Çok boyutlu gauss süreçlerine dayanan parametrik şekil tanıma yöntemleri ve bu yöntemlerle kalp aritmilerinin belirlenmesi
Parametric pattern recognation methods based on multi dimensional gauss processes and arrhythmias of heart are determined by these methods
- Tez No: 39132
- Danışmanlar: PROF.DR. ERDAL PANAYIRCI
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Kardiyoloji, Electrical and Electronics Engineering, Cardiology
- Anahtar Kelimeler: Aritmi-kardiyak, Biyomedikal mühendisliği, Kalp, Öğrenme, Şekil tanıma, Arrhythmia-cardiac, Biomedical engineering, Heart, Learning, Shape recognition
- Yıl: 1993
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Bu tezde, çeşitli bilim dallarında önemli uygulama alanları bulan“Sekil Tanıma”ve“öğrenme”konuları ince¬ lenmekte ve bu kavramlar yardımıyla kalp işaretler indeki biçim bozukluklarını belirlemek için yeni bir yöntem ge- l işti r iImiştir. Tezin ikinci bölümünde kalp işaretlerinin temel ö- zellikleri, algılanması ve bu işaretlerdeki çeşitli bo¬ zukluklar anlatılmıştır. Üçüncü bölümde, parametrik şekil tanıma ve öğrenme yöntemleri ayrıntılarıyla verilmektedir. Ayrıca, pratik¬ te hesaplama ve gerçekleştirme yönünden oluşan problemler incelenmekte ve bu problemlerin çözüm yolları araştırıl¬ maktadır. Dördüncü bölümde, Parametrik şekil tanıma teorisin¬ den yararlanarak, şekil sınıflarının, ortalamaları ve ko- varyans matrisleri bilinmeyen Gauss dağılımları ile be¬ lirlendiği bir şekil tanıma problemi çözülmektedir. Son bölümde, Elektrokardiogram işaretleri Paramet¬ rik Sekil Tanıma yöntemiyle sınıflanarak; Normal ve Arit- mili kalp dalga biçimleri bu yöntem yardımıyla belirlen¬ miştir. V
Özet (Çeviri)
SUMMARY PARAMETRIC PATTERN RECOGNATIDN METHODS BASED ON MULTI DIMENSIONAL GAUSS PROCESSES AND ARRHYTHMIAS OF HEART ARE DETERMINED BY THESE METHODS In the last -Few years,“Pattern Recognat ion”and“Learning”techniques which have many applications in various -Fields o-F science, have developed a great deal. These -Fields of application are over the problems o-F handwriting recognation, Elektroanse-Fologram and Elektro- kardiogram analysis, statistical communication systems analysis etc. Pattern recognation is event in which patterns or objects which have similar properties or relations are recognized and classi-Fied by some special -Features and measured properties. Pattern class is a term used -For sets o-F patterns which have common properties. For example every letters o-F the alphabet can be represented as a pattern class. Pattern recognation systems are usually made up o-F two parts. The -First part is the selection o-F necessary properties or the measurements. This is called -Features extraction. The -Features which do not have the exact properties have high error. The second part is classifi cation by these -Features. If the features which determine the pattern classes are defined by probablity distribution rules, the classi fication is done by statistical decision theory. This type of pattern recognation is called parametric pattern recognation. Non parametric pattern recognation technigues are used when the parametric model is not sufficient. In this way of classification, every division of feature VIspace is defined by a pattern class and a linear discriminant -Function is de-Fined -For every division o-F.features space. In the both of the methods of classification, it is necessary to determine the real values of the parameters which define the pattern classes by the sample values. In figure 1 The block diagram of pattern recognation system is given. PATTERNS FEATURE SELECTION FEATURE EXTRACTION CLASSIFICATION LEARNING DECISION ? Figure 1: Block Diagram of Pattern Recognation System The parametric pattern. recognation method is chosen in this thesis. The probablity rules are used for recognizing the patterns. Priori information is used for making a decision in parametric pattern recognition theory. This term gives information about the pattern classes, probability of their activeness, and the distri bution of the sets. The Bayes decision rule are developed by priori information. The most important properties of Bayes rule is to use the prior information. Also it minimizes the error in pattern recognation. A variable x from the active class w± is defined by the conditional probability which is : Pt(x) = P(X=x/Wi) i=l,2,..,N VIIThe Posteriori probability term is used to maintain easiness in calculations. This is the priori probability term which varies by the results o-f measurements. It is given by : P<w1/X=x> i=l,2..N Basic Bayes is then j = l,2,..,N (j=|=k) P(w*/X=x) > P(wj/X = x) -> Six) = d* and the rule -for the learning process is : k=l,2,..,N (k:f=j> P(wj/x,y) > P(wR/x,y) - > Six) = d. Two problems appear as the learning process is done on computers. These problems are : 1-) The memory problem which appears as various posteri ori probability distributions are created in every learning step 2-) The need -For many calculations -for creating new posteriori probability -Functions in every step If these problems have the some mathematical repre- sations o-F posteriori probability distribution, the de termination o-F these types of finite number of parameters will be enough. The function which satisfy this property is called reproducing distribution family. This distri bution family is defined by sufficient statistic. In Section Four, the parametric learning and pattern recognition technigues where the general theory is given and the computer simulations of the model is done. VÎİÎThe -Fun deme ntal model parameters are: 1-) The pattern recognation system is based on two classes as w0 and Wi. 2-) The mean value au, covariance matrix E± are Gauss distribution parameters. Distribution is de-fined by: Wi : Fi % NKUijEi > i=0, 1 3-) The öi parameter where the real value is unknown o-f the Ft distribution is de-fined by 6i=9(«M2i). Zt is the inverse o-f the covariance matrix Zi=E, 4-) Y1 = (Yii, Yi2,.., Yoi ), is the represatations o-f the n4 number of learning samples taken from the pattern class Wi. These samples are the Gauss distributions which have Ui as mean value and Ei as covariance matrix. They are statistically independent IM-dimen- sional-random variables. 5-) xk=(xi, x2,.., x*) is the k, IM-dimensional variable. 6-) P(wo)=P(w!)=l/2 is given Since the learning process is the same -For every class, the“i”index will be dropted. The probability density -Function o-F the learning samples is: 1 T -1 Pvk(yk)=.expC-l/2(y^-M>.E. <yk-u) 3 NX'S 1 /'Z (2ir). |E| (1) IXWith the help o-f learning samples, P© <. ) priori probability density -function can be determined according to the 6 parameter. First it is shown that P© (. ) priori probability density -Function is an element o-F the reprocuding distribution -family. A-fter this process, P© <. ) is calculated as a WishardxGauss distribution. The parameters o-f this distribution is: Wishard distribution parameters: T V0 = -rn+N+1, 0O = <T_m+m. m_m. m-m) /Vo Gauss distribution parameters: Mo=m-m, Wo = ~m (2) A-fter the priori probability -function calculation, PeCzjU/y“) posteriori probability -function can be calcu lated. Again this -function is calculated as having same distribution and di-fferent parameters. The parameters belonging to these probabilities are: Wo» Ho+n. mn v-,-, = Vo+n, wn = Wo+n Mn= w0+n Vo.Mw0.«o-Ho+ (n-1 ).Sn+n.mn.iiin-Wn.«n. Mr. 0”= V0+n (3) A-fter these probabilities are calculated, xk=(xi,x2,.., Xi<) -Feature vectors which the pattern classes they belong to are unknowns can be class-fied by the help o-f the Bayes rule and a rule can be obtained obeying the above conditions.At the last part, computer simulations are done -For iterative algorithms which are determined by pattern re- cognations systems that calculate pattern classes with Gauss distributions. By this simulations Mni ve 0ni pa rameters o-F posteriori probability -Function is calculated iteratively. In the case that the n* sample number is increased 0m parameter matrix converges to real L± cova- riance matrix values. In Section Five, a computer simulation and an appli cation are done showing that parametric pattern recogni tion methods can be used to determine the abnormalities in human heart which has a drastic importance in human li-Fe. The heart abnormalities, arithym, can be divided in two parts as pattern -Forms and rithym abnormalities. This thesis -Focuses on pattern abnormalities. The heart beat amplitude values used in this thesis varies through the integer values in the range o-F 0-200 and are produced as datas -from a sampling simulator having a 400 Hz -Frequency In the application two types o-F heart beat is used. These beats consist o-F a class o-F healty heart beats having 75 beats/ min and a class o-F beats which have T and P waves i nter-ferenci ng in ari thymic periods some cases. For healthy beats the values o-F amplitude o-F important parts are changing as base line 40, P wave 50-54, R wave 110-200, T wave 69-72 respectively. In the simulation the P wave value o-F arithymic beats are taken as having 40 base line values o-F period. In this section, the pattern recognition system consist o-F two parts. The -first class is the healty beat and the second is the arithymic beat. In the pattern classes, the mean value is «i, the covariance matrix is Ei where i=0,l. Bince it is considered that these values are unknown, the pattern recognition system will learn these values. In the -first part o-f the computer simulation, six dimensional learning samples are taken -from the pattern classes. Every sample, has a projection as a vector. With the help o-f these samples the Mi and 0m parameters XIo-F the posteriori probability density -Function can be calculated iteratively. These parameters can be learned per-Fectly at the value of nt=512. The 0"i i=0, 1 parame ters of both the classes converges to the real value o-F Et covariance matrix. After the process of learning of the unknown para meters, the classification of xk=(xi, x3,.., xH) feature vectors of unknown classes can be done, In this classi fication the Bayes decision rule developed in this thesis is used. By using perfectly learned covariance matrix, for k=5, 10 samples from the healty and arithymic classes, it is calculated that there exits a y.15 error in classifica- cation according to the classification algorithm develo ped in this thesis. The system performance happens to be */.85. As the value of k increases the probability of error converges to zero. Xîl
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