The use of principal component analysis in creating an composite indicators of change in the quality of system

Abstract

In the article is given the method of constructing the integral characteristics of changes quality a system based on the recorded measurements. Constructing of latent composite indicators of changes of the quality system on the basis of statistical indicators for a number of consecutive observations is based on the principal component method, taking into account the presence of noise in the measured data (SNR-based algorithm). The algorithm provides signal isolation in a multidimensional data array with noise under conditions of a priory uncertainty about the properties of the signal based on a given signal-to-noise ratio. In classical PCA informativeness of composite indicators is given a prior and is provided by selecting the number of principal components. In the proposed algorithm the information content of the solution is evaluated a posteriori on the basis of variance criterion and the selected parameter signal-to-noise ratio. With the proposed algorithm is construction integral indicators of the quality of life of regions of the Russian Federation for the years 2007–2014.