Localization of vectors–patterns in the problems of parametric classification with the purpose of increasing its accuracy - Aouati, Mourad (Eastern-European Journal of Enterprise Technologies, 2016)
The problem of the accuracy of classification, determined by the share of the correctly classified objects with the use of parametric methods of pattern recognition, is examined. In particular, we analyzed the influence of deviation from the normal law of distribution of variables of the space of features – random variables, in essence – and the inequality of covariance matrices of classes on the accuracy of classification. It was found that the inequality of covariance matrices of the divided classes leads to the shift of the dividing surface; however, the magnitude of this displacement may not become the essential factor, which influences the accuracy of classification. It is shown for the space of variables of dimensionality (N×2) that for the randomly selected classes inside the square with the length of the edge, equal to two, the accuracy of classification for classes A and B proves to be different and depends on the position of the straight line, which divides the classes. It is shown that localization of vectors-patterns in the space of features can be selected in accordance with the plans of full factorial experiment (FFE). Due to this localization, the equality of covariance matrices of the classes is ensured and the share of the correctly classified objects increases. We proposed, to overcoming the main shortcoming of the given research, connected to the absence of functional dependencies, which make it possible to quantitatively evaluate the accuracy of classification at various variants of arrangement of FFE plans, to use the methods of experimental optimization. Its purpose is the selection of such coordinates of the centers of plans and their geometric characteristics for classes A and B, which ensure the maximum share of the correctly classified objects based on the obtained decision rules. The realization of this approach may become the reserve for the increase in the accuracy of classification with application of the methods of parametric optimization.