Probalistic Networks and Fuzzy Clustering as Generalizations of Naive Bayes Classifiers

Although at first sight probabilistic networks and fuzzy clustering seem to be disparate areas of research, a closer look reveals that they can both be seen as generalizations of naive Bayes classifiers. If all attributes are numeric (except the class attribute, of course), naive Bayes classifiers often assume an axis-parallel multidimensional normal distribution for each class as the underlying model. Probabilistic networks remove the requirement that the distributions must be axis-parallel by taking the covariance of the attributes into account, where this is necessary. Fuzzy clustering is an unsupervised method that tries to find general or axis-parallel distributions to cluster the data. Although it does not take into account the class information, it can be used to improve the result of naive Bayes classifiers and probabilistic networks by removing the restriction that there can be only one distribution per class.