Face recognition using ten-variate prediction ellipsoidsfor normalized datawith different quantiles

Abstract

Facial recognition technology plays a pivotal role in various domains, including security systems, entertainment, and identity ver-ification. However, the low probability of identifying a person by face can have negative consequences, highlighting the need forthe development and improvement of face recognition methods. The object of research is the face recognition process, with the subject of the research being a mathematical model for face recognition.One common approach in pattern recognition is usingdecision rules based onprediction ellipsoid. A significant challenge in its application is ensuring that the data conforms to a multivariate normal distribution. However, real-world data often doesn't adhere to this assumption, leading to reduced recognition probability. Therefore, there's a necessity to enhance mathematical models to accommodate such deviations.Another factor that can impact the outcome is the selection of different distribution quantiles, such as those from the Chi-square and F-distribution.For large datasets, the utilization of Chi-square and F-distribution in prediction ellipsoids typically results in similar probabilities, but there are data for which this is not the case and the application of predictionellipsoids with different quantiles of the distributions gives different results.This study investi-gates theapplicationof prediction ellipsoids in facial recognition tasks using different normalization techniques and distribution quan-tiles. The purpose of the work is to improve the probability of face recognition by building a ten-variate prediction ellipsoid for nor-malized data with different quantiles of distributions. We conducted experiments on a dataset of facial images and constructed predic-tion ellipsoids based on the Chi-square and F-distribution, utilizing both univariate and multivariate normalization techniques.Our findings reveal that normalization techniques significantly enhance recognition accuracy, with multivariate methods, such as the ten-variate Box-Cox transformation, outperforming univariate approaches. Furthermore, prediction ellipsoids constructed using the Chi-square distribution quantile generally exhibit superior performance compared to those constructed using the F-distribution quantile. Future investigations could explore the efficacy of alternative normalization techniques, such as the Johnson transformation, and ana-lyze the construction of prediction ellipsoids with alternative components of the ellipsoid equation.