A Methodology to simulate random pyramids: some comments

• Type: Article in International Conference Proceedings Book
• Date: 2007

Authors

Vasco Machado (Author) FEUP; Fernanda Campos de Sousa (Author) FEUP

Conference proceedings International

Title: Proceedings of the conference "Probability and Statistics in Science and Technology

Pages: 17-18

Probability and Statistics in Science and Technology 2007

Feup, Porto, 30 de Agosto a 1 de Setembro de 2007

Scientific classification

FOS: Natural sciences

Other information

Abstract (EN): The application of a classification method to a dataset produces, on the objects to classify, a group of classes organized second a structure (a partition, a hierarchy, a covering, a pyramid, etc.). This structure depends, not only of the dataset, but also of the intrinsic nature of the classification method used. When a classificatory structure is obtained becomes important to discover which part is exclusive responsibility of the used method. This aspect is one of the problems studied in Cluster Validation. A tool of great usefulness in validation is the random generation of classification structures. The motivation to develop generation algorithms of classification structures have been intensifying among the scientific community, leading to several studies. In this work a random generation method of pyramidal structures is presented and discussed. This method appears as an extension of previous works in random generation of dendrograms developed by Lapointe and Legendre (1991), Sousa (2000) and Podani (2000). The dendrograms considered in these works are fully ranked dendrograms, i. e., they are generated under the three aspects that characterize them completely: the topology, the aggregation level indexes and the terminal nodes. In the characterization of a pyramid the three referred aspects must also be considered and the pyramids random generation presented in this work takes account all of them. Fixed a number of terminal nodes of the pyramid the developed algorithm generates a random pyramid, generating in each level the two classes to be merge, among the possible classes. A simulation study is made to evaluate the performance of the algorithm. In particular is analyzed if the method generates pyramids in a uniform way, in sense of Furnas (1984).

Language: Portuguese

Type (Professor's evaluation): Scientific