FACE RECOGNITION USING THE TEN-VARIATE PREDICTION ELLIPSOID FOR NORMALIZED DATA BASED ON THE BOX-COX TRANSFORMATION

Abstract

Context. Face recognition, which is one of the tasks of pattern recognition, plays an important role in the modern information world and is widely used in various fields, including security systems, access control, etc. This makes it an important tool for security and personalization. However, the low probability of identifying a person by face can have negative consequences, so there is a need for the development and improvement of face recognition methods. The object of research is the face recognition process. The subject of the research is a mathematical model for face recognition. One of the frequently used methods of pattern recognition is the construction of decision rules based on the prediction ellipsoid. An important limitation of its application is the need to fulfill the assumption of a multivariate normal distribution of data. However, in many cases, the multivariate distribution of real data may deviate from normal, which leads to a decrease in the probability of recognition. Therefore, there is a need to improve mathematical models that would take into account the specified deviation. The objective of the work is to increase the probability of face recognition by constructing a ten-variate prediction ellipsoid for data normalized by the Box-Cox transformation. Method. Application of the Mardia test to test the deviation of a multivariate distribution of data from normality. Building decision rules for face recognition using a ten-variate prediction ellipsoid for data normalized based on the Box-Cox transformation. Obtaining estimates of the parameters of the univariate and ten-variate Box-Cox transformations using the maximum likelihood method. Results. A comparison of the results of face recognition using decision rules, which were built using a ten-variate ellipsoid of prediction for data normalized by various transformations, was carried out. In comparison with the use of univariate normalizing transformations (decimal logarithm and Box-Cox) and the absence of normalization, the use of the ten-variate Box-Cox transformation leads to an increase in the probability of face recognition. Conclusions. For face recognition, a mathematical model in the form of a ten-variate prediction ellipsoid for data normalized using the multivariate Box-Cox transformation has been improved, which allows to increase in the probability of recognition in comparison with the use of corresponding models that are built either without normalization or with the use of univariate normalizing transformations. It was found that a mathematical model built for normalized data using a multivariate Box-Cox transformation has a higher probability of recognition since univariate transformations neglect the correlation between geometric features of the face.