Aprendizado de métricas utilizando uma função de distância parametrizada e o algoritmo K-means com aplicação na solução de problemas de classificação

Abstract

The use of different metrics in machine learning algorithms is able to change the results of analyzes carried out in databases. By varying how to measure distances or data similarities we can generate reflexes for information capture, which can influence the decision-making. In this sense, metric learning methods have been approached and applied in several branches of the research in the world, in order to find better metrics for problems of cluster analysis, classification, data mining, among others related data pattern recognition. The metric learning method used as the basis of this work was ori-ginally formulated as an optimization problem, in order to minimize a parameter set of Mahalanobis distances. In the original method, it is necessary to define a list of similar or dissimilar vectors pairs, which allow the correction of the distance measurement pa-rameters. In this work, a new method is proposed, which does not require the pairwise comparison, but only the distance comparison from each vector of a training set to two points: one defined by the Seeded k-means and other defined by an expert as being an expected centroid. The distance between the vector and the two centroids is used as correction factor of the parameters for measuring distances. The new learned parame-ters for distances measurement can change the clusters improving the results compared to the Euclidean metric. The major contribution of this study was the formulation of a method to learn these parameters that reduces the complexity in time if compared to other methods proposed in the literature. The proposal of PLM – Parameter Learning Method – have been demonstrated significant improvements in classification problems for several UCI Machine Learning Repository databases.