Çok boyutlu Gauss süreçlerine dayanan parametrik şekil tanıma yöntemleri ve bu yöntemlerle kalp aritmilerinin belirlenmesi

Abstract

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.

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 VI space 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 VII The 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 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. VÎİÎ The -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.