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Elektromiyografik işaretlerin bulanık sınıflayıcıları sınıflandırılması

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  1. Tez No: 46252
  2. Yazar: HÜSEYİN ŞEKER
  3. Danışmanlar: DOÇ.DR. MEHMET KORÜREK
  4. Tez Türü: Yüksek Lisans
  5. Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
  6. Anahtar Kelimeler: Bulanık kümeler, Bulanık mantık, Sınıflandırma, Fuzzy sets, Fuzzy logic, Classification
  7. Yıl: 1995
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: Belirtilmemiş.

Özet

ÖZET 1960' h yıllarda ilk olarak Azeri asıllı Prof.Dr. Lütfî A. Zadeh tarafından ortaya atılan Fuzzy Kümeler teorisi o günden bu yana işaret işlemeden, kontol sistemlerine; tipta uzman sistemlerin oluşturulmasmdan endüstri mühendisliğinde verimliliğin arttırılmasına kadar her alanda uygulanma imkanı bulmuştur. Bir küme elemanın bir kümeye aiüiliğini Üyelik Değeri ile ifade eden Prof.Dr. Zaden, insan mantığına en yatkın algoritmayı ortaya atmıştır. Klasik işaret veya patem sınıflama işlemlerinde bir işaretin veya paternin bir sınıfa ait olup olmaması önemlidir. Bununla beraber fuzzy mantığında önemli olan“ işaret/patern bir sınıfa ne kadar aittir?”sorusuna cevap bulmaktır. Bu amaçla O ile l arasında sonsuz sayıda değer alabilmektedir. Bu değerlere Üyelik Değeri denir, örneğin bir hasta ve iki muhtemel hastalık düşünelim. Yapılan araştırma sonucunda hastalıklardan birisinin üyelik değeri 0.485 diğeri ise 0.515 çıksın. Klasik mantıkta direkt olarak üyelik değeri 0.515 olan hastalık teşhis edilirdi. Ancak burada bir şüphe sözkonusudur. Dolayısıyla Fuzzy tabanlı algoritmalar çok bilgi içermektedir. Ayrıca bu mantıkta üyelik değerlerinin en iyi şekilde tespiti önemlidir. Bu amaçla üyelik fonksiyonları oluşturulur. En iyi sonuç veren fonksiyonlar o konudaki uzman kişilerden alman bilgiler neticesinde oluşturulan fonksiyonlardır. insan için hayati önem için taşıyan organlar vardır. Bunlardan birisi de hareketlerimizi iskeletle beraber sağlayan kaslardır. Kaslardaki bir arıza bütün bir uzvu etkileyebilmektedir. Bu nedenle diğer biyolojik işaretlerde olduğu gibi elektromiyografik işaretlerin de işlenmesi ve yorumlanması gerekmektedir. Buradan hareketle bu çalışmada daha önce bir yüksek lisans tezi için elde edilmiş olan kol kaslarından alman elektromiyografik işaretlerin sınıflaması bir çok fuzzy sınırlayıcı algoritması kullanılarak yapılmıştır. Karşılasürmalı sonuçlar, tablolar ve grafikler halinde verilmiştir. V

Özet (Çeviri)

SUMMARY in the study named“ Classification of Electromiographic (EMG) Signals By Using Fuzzy Classifiers”, some of classification algorithms based on Fuzzy Set Theory are used to classify EMG signals which is very important for humans. EMG signals used in the study was obtained from muscle of upper-limb. Four ann behaviors are used to classify. EMG signals are modeled by AR (Auto Regressive) Models and the four parameters (al, a2, a3, a4) from this model are used as feature vectors. As classifiers, Fuzzy Set Theory-based classifiers are used. Since Fuzzy Sets were fîrst introduced by Prof. Dr. L.A. Zadeh in 1965, Fuzzy Sets have become very popular subject that many researchers and scientists use widely,and fuzzy sets have advanced in wide variety of disciplines; e.g. control theory, topology, Hnguistics, optimization, category theory, automata, decision making. The results derived from applications have shown that Fuzzy sets being a generalization of conventional set theory (Crisp-Hard-0/1 Logic), yield better results than conventional set theory. in crisp sets, if an element of a set belongs to this set, its degree is l, othenvise O (zero). But no elements in ali sets belong to a set crisply. it has to have a degree. in fuzzy sets, this degree is called“Membership Value”and,“Membership Function”through which membership value is obtained ör calculated. Lets an example about the set of numbers H from 6 to 8. in crisp sets, we can write H={r eR | 6 <r<8} Equivalently, H is described by its Membership Function (MF), mH : R-»{0,1) defîned as; l 6<r<8 mH(r)=(1) O othenvise The crisp set H and the graph of mH are shown in tiie left half of Fig.l. Every real number (r) either is in H, ör is not. Since mH maps ali real numbers vir eR onto the two points {0,1}, crisp sets correspond to two-valued logic- is ör isn't, on ör of£ black ör white, l ör 0. in logic, values of mH are called“trath values”with refrains to the question“ Is r in H ?”. The answer is yes, if and only if mH=l; otherwise, no. Now, consider next the fuzzy sets. in Fiğ. l, only for 7, mH(7)=l. The reste of the sets have different membership values in membership function. Although crisp set has two level O ör l, fuzzy set infînite level between O and 1. This can be called multi-level-logic. This is a F set of real numbers that are close to 7. This idea can be extended. The membership function is me basic idea in fuzzy set theory; ite values measure degrees to which objects (elemente of a fuzzy set) satisfy imprecisely defîned properties. in order to manipulate fuzzy sete, we need operations for combining them. Zadeh defined“classical”operations for fuzzy subsets mA and mB. as follows for ali x; :, : ( mH, :“ :;ı[;1 :\^ : ”^ V '. :'. 6 ':?;. x:.8=::.=...r,'.“'..// ”'..' '.=;_; -;6--.. 7 ': S-.;/;'“': ;:'';.. Crîsp Sete...'.. V::;..;. > :..;. : Fuzz? S^ts::.:.. -.. Figüre-1 Membership Functions for hard (crisp) and fuzzy subsets of R (=) EcpıalityA=B<^> mA(x)=mB(x); (c) ContainmentAç B <^> mA(x) < mB(x); (») ComplementmD(x)==l-mA(x) A (n) IntersectionmAnB(x)=min{mA(x), mB(x)}; (u) UnionmAuB(x)=max{mA(x),mB(x)}. viiThe fîrst and main problem in fuzzy sets is how to obtain the best Membership Function for a system. The main idea is that the function can be obtained by means of experts in this system. But it is very hard to reach to experts. Recentiy, some methods that membership function can be obtained directly from numerical data. in this study, several membership functions such as triangular membership function are evaluated to represent each feature vector of each EMG class. Fuzzy Relation matrix used in decision making is obtained firom Membership Functions. in the study, unleveled signal is classified using membership function and fuzzy relation matrix obtained from membership functions. in Fuzzy Set Theory, pattern ör signal classification is different from conventional methods. Conventional methods assigns a signal to a particular class. This is important decision in mis method. However, in fuzzy set theory - based pattern/signal classifiers, fuzzy classifiers assigns class membership to a pattern/signal rather than assigning the vector to a particular class. A signal's membership values should provide a level of assurance to accompany the resultant classification. For example, ifa signal is assigned 0.9 membership in öne class and 0.05 membership in two other classes, we can be reasonably sure the class of 0.9 membership is the class to which the signal belongs. On the other hand, if a signal is assigned 0.55 membership in öne class, 0.44 membership in class two, and 0.01 membership in class three, then we should be hesitant to assign the signal based on these results. However, we can feel confident that it does not belong to class three. in such a case the signal might be examined further to determine its classification, because the signal exhibits a high degree of membership in both classes öne ör two. hı fuzzy set theory-based- pattern classification algorithms, a distance from group center is used to evaluate the membership values. The fîrst algorithm we uy to explain is ”Fuzzy C-Mean (FCM)". in this algorithm, sum of memberships that a signal has for ali classes is l, and we can calculate the membership values for a unlabeled signals for ali classes. As C, number of class (i, j = 1,2,3,...C); <*& distance from i. group center for k. x signals in this group ; d* distance from j. group center for k. x signals in this group, membership value of x is U;(x)for i. class is calculated as follow; viiiUi(x> Ç_ r j l2/(m-l) V İ& (2) ^ d: j=iu 0<Su(xk)<n (3) k=l C E Ui(xk) = 1 (4) i=l m[l,<x) is parameter which determines the degree of fuzzy. For m-»oc, Uj(x)-»1/C. Moreover, from (2), relative distance are used. That is, a membership degree of x for a class is based on the rests. In this algorithm, in a case of equal distance for all classes, equal membership degree is obtained for all classes. To remove this ill-defined case, a novel theory is introduced: Fuzzy Possibilistic Approach. In this approach, membership degree of x for a class is not based on the rests. It is determined by distance just from its group center and a parameter that represents this class. So, in this algorithm, sum of memberships for all classes might be less than or more than 1. Another fuzzy algorithm is Adaptive Fuzzy approach. In adaptive algorithm, distance used is different from the above. Geometric interpretation of the distance called adaptive distance is illustrated in Fig.2. In this figure, t{ is called group radius to be determined for each class. This distance can be written as follows; DLK4-1İ)2 (5) In this study, the algorithms is evaluated to obtain membership values of EMG signals for each class. The values is used during classification. As classifiers, Fuzzy K-Nearest Neighbor and Fuzzy Nearest Membership classifiers are used. Important feature of the algorithms is that there is no assumption and it does not need a priori infonnation. The advantage of the algorithms is that no arbitrary assignment are made by the algorithm. IXIn the chapter 6 and 7 of the thesis, the results obtained from the algorithms are submitted as compared to each other by using tobies and 2 and 3-D graphics. m this study, different types of fuzzy algorithms for signal classification applied to EMG signals is evaluated. In chapter 6, used membership functions give better results compared to each other. But, better membership functions can be evaluated to be able to reach %100 classification. In chapter 7, four different membership framing algorithms (fuzzy c-mean, fuzzy possibilistic c-means, adaptive fuzzy c-means and adaptive fuzzy possibilistic c-means) and two fuzzy classification algorithms (fuzzy K-nearest neighbor classifiers and fuzzy nearest neighbor classifiers) are evaluated. As membership training algorithms, the classifiers show that better algorithm is fuzzy c-mean. But, the others have superiority compared to each other. Figure-2 Geometric interpretation of adaptive distance from a spherical shell. V;, group center for class i; x, and x2 points/signals/patterns ; dn and di2 normal distance for class i; ri5 group radius for class i ; Da and Di2 adaptive distance for x, and x2 for class i.

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