An examination of clustering method using Bayesian and Markov networks and an application

Since probabilistic network models emerged, probability has become an acceptable measure for uncertainty. Expert systems which use probability as a measure of uncertainty are called probabilistic expert systems. Due to complications that arise in definition of joint probability function of variables, probabilistic network models are used. These network models that include Bayesian and Markov networks are based on the graphical representations of relationships among variables. Models obtained by the usage of probability theory and graph theory are called probabilistic network models. Formation of these models is a type of statistical model formation and graphs are used to represent these models. Graphs play an important role in displaying joint probability functions and facilitating the derivation of effective results from observations. In these graphs, variables represent nodes and the edges represent dependence between variables and causal effect. Markov network models, one of the probabilistic network models most frequently used are determined by undirected graphs. Bayesian networks, another type of these models, are determined by directed acyclic graphs. In the thesis study, estimation from data will be made instead of expert views for model structure and conditional probabilities. In addition, the case that the database does not have missing data will be considered. vii The method that brings variables together to obtain the structure of joint probability function of a graph is called clustering method. In this study, clustering methods will be given for Markov and Bayesian network models which are probabilistic network models. In practice, a survey study has been made on 74 women who have breast cancer in and around Ankara province. For study, the best model for the variables in question was obtained by using UnBBayes program. After the best Bayesian network model is obtained, a Markov network model that fits the model has been found. Clustering algorithms have been applied on these obtained models. Thus, the clusters of the variables in question have been shown. In addition, HUGIN package program has been used for numbering of nodes suitable for the model and for information such as cluster graphs and moral graphs. Key Words : Bayesian networks, Markov networks, learning, clustering methods, directed graphs, undirected graphs, triangulated graps, cluster graphs, cluster tree