Feature space partitioning techniques in non-parametric pattern recognition

Abstract

In this dissertation, we propose feature space partitioning techniques for fast pattern classification when the distributions of the patterns are not known. Three partitioning techniques are suggested, each partitions the feature space into a set of open parallelpipes. The first technique is based on the multivalued switching function minimization procedure. The procedure is modified to suit for the pattern classification purpose, and the bound of the probability of error of the proposed classification scheme is calculated. It is applied to the classification of the white blood cells into a six categories, which shows that about 80% of the test samples are preclassified without increasing the probability of classification error significantly in comparison with the conventional classification schema. The second technique aims at constructing the classification scheme such that its probability of error is comparable to that of the nearest neighbor decision scheme. The first technique is modified for this purpose, whereby it is shown that the above two probabilities become the same as the number of the training samples increases. Simulation is performed to show reduction of the classification time by the proposed classification scheme. The last partitioning technique, called the ordered partitioning, aims at quich finding of the k nearest neighbors and partitions the whole feature space based on the order of the training samples in each axis. For the two dimensional case, it is proved that the number of the visited training samples to compute the k nearest neighbors of a test sample is independent of the number of the training samples if these two types of samples are drawn from the same uniform distribution. Simulations show that the proposed technique requires less distance calculations to find the k nearest neighbors of a test sample than the conventional techniques.