the line connecting the J and J80 (or J60) points. Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

6 2094 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO., NOVEMBER 2007 iii) The T-wave amplitude, which is the amplitude deviation o the T-wave peak rom the isoelectric line. iv) The T-wave normal amplitude together with its respected polarity which reer to the amplitude and polarity o normal beats or a speciic ECG lead. It was calculated using the irst 30 s o each recording and was computed by using the mean value o the T-wave amplitudes at this interval. In order to deine the class o each beat, three medical experts annotated independently each beat as normal, ischemic or arteact. In the case o disagreement, the decision was taken by consensus. Ater removing the arteacts and the misdetected beats the remaining were diagnosed as normal or ischaemic. Thus, the dataset was deined as:, with being the th eature vector (,, and o the th beat), the class o the beat (normal or ischemic), and is the number o beats in the dataset. The class is represented either as or i.e., i the beat is normal and i the beat is ischaemic. The ischemic beat categories and the number o beats in each category are also shown in Table III. C. Initial Set o Rules ) Arrhythmic Set o Rules: The three RR-intervals window was used to classiy the middle RR interval into one o the our categories: ) ventricular lutter/ibrillation (VF), 2) premature ventricular contraction (PVC), 3) normal sinus rhythm (N), and 4) 2 heart block (BII). Also, i the classiication process ails, the middle RR interval was classiied as (5) unclassiied. Three rules were used or the classiication (see the irst equation shown at the bottom o the page). In the case that none o the three rules was true, then the interval was classiied as while is the case o more than one o the three rules was true the interval was unclassiied (5). 2) Ischemic Set o Rules: In the case o ischemic beat classiication, the rules used in [37] were employed. The eature vector was used to classiy the beat as normal or ischemic (see the second equation shown at the bottom o the page). D. Crisp Models ) Arrhythmic Crisp Model: The arrhythmic beat classiication crisp model includes three crisp rules Rule I OR then is classiied as Rule I OR OR OR then is classiied as Rule I OR then is classiied as Rule I OR OR OR OR then the beat is classiied as ischemic else the beat is classiied as normal Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

7 TSIPOURAS et al.: FRAMEWORK FOR FUZZY EXPERT SYSTEM CREATION 2095 [see (7) (9), shown at the bottom o the page], where,,, and,. The inal decision o the was made using the results rom all rules, i.e.,:, where is a vector containing all thresholds used in the model and is a unction that combines the outcomes o all crisp rules and its deinition depends on the error unction that was used. In the case o the CME unction (5), see (0), shown at the bottom o the page. In a similar way, i the MSE unction was used (6), then was deined as (), shown at the bottom o the page. 2) Ischemic Crisp Model: The ischemic beat classiication crisp model includes one crisp rule [see (2), shown at the bottom o the next page], where,. The inal decision o the was made as:, where and, i the CME unction (5) was used or optimization, was deined as i i while, i the MSE unction (6) was used, then as i i is true is alse (3) was deined is true is alse. (4) OR (7) OR OR OR (8) OR (9) i only is true i only is true i all, and are alse i only is true i more than one o the, or are true (0) i only is true i only is true i all, and are alse i only is true i and are true i and are true i and are true i all and are true () Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

8 2096 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO., NOVEMBER 2007 E. Fuzzy Models ) Arrhythmic Fuzzy Models: Several uzzy models were developed, depending on the selection o the uzzy membership unction and the and deinitions. Each uzzy model, where was the uzzy membership unction and were the and deinitions had three uzzy rules, deined as (5) (7), shown at the bottom o the page, where,,,, and,,, 2 (i the and do not need parameters, then,,, and, ). The inal decision or each was made combining the results o all uzzy rules:, where is a vector containing all parameters used in the model ( is a parameter deined below) and is the deuzziication unction, which combines the outcomes o all uzzy rules and its deinition depends on the error unction used. In the case o CME, was deined as (8), shown at the bottom o the next page. The deuzziication unction is problem-speciic and it is designed so as to relect the expert s knowledge on this speciic domain. Each was considered a priori normal sinus rhythm (category 3). Thereore, i the maximum value o the results o the three rules is, then was classiied as normal sinus rhythm ( is a parameter). I the maximum value o the results o the three rules was, then was classiied in the category o the rule that had the maximum result, i.e., in category i the was the maximum, category 2 i was the maximum and category 4 i was the maximum. Finally, i the maximum value o the results o the three rules was but two or more o the rules had the maximum value, then was classiied as category 5 (unclassiied). I MSE was used, was deined as (9) OR OR OR OR (2) R d l = S norm T norm g dec (RR l0 ) g dec (RR l 2) g dec (RR l+ 3) g dec (RR l0 + RR l + RR l+ 4) (5) R 2 d l 2 = S norm T norm g inc RR l0 2 g inc RR l RR l RR l T norm g inc RR l+ RR l0 23 g inc RR l RR l T norm g dec (RR l0 0 RR l 25) g dec (RR l0 26) g dec (RR l 27) g dec RR l0 + RR l RR l+ T norm g dec (RR l 0 RR l+ 29) g dec (RR l 20) g dec (RR l+ 2) g dec RR l + RR l+ 2RR l (6) R 3 d l 3 = S norm T norm g inc (RR l 3) g dec (RR l 32) g dec (RR l0 0 RR l 33) 3 T norm g inc (RR l 34) g dec (RR l 35) g dec (RR l+ 0 RR l 36) 32 3 (7) Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

9 TSIPOURAS et al.: FRAMEWORK FOR FUZZY EXPERT SYSTEM CREATION ) Ischaemic Fuzzy Models: Again, several uzzy models were developed, depending on the selection o the uzzy membership unction and the and deinitions. Each uzzy model included a single uzzy rule [see (20), shown at the bottom o the page], where,,, 2 (i the and does not need parameters, then, ). Again, the inal decision or each uzzy model was made using a problem-speciic deuzziication unction:, where ( is deined below) and was deined as i else (2) when the CME unction was used, while in the case o using the MSE unction, then was deined as (22) Detailed versions o the equations o the uzzy rules or both arrhythmic and ischemic uzzy models, or speciic selections o uzzy membership unctions and and deinitions are presented in the Appendix. F. Expert Systems Once a uzzy model were created, the parameters entering the model must be identiied thus, a cost unction was imized. It should be mentioned that the number o parameters entering each uzzy model diers signiicantly, depending on the uzzy membership unction selection and the and deinitions. Both mean square error and conusion matrix cost unctions, deined in (5) and (6), respectively, were tested. To perorm the optimization a training dataset was needed, which was a randomly selected subset o or, depending on the problem. In the case o arrhythmic beat classiication, the contained 250 patterns rom classes VFL and BII, 000 patterns rom class PVC and patterns rom class N. Thus, the size o the dataset or the arrhythmic beat classiication was 500 beats. Appropriate weights were used or each class so as there would be no bias or larger classes (i.e., each VFL or BII pattern entered the optimization procedure 40 times and each PVC pattern ten times). In the case o ischemic beat classiication the contained 3766 normal and 3932 ischemic beats, and, thus, its size was 7698 beats (the training set was constructed by selecting iteratively the irst beat out o a sequence o ten beats). and are shown in Table III. The optimization method that it was used is a modiication o controlled random search (MCRS) [47]. The MCRS is inspired rom simplex method or local optimization, because o the irregular simplex comprised rom points, which is maintained in each iteration o the method. In the main step o the algorithm, the simplex s points are used to obtain a trial point which, under certain conditions, will replace the previous best rom the simplex. Note that i more than one global ima exist, the method will locate only one o them. The MCRS method is described in the Appendix. Given a speciic uzzy model (e.g., where the sigmoid unction was selected as uzzy membership unction and the -max deinition or the and ), a cost unction (e.g., the mean square error), a training dataset and a range where the model s parameters were constrained, the MCRS algorithm was applied or a speciied number o iterations or until a stopping criterion was met (see Appendix), and it attempted to optimize the value o the cost unction with respect to the parameters entering the uzzy model (e.g., the parameters used or the uzzy membership unctions and the parameters o the and,i any). The FES was ormulated by setting the parameters o each model to the best solution ound. i i i i i and two or more o the, or are equal (8) (20) Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

10 2098 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO., NOVEMBER 2007 TABLE IV SENSITIVITY (%), SPECIFICITY (%) POSITIVE PREDICTIVE VALUE (%) OF THE CRISP MODEL THE AVERAGE CONFUSION MATRICES FOR ALL FUZZY EXPERT SYSTEMS FOR THE ARRHYTHMIC BEAT CLASSIFICATION PROBLEM, USING THE CME COST FUNCTION IV. RESULTS The crisp model and the FESs (all combinations between the uzzy membership unctions and the and deinitions) were tested using both MSE cost unction and total accuracy cost unction (CME), or both arrhythmic and ischemic beat classiication. The test dataset consisted o the remaining patterns o ater selecting (the selection was made as described above or each problem) both and are presented in Table III. Ten dierent pairs o and were created. The crisp model o both arrhythmic beat classiication and ischemic beat classiication problems were evaluated or all datasets, resulting to ten normalized conusion matrices which were combined using gross statistics to result to the average conusion matrix. Finally, sensitivity (Se), speciicity (Sp), and positive predictive value (PPV), or the average conusion matrix, were calculated. The same procedure was ollowed or the FESs they were optimized (using ) and evaluated (using ) with each pair o them. The maximum number o iterations o the MCRS algorithm was set to this ensures that the algorithm would stop either when the convergence criterion was satisied (Appendix, MCRS algorithm, Step, third bullet), or when the maximum number o iterations was reached. For the arrhythmic beat classiication problem, Se, Sp, and PPV o the crisp model and the FESs created using the CME cost unction are presented in Table IV. The results using the MSE cost unction are quite similar the average absolute dierence is 0.25% while the maximum absolute dierence is 2.25%. For the ischemic beat classiication problem, all evaluation results are presented in Table V. In Table VI, accuracy or the crisp model and all FESs, or both arrhythmic and ischemic beat classiication problems, using both and MSE cost unctions are presented, along with the number o parameters entering each uzzy model. From the obtained results it is clear that the application o the proposed methodology improved the eiciency o the initial crisp model the best FES or the arrhythmic beat classiication results to 96.43% accuracy, improving by 5.36% the corresponding accuracy o the crisp model, while, in the case o the ischemic beat classiication the corresponding improvement is.27%. The number o beats in test sets is suiciently large thus, the error rates, deined as:, o the crisp model and the best uzzy model in both cases (i.e., arrhythmic and ischemic beat classiication) can be approximated using normal distributions [48]. I the observed dierence in is deined as:, then is also normally distributed, with variance:, where the number o test records (i.e., number o beats), is the accuracy o the crisp model and is the accuracy o the best uzzy model. At 95% conidence level, the upper bound or the standard normal distribution is.96, and, thus, the conidence interval or the true dierence is given by:. Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

11 TSIPOURAS et al.: FRAMEWORK FOR FUZZY EXPERT SYSTEM CREATION 2099 TABLE V SENSITIVITY (%), SPECIFICITY (%) POSITIVE PREDICTIVE VALUE (%) OF THE CRISP MODEL THE AVERAGE CONFUSION MATRICES FOR ALL FUZZY EXPERT SYSTEMS FOR THE ISCHEMIC BEAT CLASSIFICATION PROBLEM, USING BOTH CME MSE COST FUNCTIONS For arrhythmic beat classiication, the conidence interval or at 95% conidence level is, which does not spam the zero value, and, thus, the observed dierence is statistically signiicant. Similarly, or ischemic beat classiication, the conidence interval or at 95% conidence level is, which also does not spam the zero value, and, thus, the observed dierence is statistically signiicant. In both cases the observed dierence is also statistically signiicant i the conidence level is set to 99% in this case, the upper bound or the standard normal distribution is 2.58 and the conidence intervals or are and or arrhythmic and ischemic beat classiication, respectively. The selection o the cost unction does not have an impact on the obtained results or both CME and MSE cost unctions the results were similar or arrhythmic and ischemic beat classiication. The obtained results are slightly improved i a parameter-based approach was incorporated or the and deinitions (i.e., Dompi, Dubois Prade or Yager class), compared to the approaches which are based on parameter-ree deinitions (i.e., imum and maximum, algebraic product and probabilistic OR, Einstein product and sum). An average increase.2% exists independently o the exaed problem or the incorporated cost unction or the uzzy membership unction selection. The extra and parameters make the uzzy models more lexible, and, thus, the optimization results to better FESs. However, with respect to the uzzy membership unction selection, the FESs or the arrhythmic beat classiication problem using uzzy membership unctions with less parameters (sigmoid or sum o a sigmoid and its gradient) have slightly better results than the ones with more parameters (nested sigmoid or sum o two sigmoids) the results o the FESs or the arrhythmic beat classiication problem when the sigmoid or sum o a sigmoid and its gradient uzzy membership unctions are incorporated are 0.22% on average better than when the nested sigmoid or sum o two sigmoids uzzy membership unctions are used. The FESs, or the ischemic beat classiication problem show similar perormance. In all cases, the linear uzzy membership unction has the worst results.2% reduction or arrhythmic beat classiication and.9% or ischemic beat classiication. V. DISCUSSION In this paper, we describe a methodological ramework or the automated generation o FESs, which are based on an initial crisp model that includes a set o rules. The set o rules is represented in DNF, using the crisp memberhip unction, ormulating a crisp model. Then, the rules o the crisp model are transormed to uzzy ones, org the uzzy model. This uzziication is based on the use o a uzzy membership unction instead o the crisp one and the use o and instead o the binary operators. The produced uzzy models are tuned using global optimization. Given an initial set o rules, the pro- Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

12 200 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO., NOVEMBER 2007 TABLE VI ACCURACY (%) FOR THE CRISP MODEL ALL FUZZY EXPERT SYSTEMS, FOR BOTH ARRHYTHMIC ISCHEMIC BEAT CLASSIFICATION PROBLEMS, USING BOTH CME MSE COST FUNCTIONS posed methodology can automatically produce a FES, or any problem under consideration. This is a due to: a) the employment o the DNF which can be used to every logical expression b) the transormation o the crisp rules into uzzy rules is perormed using a uzzy membership unction and an approach or the binary operators and thereore, it can be carried out or any set o rules written in a DNF in an simple and automated manner and c) the optimization technique is a derivative-ree algorithm and it does not need any inormation other than the obective unction. There are some approaches proposed in the literature which are based on the same philosophy, i.e., proposing a model and optimizing its parameters [5] [7]. In [6] and [7], the methodology ollowed is designed or a speciic problem, and it is not a general approach. In [5], a ramework or the development and optimization o uzzy models is described, but the initial model is based on the entropy o the data and not on a set o rules. Also the methodology is evaluated using only artiicial data. All the optimization techniques used in [5] [7] are derivative ree. In the proposed methodology, although the optimization technique does not require derivatives, there are available or all uzzy models, except is the case where the imum & maximum approach is used or the and deinition [49]. We have not tested other optimization methods MCRS is a recently developed global optimization technique, having several advantages and presenting superior robustness among its peers, although is not the most eicient one [47]. Furthermore, our main concern was to locate the global imum and not to ind the most eicient optimization method. However, this must be exaed in a uture communication. This general ramework is evaluated in the development o FESs or two cardiovascular domain problems, the arrhythmic and the ischemic beat classiication, using ECG recordings. Medical experts provided the initial set o rules, which are represented in a DNF, org the crisp model. The crisp rules are transormed into uzzy, using several dierent combinations o common uzzy membership unctions and approaches or the and deinitions. However, or both presented applications, the deuzziiers are designed based on knowledge provided by experts on the speciic domains and they are not common approaches proposed in the literature. These, task-speciic deuzziication procedures can be considered as an advantage compared to common deuzziication procedures, since they relect the experts knowledge or the speciic domains, but they have also the disadvantage that known implicit input-output ormulas, proposed in the literature, cannot be applied. The MCRS algorithm is used to tune the parameters o the models. The MIT-BIH arrhythmia database and the ESC ST-T database are used or the model s optimization, or the arrhythmic and the ischemic beat classiication, respectively. In both cases, the obtained results indicate a signiicant improvement compared to the initial crisp models. Thus, our methodology can be proven to be a useul tool or the improvement o the eiciency o existing knowledge-based systems. Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

13 TSIPOURAS et al.: FRAMEWORK FOR FUZZY EXPERT SYSTEM CREATION 20 TABLE VII SUMMARY OF PREVIOUS METHODS FOR ARRHYTHMIC BEAT CLASSIFICATION ISCHEMIC BEAT CLASSIFICATION The proposed methodology produced very eicient FESs or the arrhythmic beat classiication problem, which present several advantages compared to other methods or arrhythmic beat classiication: a) they use only the RR-interval signal, which can be extracted with high accuracy even or noisy or complicated ECG recordings (e.g., the 200 series o the MIT-BIH arrhythmia database), while the extraction o all other ECG eatures or any other type o ECG analysis is seriously aected by noise b) they are based on medical knowledge, which is usually ignored in similar systems c) they perorm in real time d) all other approaches use closed datasets, i.e., datasets containing data belonging only to the classes that are classiied, which is not possible in real lie data. In the proposed method the dataset does not contain data only rom the classes that are classiied a more realistic approach is used: three classes (VF, VT, BII) are classiied and the remaining data are classiied as N e) they are ully automated and ) interpretation is available or the decisions made. A limitation is the use o the actual beats instead o QRS detection in the VF episodes o the 207 record. A summary o the results obtained or arrhythmic beat classiication by other methods is shown in Table VII all methods are evaluated using the MIT-BIH arrhythmia database. Most o the approaches are based on the analysis o the ECG signal [8] [26] while the approaches proposed in [27], [28] and in the present work is based on the analysis o the RR-interval signal only. All methods indicate high perormance, 94.26% 98.49% the proposed FESs results in comparable perormance. However, some o the methods are evaluated using very small datasets [8], [9], [22], [23]. In [20], initial labeling o the beats was required and there was no automatic QRS detection. A similar approach was used in [26] or the iducial points. In [2], the primary obective was to perorm clustering with a human expert perorg the inal beat classiication. In our case, the resulted FES is evaluated using all records rom the MIT-BIH arrhythmia database. It is ully automated, compared to [20] and [2] and there is no training stage, as in other approaches [8], [22]. Table VII also presents a summary o previous methods or ischemic beat classiication. A direct comparison is not easible, since the evaluation is made with other datasets [34], [35], or dierent subsets o the ESC ST-T database [32], [39], [40], or employing dierent perormance measures [34], [39], [40]. The FESs produced rom the methodology, present several advantages compared to other methods or ischemic beat classiication: a) they are based on medical knowledge. In [36] a medical rule-based methodology is employed, however the results are rather poor b) they perorms in real time c) they are ully automated and d) they can provide interpretation or the decisions made. Most o the proposed approaches are based on ANNs [32], [38], and, thus, interpretation is not available. The interpretation ability characterizes also the methods proposed in [7] and [36]. In [7], genetic algorithms were utilised or ischemic beat detection the latter perormed better than our approach but it requires high computational eort and processing time to tune the parameters and it is not based on medical knowledge. Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

14 202 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO., NOVEMBER 2007 The application o the proposed methodology is not limited to medical domain problems and can be extended to other domains or problems having the same structure, i.e., decision based on a set o rules. An additional advantage is that the method can be used along with data ing methods, which usually lead to a set o crisp rules. The incorporation o data ing or the initial set o rules acquisition leads to a ully automated method, where only the diagnostic experience o doctors is needed. However, the proposed methodology has some limitations: a) it is not easy to express the uzzy inerence model to a closed orm, b) it is limited to applications that are based on crisp rules, and c) it greatly depends on the selection and the quality o the initial set o rules. The third limitation can be overcame i the initial set o rules is combined with a data ed set o rules. VI. CONCLUSION A methodology or FES creation is proposed. The methodology, which is ully automated, uses an initial set o crisp rules, provided by experts, and produces a FES. The methodology has been tested in the arrhythmic and ischemic beat classiication problems and the produced FESs indicate signiicant improvement o the initial classiication system, which is based on expert s knowledge and has the orm o a set o rules. The obtained results are also ully interpretable, which is a maor advantage compared to other approaches proposed in the literature or the speciic problems. In the proposed methodology, the initial crisp set o rules are detered by experts. Starting rom a crisp set o rules and then transorg it into a uzzy model allows our methodology to be applied in cases where the initial set o rules is strictly crisp. Based on this eature, an alternative is to extract rules rom the data, using a data ing technique, instead o a knowledge-based origin o the initial set o rules. In this case, the methodology would be ully automated, data driven, but the knowledge introduced rom the experts through the initial set o rules, would be lost. Furthermore, hybrid approaches, combining to expert s knowledge and data-ed rules are also applicable. In this context, also the ability to automatically predetere some o the uzzy model s basic aspects, such as the uzzy membership unction and the and deinitions based on the natural characteristics o the problem, is a signiicant ield o research. Another important eature is that the gradient is available or some o the uzzy models this eature can lead to the use o more eicient optimization methods, which take advantage o the irst derivative inormation. APPENDIX In this Appendix, details regarding the equations o the uzzy models (5) (2) will be provided along with a detailed description o the MCRS algorithm. Substituting in (5) (7), the sigmoid membership unction (Table III) and the imum and maximum deinitions or the and, or the arrhythmic uzzy rules it, see (23) (25), shown at the bottom o the page. In (9), the results o the uzzy rules are used without the use o a deuzziier. In (8), is used, which can be considered as a separate uzzy model, using, and uzzy rules and maximum deuzziier [see (26), shown at the bottom o the next page]. Again, substituting in (20), the sigmoid membership unction (Table III) and the imum & maximum deinitions or the and, or the ischemic uzzy rule, it is (27), shown at the bottom o the next page. R d =max +e +e +e +e (23) R d = max +e +e +e +e +e +e +e +e +e +e +e +e (24) R d = max +e +e +e +e +e +e (25) Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

15 TSIPOURAS et al.: FRAMEWORK FOR FUZZY EXPERT SYSTEM CREATION 203 The MCRS algorithm, which is a modiication o the Price s algorithm seeking or one global imum in a given domain, is described. MCRS Algorithm Input Data, an integer such that, where is the space dimension (suggested value: ), a small positive constant (suggested value ), a rather large positive constant (suggested value ) Step 0: Set. Form the initial set by picking points randomly rom. Evaluate or. Step : and let the corresponding point be denoted as. Similarly and let the corresponding point be denoted as. IF polish via a local search procedure and STOP. Step 2: Choose random by points rom. Calculate the weighted centroids:,, where, max R d R d R d = max +e +e +e +e +e +e +e +e +e +e +e +e +e +e +e +e +e +e +e +e +e +e (26) R d = max +e +e +e +e +e +e +e (27) Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.

16 204 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO., NOVEMBER 2007 Calculate the trial point as: where i and i IF REPEAT Step 2 Compute. Step 3: IF THEN Calculate the success rate (the raction o unction evaluations that led to a new lower upper bound) IF success rate set, and GOTO Step 2 Calculate, compute IF, set, and GOTO Step 2 Set, and GOTO Step ENDIF Step 4: Set Increment and GOTO Step. ACKNOWLEDGMENT The authors would like to thank Pro. I. Lagaris or his help and support throughout this research. REFERENCES [] L. H. Tsoukalas and R. E. Uhrig, Fuzzy and Neuralapproaches in Engineering. New York: Wiley, 997. [2] L. X. Wang, A Course in Fuzzy Systems and Control. Upper Saddle River, NJ: Prentice-Hall, 997. [3] J. Giartano and G. Riley, Expert Systems, Principles and Programg. Boston, MA: PWS, 998. [4] S. H. Liao, Expert system methodologies and applications-a decade review rom 995 to 2004, Expert Syst. Appl., vol. 28, pp , [5] W. Pedrycz and J. V. d. 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17 TSIPOURAS et al.: FRAMEWORK FOR FUZZY EXPERT SYSTEM CREATION 205 [38] C. Papaloukas, D. I. Fotiadis, A. Likas, and L. K. Michalis, An ischemia detection method based on artiicial neural networks, Arti. Intell. Med., vol. 24, pp , [39] N. Maglaveras, T. Stamkopoulos, C. Pappas, and M. Strintzis, ECG processing techniques based on neural networks and bidirectional associative memories, J. Med. Eng. Technol., vol. 22, pp. 06, 998. [40] S. Papadimitriou, S. Mavroudi, L. Vladutu, and A. Bezerianos, Ischemia detection with a sel-organizing map supplemented by supervised learning, IEEE Trans. Neural Netw., vol. 2, no. 3, pp , May 200. [4] N. Maglaveras, T. Stamkopoulos, C. Pappas, and M. G. Strintzis, An adaptive backpropagation neural network or real-time ischemia episodes detection: Development and perormance analysis using the European ST-T database, IEEE Trans. Biomed. Eng., vol. 45, no. 7, pp , Jul [42] MIT-BMH Arrhythmia Database. Cambridge, MA: MIT Press, 997, Harvard-MIT Div. Health Sci. Technol. [43] J. Pan and W. J. Thompkins, A real-time QRS detection algorithm, IEEE Trans. Biomed. Eng., vol. 32, no. 3, pp , Mar [44] P. S. Hamilton and W. J. Tompkins, Quantitative investigation o QRS detection rules using the MIT/BIH arrhythmia database, IEEE Trans. Biomed. Eng., vol. 33, no. 2, pp , Dec [45] European ST-T Database Directory. Pisa, Italy: S.T.A.R., 99. [46] K. Daskalov, I. A. Dotsinsky, and I. I. Christov, Developments in ECG acquisition, preprocessing, parameter measurement, and recording, IEEE Eng. Med. Biol., vol. 7, no., pp , Jan [47] F. V. Theos, I. E. Lagaris, and D. G. Papageorgiou, PANMIN: Sequential and parallel global optimization procedures with a variety o options or the local search strategy, CPC, vol. 59, pp , [48] P.-N. Tan, M. Steinbach, and V. Kumar, Introduction to Data Mining. Reading, MA: Pearson Addison Wesley, [49] M. G. Tsipouras, C. Voglis, I. A. Lagaris, and D. I. Fotiadis, A ramework or uzzy expert system creation, in Proc. 7th Int. Workshop Math. Meth. in Scat. Theory Biomed. Eng., 2006, pp Markos G. Tsipouras (S 07) was born in Athens, Greece, in 977. He received the Diploma degree and the M.Sc. degree in computer science rom the University o Ioannina, Ioannina, Greece, in 999 and 2002, respectively. He is currently pursuing the Ph.D. degree in the Department o Computer Science, University o Ioannina. His research interests include biomedical engineering, decision support and medical expert systems, and biomedical applications. Costas Voglis was born in Ioannina, Greece, in 978. He received the Diploma degree and the M.Sc. degree in computer science rom the University o Ioannina in 999 and 2002, respectively. He is currently pursuing the Ph.D. degree in the Department o Computer Science, University o Ioannina. His research interests include local and global optimization. Dimitrios I. Fotiadis (M 0 SM 07) was born in Ioannina, Greece, in 96. He received the Diploma degree in chemical engineering rom the National Technical University o Athens, Athens, Greece, and the Ph.D. degree in chemical engineering rom the University o Minnesota, Minneapolis. Since 995, he has been with the Department o Computer Science, University o Ioannina, where he is currently an Associate Proessor and Director o the Unit o Medical Technology and Intelligent Inormation Systems. His research interests include biomedical technology, biomechanics, scientiic computing, and intelligent inormation systems. Authorized licensed use limited to: IEEE Xplore. Downloaded on March 6, 2009 at 04:54 rom IEEE Xplore. Restrictions apply.