Aprimoramento do poder discriminatório de funções elipsoidais modificadas por cargas fatoriais rotacionadas na formação otimizada de agrupamentos

Abstract

The technological advent provided the rise of data collection in companies, governments and various industrial segments. In this respect, techniques that seek to perform groupings and discrimination of clusters are widely used in datasets with multiple variables, bringing the need to use specific tools, which contemplate the existing variance-covariance structure. Based on this, this work presents a proposal to improve the discriminatory power of confidence regions in the formation and estimation of optimal clusters, using multivariate and experimental techniques to extract information in an optimized way in correlated datasets. Factor analysis was used as the exploratory multivariate method, tuning the rotation for factor loads through the mixture design, and agglutinating the total variance explained functions by the mean square error afterwards. The optimization of this step is performed through the sequential quadratic programming algorithm. Knowing the optimal scores, a multilevel factorial design is formed to contemplate all combinations of the linkage methods and the types of analysis, seeking to find the parameter that presents the least variability, generating confidence ellipses with better discrimination between groups. A strategy to analyze the levels of agreement and the inversions existence in the formation of clusters is proposed using the Kappa and Kendall indicators. Motivated by the need for strategies to classify substations in the face of voltage sag phenomena, which cause faults in the distribution of electricity, the method was applied to a set of real data, representing the power quality indexes of substations located in southeastern Brazil. Optimum values were found in the factor loads rotation and the parameterization “Wardanalysis of covariance” was defined as the ideal strategies to create the clusters in this dataset. Thus, low variability clusters and precise confidence ellipses were generated to estimate the voltage sag patterns, promoting a better discriminatory power in the clusters’ classification through the regions of confidence. The confirmatory analysis inferred that the “Ward” linkage proved to be the most robust method for this dataset, even under the influence of disturbances in the original data.