| dc.description.abstract | The main objective of this thesis is the development of a methodology based on fuzzy set theory for several practical pattern recognition problems. Pattern recognition (PR) encompasses a range of problems from feature extraction to classification. The two problems are somewhat overlapping and are amenable to similar approaches. The former is very data-specific; the latter forms the present subject.
The choice of class labels and the selection of features for classification are often based on subjective judgment of the system designer. The relationship between a pattern sample characterized by its feature values and the association of an appropriate class label is a fuzzy process if performed by a human being. It is natural to seek its relevance to the design of automatic PR systems for use as decision support systems to human decision makers. In this thesis, supervised, unsupervised and decision tree classifiers and adaptive training of such classifiers are studied in the framework of fuzzy set theory. The techniques developed are tested on three data sets: two from speech processing (vowel recognition and voiced-unvoiced-silence (V/U/V/S) detection) and the classical IRIS data of Fisher in numerical taxonomy. Though the data is not extensive, they are suited for the range of PR problems considered here.
Initially, the problem of supervised pattern classification in the framework of fuzzy sets is considered. It is assumed that there are a finite number of labeled sample patterns, the class labels of which are predefined on the basis of the data-specific knowledge and the attempted recognition task. For simplicity, an exponential membership function is chosen and a max-min decision scheme is proposed for classification. One of the examples considered is data on six vowels, uttered in consonant-vowel-consonant context by five speakers. The scheme works well even with a limited amount of training data and test patterns with missing observations. The recognition scheme can be formulated as a hierarchical classifier when the number of classes and/or features is large.
Central to the concept of a fuzzy set is the notion of a membership function, which enables one to perform quantitative calculations with fuzzy sets. A method of estimating the parameters of a more general class of membership function of fuzzy sets using the information contained in histograms is presented.
The design of PR schemes when there are no labeled samples is a more complex problem. A procedure for designing a fuzzy binary decision tree using unlabeled samples is developed. The fuzzy ISODATA clustering algorithm is implemented at the root node of the decision tree to split all the available samples into two dissimilar groups, and the best feature among the available features is selected based on some separation index. At subsequent nodes, samples of the cluster are further divided. The procedure is continued till further "dissection" is impossible. The decision tree so designed can be used for classification of future sample patterns. The procedure indicated gives an initial tree specification amenable for further optimization.
Hierarchical clustering procedures based on fuzzy set models, applicable for large databases, are then considered. The computational complexity of hierarchical clustering procedures is due to the need for storing the similarity matrix of the order of the size of the sample set. A novel two-level clustering procedure is developed to reduce the problem of storing the similarity matrix. The first level, which gives the initial configuration of the data, consists of a multistage evolutionary clustering procedure. Here, a small subset of the entire sample set is clustered at each stage. Cluster representatives obtained at any stage are utilized as samples, with some more samples from the original set, in the next stage. This procedure is repeated till all the samples are exhausted. The initial configuration is dynamically refined at the second level. This is done using the max-min classifier. The technique is illustrated by an efficient scheme for V/U/V/S classification of speech.
When it is possible to identify at least one sample from each class in the unlabeled sample set, the training of a pattern classifier is another interesting PR problem. A sequential fuzzy learning scheme is proposed for such a purpose. The method is similar to clustering and is suitable for situations in which data is obtained online. Learning is based on simultaneous fuzzy decision making and estimation. It uses conditional fuzzy measures on the unlabeled samples. An exponential membership function is assumed and the parameters constituting this membership function are estimated in a recursive fashion. This is done using the induced possibility of occurrence of each class obtained by using the membership of the new sample in that class and the previously computed average possibility of occurrence of that class. An inductive entropy measure is defined in terms of induced possibility distribution to measure the extent of learning. As a consequence of learning, the recognition accuracy improves with the number of samples used for learning.
The thesis is concluded by noting some of the features of fuzzy PR methods in comparison with statistical methods. | |
