The present paper discusses a nonparametric algorithm for detecting clusters. In the algorithm a positive value called potential is associated with each datum based on dissimilarities. By defining subordination relations among data, hierarchical structure is introduced into the data set. As a result of the introduction of hierarchical structure, the data set is divided into some subsets called subclusters. A procedure for constructing clusters from the subclusters is also considered. The proposed algorithm can be applied to a very wide range of data set and has great ability to detect clusters, which is verified by computer simulation.

The present paper discusses a nonsupervised multicategory problem in terms of nonparametric learning. An algorithm for seeking modes of an unknown multidimensional probability density function (pdf) is considered by employing a hypercubic window function. The convergence proof of the algorithm is also presented. The discriminant function for multicategory problems is constructed by using the estimates of the modes of the multimodal pdf. An application of the mode estimation algorithm to nonparametric signal detection is described. The analytical result shows that our machine nearly converges to the optimal machine without supervision.

In this correspondence, an approach to unsupervised pattern classifiers is discussed. The classifiers discussed here have the ability of obtaining the consistent estimates of unknown statistics of input patterns without knowing the a priori probability of each category's occurrence where the input patterns are of a mixture distribution. An analysis is made about their asymptotic behavior in order to show that the classifiers converge to the Bayes' minmum error classifier. Also, some results of a computer simulation on learning processes are shown.

This paper presents properties of several different algorithms suitable for multicategory classification of hand-printed alphanumeric characters. In the character reader the input patterns are generally composed of the template characters and their distorted ones. Using the template patterns, a nonparametric procedure is developed for determining linear discriminant functions. Furthermore, we propose the mechanism which has the ability to recognize even a misprinted character by using the information of the preceding character. The algorithms offer the following advantages: flexibility (cost assignments), simplicity, adaptation, and acceptable performance. Performance of the machines is analyzed and convergence proofs of the learning procedures in the machines are derived. We also present some results of computer experiments.