In order to categorize a set of data which consists of some categories, it is important to know the probability distribution of the data of each category. Using these probability distributions, one can classify the data. In most cases, such as speech and image recognition problems, the data, for training are categorized in advance. But there are some cases when only the uncategorized data are available. For example, when a baby learns phonation, it is hard to give it the samples of each phone separately, it learns the number of the phones and how to phonate each of them through observing only the uncategorized data and making communication with the parents or the teacher. In this article, the authors give an algorithm for this situation. In the algorithm, the distribution of whole data is described with a finite mixture model. The model can observe only the uncategorized data but can make a kind of communication with the teacher (which is the probability source). The parameters of the model are estimated using the EM algorithm and the number of the categories are determined through a communication with the teacher. A numerical simulation of a simple image recognition problem is given.