Contribuições aos Processos de Clustering com Base em Métricas não-Euclidianas

In this work we present a new clustering method that groups up points of a data set in classes. The method is based in a algorithm to link auxiliary clusters that are obtained using traditional vector quantization techniques. It is described some approaches during the development of the work that are based in measures of distances or dissimilarities (divergence) between the auxiliary clusters. This new method uses only two a priori information, the number of auxiliary clusters Na and a threshold distance dt that will be used to decide about the linkage or not of the auxiliary clusters. The number os classes could be automatically found by the method, that do it based in the chosen threshold distance dt, or it is given as additional information to help in the choice of the correct threshold. Some analysis are made and the results are compared with traditional clustering methods. In this work different dissimilarities metrics are analyzed and a new one is proposed based on the concept of negentropy. Besides grouping points of a set in classes, it is proposed a method to statistical modeling the classes aiming to obtain a expression to the probability of a point to belong to one of the classes. Experiments with several values of Na e dt are made in tests sets and the results are analyzed aiming to study the robustness of the method and to consider heuristics to the choice of the correct threshold. During this work it is explored the aspects of information theory applied to the calculation of the divergences. It will be explored specifically the different measures of information and divergence using the Rényi entropy. The results using the different metrics are compared and commented. The work also has appendix where are exposed real applications using the proposed method

Algoritmos de agrupamento aplicados a dados de expressão gênica de câncer: um estudo comparativo

The use of clustering methods for the discovery of cancer subtypes has drawn a great deal of attention in the scientific community. While bioinformaticians have proposed new clustering methods that take advantage of characteristics of the gene expression data, the medical community has a preference for using classic clustering methods. There have been no studies thus far performing a large-scale evaluation of different clustering methods in this context. This work presents the first large-scale analysis of seven different clustering methods and four proximity measures for the analysis of 35 cancer gene expression data sets. Results reveal that the finite mixture of Gaussians, followed closely by k-means, exhibited the best performance in terms of recovering the true structure of the data sets. These methods also exhibited, on average, the smallest difference between the actual number of classes in the data sets and the best number of clusters as indicated by our validation criteria. Furthermore, hierarchical methods, which have been widely used by the medical community, exhibited a poorer recovery performance than that of the other methods evaluated. Moreover, as a stable basis for the assessment and comparison of different clustering methods for cancer gene expression data, this study provides a common group of data sets (benchmark data sets) to be shared among researchers and used for comparisons with new methods

Algoritmos de agrupamentos fuzzy intervalares e índice de validação para agrupamento de dados simbólicos do tipo intervalo

Symbolic Data Analysis (SDA) main aims to provide tools for reducing large databases to extract knowledge and provide techniques to describe the unit of such data in complex units, as such, interval or histogram. The objective of this work is to extend classical clustering methods for symbolic interval data based on interval-based distance. The main advantage of using an interval-based distance for interval-based data lies on the fact that it preserves the underlying imprecision on intervals which is usually lost when real-valued distances are applied. This work includes an approach allow existing indices to be adapted to interval context. The proposed methods with interval-based distances are compared with distances punctual existing literature through experiments with simulated data and real data interval