부산대학교 도서관

In this memory it is developed a methodology to tackle problems about the classifications and representations population's members through structures called "Pyramids". Pyramidal trees, introduced by E. Diday, are a logical generalization of ultrametric trees. They are less restrictive structures where recovering replaces the concept of partition, obtaining a representation which bears information is closer to the dissimilarities. A new formalization of mathematics bases of the pyramidal models is developed. In this sense, the axiomatic has fixed and new theorems of existence and uniqueness of the pyramid induced from pyramidal dissimilarity, they are considered, and mutually. An algorithm of pyramidal classification is designed in order to obtain an easiest pyramid. The spare groups in an indexed pyramid are characterized. A suitable criterion to the pyramidal models is definited to calculate the distance between groups. From mentioned algorithm and using this criterion indexed pyramid in strict sense, without reversals, crossings and spare groups. Moreover, a computer programming of the algorithm is developed in Turbo Prolog.In applied problems is necessary to measure the fitting between the pyramidal tree from some algorithm and the initial structure. Using some simulation techniques by means of Monte Carlo methods, sample distribution of is obtained, to tabulate a goodness-of-fit test of the pyramidal representation using the minimum method and the maximum method. Finally, we have studied the efficiency of the maximum method and the minimum method through other simulation tests.