Wavelet Domain Approximate Entropy-Based Epileptic Seizure Detection

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1 Wavelet Doman Approxmate Entropy-Based Epleptc Sezure Detecton A.S. Muthanantha Murugavel #1, S. Ramakrshnan *2 # Department of Informaton Technology Dr.Mahalngam College of Engneerng and Technology Pollach , Tamlnadu, Inda 1 as_ananth2k1@yahoo.com 2 ram_f77@yahoo.com Abstract The electroencephalogram (EEG) sgnal plays an mportant role n the detecton of eplepsy. The EEG recordngs of the ambulatory recordng systems generate very lengthy data and the detecton of the epleptc actvty requres a tmeconsumng analyss of the entre length of the EEG data by an expert. The am of ths work s to develop a new method for automatc detecton of EEG patterns usng wavelet based approxmate entropy (ApEn) and probablstc neural network (PNN). Our method conssts of EEG data collecton, feature extracton and classfcaton stages. ApEn s a statstcal parameter that measures the predctablty of the current ampltude values of a physologcal sgnal based on ts prevous ampltude values. In feature extracton stage we use best bass mother wavelet functons and wavelet thresholdng technque. For the feature selecton we have used a new methodology, that s mnmal varance wthn class and maxmal absolute dfference between classes are used for feature selecton. In classfcaton stage we mplement PNN to detect epleptc sezure detecton. It s known that the value of the ApEn drops sharply durng an epleptc sezure and ths fact s used n the proposed system and overall accuraces as hgh as 100% can be acheved by usng the proposed system.. Keywords approxmate entropy (ApEn), wavelet transform, artfcal neural network (ANN), electroencephalogram (EEG), EEG classfcaton, eplepsy, sezure detecton, probablstc neural network (PNN). I. INTRODUCTION Eplepsy s a chronc dsorder characterzed by recurrent sezures whch may vary from muscle jerks to several convolutons. Estmated 1% of world populaton suffers from eplepsy [1], whle 85% of them lve n the developng countres. Epleptc detecton s done from electroencephalogram (EEG) sgnal as eplepsy s a condton related to the bran s electrcal actvty. Electroencephalogram (EEG) s routnely used clncally to dagnose, montor and localze epleptogenc zone. Occurrence of recurrent sezures n the EEG sgnal s characterstcs of eplepsy. In majorty of the cases, the onset of the sezures cannot be predcted n a short perod, a contnuous recordng of the EEG s requred to detect eplepsy. The entre length of the EEG recordngs s analyzed by expert to detect the traces of eplepsy. The tradtonal methods of analyss are tedous and tmeconsumng and so many automated epleptc EEG detecton systems have been developed [2]. Ths paper dscusses an automated epleptc EEG detecton system usng probablstc neural network (PNN) usng a tme-frequency doman feature of the EEG sgnal called approxmate entropy (ApEn). EEG data s frst dgtzed. The dgtal EEG data s fed as an nput to an automated sezure detecton system n order to detect the sezures present n the EEG data. Approxmate Entropy drops abruptly due to the synchronous dscharge of large groups of neurons durng an epleptc actvty. Hence, t s a good feature to make use of n the automated detecton of eplepsy. Entropy s a thermodynamc quantty descrbng the amount of dsorder n the system. From an nformaton theory perspectve, the above concept of entropy s generalzed as the amount of nformaton stored n a more general probablty dstrbuton. Frst Shannon appled the concept of nformaton or logcal entropy to the scence of nformaton theory and data communcatons. Recently, a number of dfferent entropy estmators [2] have been appled to quantfy the complexty of the sgnal. Entropy estmators are broadly classfed nto two categores spectral entropes and embeddng entropes. The spectral entropes use the ampltude components of the power spectrum of the sgnal as the probabltes n entropy calculatons. It quantfes the spectral complexty of the tme seres. The embeddng entropes use the tme seres drectly to estmate the entropy. Kolmogorov Sna entropy and the approxmate entropy are the embeddng entropes dscussed here [3]. The dscrete wavelet transform s a versatle sgnal processng tool that has many engneerng and scentfc applcatons. DWT employs two sets of functons called scalng functons and wavelet functons, whch are assocated wth low-pass and hgh-pass flters, respectvely. The decomposton of the sgnal nto the dfferent frequency bands s smply obtaned by successve hgh-pass and low pass flterng of the tme doman sgnal. Subas [4] deals wth a novel method of analyss of EEG sgnals usng dscrete wavelet transform, and classfcaton usng ANN. The pseudo Wgner-Vlle and the smoothed pseudo Wgner-Vlle

2 dstrbuton [5] was used for extractng features from the tmefrequency plane. PNN s predomnantly a classfer snce t can map any nput pattern to a number of classfcatons. Among the man advantages that dscrmnate PNN s: Fast tranng process, an nherently parallel structure, guaranteed to converge to an optmal classfer as the sze of the epresentatve tranng set ncreases and tranng samples can be added or removed wthout extensve retranng. Accordngly, a PNN learns more quckly than many neural networks model, whch led to ts success on varety of applcatons. Based on these facts and advantages, PNN can be vewed as a supervsed neural network that s capable of usng t n system classfcaton and pattern recognton [6]. The detecton of eplepsy, whch ncludes vsual scannng of EEG recordngs for the spkes and sezures, s very tme consumng, especally n the case of long recordngs. In addton, bo-sgnals are hghly subjectve so dsagreement on the same record s possble, so the EEG sgnal parameters extracted and analyzed usng computers, are hghly useful n dagnostcs. Automatc analyss of EEG recordngs n the dagnoss of eplepsy started n the early 1970s and lot of sezure detecton algorthms have been developed. In ths paper, approxmate entropy-based epleptc EEG detecton proposed by the author Varavan Srnvasan et al [11], s used wth some modfed approach such as wavelet doman. Snce wavelet has several advantages, t s both tme and frequency based and t can smultaneously possess compact support, orthogonalty, symmetry, and short support, and hgh order approxmaton. Therefore, man objectve of ths paper s to propose a novel feature extracton technque for the detecton of eplepsy. The wavelet transformaton s used for extractng Approxmate Entropy and a new methodology s presented for feature selecton. The methodology s appled to two dfferent groups of EEG sgnals for analyss of EEGs and EEG sub bands for detecton of epleptc sezure: 1) healthy subjects; 2) epleptc subjects durng a sezure (ctal EEG). Each EEG s decomposed nto two consttuent EEG sub bands: delta, theta, alpha, beta, and gamma usng wavelet-based flters. The features such as Approxmate Entropy of the wavelet coeffcents are used to represent the tme frequency dstrbuton of the EEG sgnals n each sub-band of the wavelet transformaton and the probablstc neural network s used to detect epleptc EEG sgnals. II. PROPOSED METHODOLOGY As n tradtonal pattern recognton systems, the epleptc sezure detecton conssts of man modules such as a feature extractor that generates a wavelet based feature from the EEG sgnals, feature selecton that composes composte features, and a feature classfer (PNN) that outputs the class based on the composte features. The data flow of the proposed approach s llustrated n Fg. 1. Test EEG Sgnal Fg. 1 Data flow dagram of the proposed system A. Dataset Descrpton Input Sgnals (EEG Sgnals) Wavelet Transformaton Feature Extracton (ApEn) Feature Selecton Traned Probablstc Neural Network Epleptc Detecton The data used n ths research are a subset of the EEG data for both healthy and epleptc subjects made avalable onlne by Dr. Ralph Andrzejak of the Eplepsy Centre at the Unversty of Bonn, Germany ( data.html) [1]. EEGs from two dfferent groups: group H (healthy subjects) and group S (epleptc subjects durng sezure) are analyzed. The type of eplepsy was dagnosed as temporal lobe eplepsy wth the epleptogenc focus beng the hppocampal formaton. Each group contans 100 sngle channel EEG segments of 23.6 sec duraton each sampled at Hz. As such, each data segment contans N=4097 data ponts collected at ntervals of 1/173.61th of 1s. Each EEG segment s consdered as a separate EEG sgnal resultng n a total of 200 EEG sgnals or EEGs. As an example, the frst 6s of two EEGs (sgnal numbers n parentheses) for groups H (H029) and S (S001) are magnfed and dsplayed n Fg. 2. Fg. 2 Sample unfltered EEGs (0 6 s) for (from top to bottom) Group H (H029) and Group S (S001)

3 B. Wavelet Transformaton Wavelet transform s a spectral estmaton technque n whch any general functon can be expressed as an nfnte seres of wavelets. The basc dea underlyng wavelet analyss conssts of expressng a sgnal as a lnear combnaton of a partcular set of functons (wavelet transform, WT), obtaned by shftng and dlatng one sngle functon called a mother wavelet. The decomposton of the sgnal leads to a set of coeffcents called wavelet coeffcents. Therefore the sgnal can be reconstructed as a lnear combnaton of the wavelet functons weghted by the wavelet coeffcents. The key feature of wavelets s the tme-frequency localzaton. It means that most of the energy of the wavelet s restrcted to a fnte tme nterval. The wavelet technque appled to the EEG sgnal wll reveal features related to the transent nature of the sgnal, whch s not made obvous by the Fourer transform. Adel et al. [7] gave an overvew of the dscrete wavelet transform (DWT) developed for recognzng and quantfyng spkes, sharp waves and spke-waves. In general, t must be sad that no tme-frequency regons but rather tme-scale regons are defned. All wavelet transforms can be specfed n terms of a low-pass flter, whch satsfes the standard quadrature mrror flter condton. One area n whch the wavelet transformaton has been partcularly successful s the epleptc sezure detecton because t captures transent features and localzes them n both tme and frequency content accurately. The wavelet transformaton analyses the sgnal at dfferent frequency bands, wth dfferent resolutons by decomposng the sgnal nto a coarse approxmaton and detal nformaton [8]. The decomposton of the sgnal nto the dfferent frequency bands s merely obtaned by consecutve hgh-pass and low-pass flterng of the tme doman sgnal. The procedure of mult-resoluton decomposton of a sgnal x[n] s schematcally shown n Fg. 3. Each stage of ths scheme conssts of two dgtal flters and two down-samplers by 2. The frst flter, h[n] s the dscrete mother wavelet, hgh pass n nature, and the second, g[n] s ts mrror verson, low-pass n nature. The down-sampled outputs of frst hgh-pass and low-pass flters provde the detal, D1 and the approxmaton, A1, respectvely. The frst approxmaton, A1 s further decomposed and ths process s contnued as shown n Fg. 3. The EEG sub bands of a2, d2 and d1are shown n fg. 4. Selecton of sutable wavelet and the number of decomposton levels s very mportant n analyss of sgnals usng the wavelet transformaton. The number of decomposton levels s chosen based on the domnant frequency components of the sgnal. In the present study, snce the EEG sgnals do not have any useful frequency components above 30 Hz, the number of decomposton levels was chosen to be 2. Thus, the EEG sgnals were decomposed nto detals D1 D2 and one fnal approxmaton, A2. Usually, tests are performed wth dfferent types of wavelets and the one, whch gves maxmum effcency, s selected for the partcular applcaton. The smoothng feature of the Daubeches wavelet of order 4 (db4) made t more approprate to detect changes of EEG sgnals. Hence, the wavelet coeffcents were computed usng the db4 n the present study. The proposed method was appled on both data set of EEG data (Sets H and S). In the dscrete wavelet analyss, a sgnal can be represented by ts approxmatons and detals. The detal at level j s defned as D j a j, k j, k ( t ) (1) kz and the approxmaton at level J s defned as A j D j (2) j J It becomes obvous that A and A D j 1 j j (3) f ( t ) A j D j (4) j J Wavelet has several advantages, whch can smultaneously possess compact support, orthogonalty, symmetry, and short support, and hgh order approxmaton. We expermentally found that tme-frequency doman feature provdes superor performance over tme doman feature n the detecton of epleptc EEG sgnals. Fg. 4 Level 2 decomposton of the band-lmted EEG nto three EEG sub bands usng fourth-order Daubeches wavelet (s = a2+d2+d1) Fg. 3 Two level wavelet decomposton

4 C. Feature Extracton The proposed system makes use of a sngle feature called ApEn for the epleptc detecton. The ApEn s a waveletdoman feature that s capable of classfyng complex systems. The value of the ApEn s determned as shown n the followng steps [9], [10]. 1) Let the data sequence contanng N data ponts be X = [x(1), x(2), x(3),..., x(n)]. 2) Let x() be a subsequence of X such that x() = [x(), x( + 1), x( + 2),..., x( + m 1)] for 1 N m, where m represents the number of samples used for the predcton. 3) Let r represent the nose flter level that s defned as r = k SD (5) for k = 0, 0.1, 0.2, 0.3,, 0.9 where SDs the standard devaton of the data sequence X. 4) Let {x(j)} represent a set of subsequences obtaned from x(j) by varyng j from 1 to N. Each sequence x(j) n the set of {x(j)} s compared wth x() and, n ths process, two parameters, namely C m (r) and C m+1 (r) are defned as follows: C m (r) = N m j 1 k N-m (6) where k = 1, f x() x(j) r for 1 j N m 0, otherwse and C m+1 (r) = N m j 1 k N-m (7) wth condtons depcted by (A) as shown at the bottom of the page. 5) We defne Φ m (r) and Φ m+1 (r) as follows: Φ m (r) = N m 1 m ln( C ( r)) N m (8) ApEn features. As t consumes more tme n processng these 60 ApEn features, there s a need to select the best thrty features. Table. 1 shows the extracted features (ApEn) for the sub bands for the sample set A. These best features are selected by our novel approach whch nvolves choosng the feature havng mnmal varance wthn the class and maxmum absolute dfference between the classes. Varance has been calculated for each class of sample set to fnd the mnmal varance. And absolute dfference between classes of sample set to fnd the maxmal dfference. TABLE I FEATURE EXTRACTION SAMPLE DATA SET A Set Sub-bands ApEn D H D2 295 A D S D A E. Probablstc Neural Network Classfer The classfcaton of EEG sgnals nto healthy and epleptc sgnals s done usng the probablstc neural network. The archtecture of the PNN s shown n Fg. 5. In machne learnng, a classfer s essentally a mappng from the feature space to the class space. An Artfcal Neural Network (ANN) mplements such a mappng by usng a group of nterconnected artfcal neurons smulatng the human bran. An ANN can be traned to acheve expected classfcaton results aganst the nput and output nformaton stream, so there may not be a need to provde a specfed classfcaton algorthm. There s no need to tran the network over the entre data set agan, so we use PNN to enable quck updates of our network as more patents data becomes avalable. Our PNN has three layers: the Input Layer, the Radal Bass Layer whch evaluates dstances between the nput vector and rows n the weght matrx, and the Compettve Layer whch determnes the classfcaton wth maxmum probablty of correctness. Dmensons of matrces are marked under ther names. Φ m+1 (r) = N m 1 m1 ln( C ( r)) N m (9) Small values of ApEn mply strong regularty n a data sequence and large values mply substantal fluctuatons [11]. In the proposed approach, ApEn s calculated for one approxmaton and for detaled nformaton such as a2 and d2. D. Feature Selecton As dscussed n the above secton, 30 ApEn features have been obtaned from each sub band leadng to a total of 60

5 Fg. 5 PNN structure, R: number of features, Q: number of tranng samples, K: number of classes. 1) Input Layer: The nput vector, denoted as p, s presented as a black vertcal bar n Fg. 5. The nput layer unt does not perform any computaton and smply dstrbutes the nput to neurons n the pattern layer. On recevng a pattern x from nput layer, the neuron x j of the pattern layer computes ts output usng the below formula. ( x x ) ( x x ) (2 ) 2 T 1 j j j( x ) exp 0.5d d 2 (10) Where d denotes dmenson of the pattern vector x, smoothng parameter and xj s the neuron vector. s the 2) Radal Bass Layer: In the Radal Bass Layer, the vector dstances between nput vector p and the weght vector, made up of each row of the weght matrx W are calculated. Here, the vector dstance s defned as the dot product between two vectors. The dot product between p and the -th row of W produces the -th element of the dstance vector matrx, denoted as W p. The bas vector b s then combned wth W p by an element-by-element multplcaton, represented as n Fg. 5. The result s denoted as n = W p b. The transfer functon n PNN has bult nto a dstance crteron wth respect to a center. In ths paper, we defne t as radbas(n) = e n2. Each element of n s substtuted nto the transfer functon and produces correspondng element of a, the output vector of Radal Bass Layer. We can represent the -th element of a as a = radbas( W p b), where W s the -th row of W, and b s the -th element of bas vector b. Radal Bass Layer Weghts: Each row of W s the feature vector of one tranng sample. The number of rows s equal to the number of tranng samples. Radal Bass Layer Bases: All bases n the radal bass layer are set to ln0.5/s, resultng n radal bass functons that cross 0.5 at weghted nputs of ±s, where s s the spread constant of PNN. Accordng to our experence, s = 0.1 can typcally result n the hghest accuracy. Summaton layer neurons compute the maxmum lkelhood of a pattern x beng classfed nto C, by averagng the output of all neurons that belong to the same class usng P( ) exp (11) ( xx ) ( x xj) N T 1 j x 0.5d d 2 N (2 ) j1 2 3) Compettve Layer: There s no bas n the Compettve Layer. In ths layer, the vector a s frst multpled by the layer weght matrx M, producng an output vector d. The compettve functon C produces a 1 correspondng to the largest element of d, and 0 s elsewhere. The ndex of the 1 s the class of the EEG segment. M s set to a K Q matrx of Q target class vectors. If the -th sample n the tranng set s of class j, then we have a 1 on the j-th row of the -th column of M. The decson layer classfes the pattern x n accordance wth Bayes decson rule based on the output of all summaton layer neurons usng Ĉ( x) arg max P ( x ), 1, 2,.., m (12) Where denotes the estmated class of pattern x, and m s the total number of classes n tranng samples. Hence, PNN employed n ths work possesses 30 nodes n the nput layer and 2 nodes n the output layer (the number of nodes n the output layer s the number of classfcatons of EEG sgnals). The performance of the neural model was evaluated n terms of tranng performance and classfcaton accuraces and the results confrmed that the proposed scheme has potental n classfyng the EEG sgnals. III. RESULTS AND DISCUSSION ApEn values are computed for selected combnatons of m, r, and N. The values of m, r, and N that are used for the experments are as follows: ) m = 1, 2, 3; r = 0% 90% of SD of the data sequence n ncrements of 10%; and N = ApEn values are computed for both normal and epleptc EEG sgnals and are fed as nputs to the two neural networks. Among the avalable 100 EEG data sets, 50 data sets are used for tranng and the remanng data sets are used for testng the performance of the neural networks. The potentalty of the ApEn to dscrmnate the two sgnals, namely, normal and epleptc EEG sgnals depends on the values of m, r, and N. Fg. 6 shows Recever Operatng Characterstcs Curve for the overall detecton accuracy (%) obtaned by the PNN usng ApEn as the nput feature. The expermental results show that our PNN usng wavelet based ApEn can well preserve the most dscrmnant nformaton of EEG sgnals and mprove the performance over the extng system n terms of detecton rate. PNN gves good overall accuracy values n the range 98% - 100%, only for a few combnatons of m, r, and N (e.g., m = 1, r = 0 SD for all the values of N and m = 3, r = 0.2 SD, N = 4097). Though the use of ANNs ncreases the computatonal complexty, the hgh overall detecton accuraces are acheved wth ths system surpasses ts dsadvantage as n any automated sezure detecton system, the detecton of the sezure wth hgh accuracy s of prmary mportance. Where N denotes the total number of samples n class C.

6 ( data.html). REFERENCES Fg. 6. ROC Curve: Overall Classfcaton Rate Our expermental results are based on data sets correspondng to fve dfferent subjects only. The optmum ApEn parameter values obtaned based on ths data may not hold good for a general case. Hence, usng a lnear separator wth known ApEn parameter values may not gve good results n stuatons where a large number of dfferent subjects are nvolved. Ths problem wll not arse n the proposed PNN-based method as t has performed well rrespectve of the ApEn parameter values used. It s shown that our wavelet based ApEn possesses good characterstcs such as robustness n the characterzaton of the epleptc patterns and low computatonal burden. Hence, an automated system usng wavelet based ApEn as the nput feature s best suted for the real tme detecton of the epleptc sezures. The proposed system s based on two types of EEG, namely, EEG sgnals of awake and epleptc subjects. It can be made more robust by acclmatzng t to the other manfestatons of EEG lke sleep EEG. [1] Guler, I., Kymk, M. K., Akn, M., & Alkan, A. AR spectral analyss of EEG sgnals by usng maxmum lkelhood estmaton. Computers n Bology and Medcne, 31, , [2] Zoubr, M., & Boashash, B. Sezure detecton of newborn EEG usng a model approach. IEEE Transactons on Bomedcal Engneerng, 45, , [3] Adel H, Zhou Z, Dadmehr N. Analyss of EEG records n an epleptc patent usng wavelet transform. J Neurosc Methods; 123(1):69 87, [4] Pradhan, N., Sadasvan, P. K., & Arunodaya, G. R. Detecton of sezure actvty n EEG by an artfcal neural network: A prelmnary study. Computers and Bomedcal Research, 29, , [5] Weng, W., & Khorasan, K. An adaptve structure neural network wth applcaton to EEG automatc sezure detecton. Neural Networks, 9, , [6] Petrosan, A., Prokhorov, D., Homan, R., Dashe, R., & Wunsch, D. Recurrent neural network based predcton of epleptc sezures n ntraand extracranal EEG. Neurocomputng, 30, , [7] Folkers, A., Mosch, F., Malna, T., & Hofmann, U. G. Realtme boelectrcal data acquston and processng from 128 channels utlzng the wavelet-transformaton. Neurocomputng, 52 54, , [8] Guler I, Ubeyl ED. Applcaton of adaptve neuro-fuzzy nference system for detecton of electrocardographc changes n patents wth partal eplepsy usng feature extracton. Expert Syst Appl; 27(3):323 30, [9] Subas, A. Automatc recognton of alertness level from EEG by usng neural network and wavelet coeffcents. Expert Systems wth Applcatons, 28, , [10] Kandaswamy, A., Kumar, C. S., Ramanathan, R. P., Jayaraman, S., & Malmurugan, N. Neural classfcaton of lung sounds usng wavelet coeffcents. Computers n Bology and Medcne, 34(6), , [11] M. Boulougoura, E. Wadge, V.S. Kodoganns, H.S. Chowdrey, Intellgent systems for computer-asssted clncal endoscopc mage analyss, 2nd IASTED Int. Conf. on Bomedcal Engneerng, Innsbruck, Austra, pp , 2004 IV. CONCLUSION In ths paper, the neural network namely Probablstc Neural Network (PNN), has been employed for the automated detecton of eplepsy. A robust and computatonally lowntensve feature such as wavelet doman based Approxmate Entropy (ApEn) has been used for the proposed epleptc detecton system and a new approach has been used for feature selecton n order to reduce the dmenson and ncrease the computaton speed. Expermental results show that overall accuraces as hgh as 100% can be acheved by ths system. As the proposed system s based on a sngle feature that has a low computatonal burden, t s best suted for the real-tme detecton of epleptc sezures from ambulatory recordngs. ACKNOWLEDGMENT The authors wsh to thank Andrzejak et al., 2001 for the benchmark eeg dataset whch s publcly avalable: