Algoritmo Wang-Landau e agrupamento de dados superparamagnético

Abstract

The method of unsupervised data classification proposed by Domany and coworkers is based on mapping the problem onto an inhomogeneous granular magnetic system whose properties can be investigated through some Monte Carlo Method. The array containing the data consists of n numeric attributes corresponding to points in an n-dimensional Euclidean space. Each data item is associated with a Potts spin. The interaction between such spins decays exponentially with the distance. This favors the alignment of the spins associated with similar objects. The physical system corresponds to a disordered ferromagnet which, in turn, is described by a Hamiltonian of a q-states Potts model. It is expected that the magnetic system exhibits three temperature-dependent regimes. For very low temperatures the system is completely ordered. At the other extreme, high temperatures, the system shows no magnetic order. In an intermediate range of temperatures, the spins within certain regions remain tightly coupled, forming grains. However, a grain does not influence the behavior of another grain. That is, the grains are non-correlated and this intermediate state is named a superparamagnetic phase. The transition from one regime to another can be identified by peaks in the specific heat versus temperature curve. We apply the method to several artificial and real-life data sets, such as classification of flowers, summary medical data and identification of images. We measure the spin-spin correlation at several temperatures to classify the data. In disagreement with the Domany and coworkers claims we found that the best classification of the data occurred outside the superparagnetic phase.