Robustification of Gaussian Bayes Classifier by the Minimum β-Divergence Method

The goal of classification is to classify new objects into one of the several known populations. A common problem in most of the existing classifiers is that they are very much sensitive to outliers. To overcome this problem, several author’s attempt to robustify some classifiers including Gaussian Bayes classifiers based on robust estimation of mean vectors and covariance matrices. However, these type of robust classifiers work well when only training datasets are contaminated by outliers. They produce misleading results like the traditional classifiers when the test data vectors are contaminated by outliers as well. Most of them also show weak performance if we gradually increase the number of variables in the dataset by fixing the sample size. As the remedies of these problems, an attempt is made to propose a highly robust Gaussian Bayes classifiers by the minimum β-divergence method. The performance of the proposed method depends on the value of tuning parameter β, initialization of Gaussian parameters, detection of outlying test vectors, and detection of their variable-wise outlying components. We have discussed some techniques in this paper to improve the performance of the proposed method by tackling these issues. The proposed classifier reduces to the MLE-based Gaussian Bayes classifier when β → 0. The performance of the proposed method is investigated using both synthetic and real datasets. It is observed that the proposed method improves the performance over the traditional and other robust linear classifiers in presence of outliers. Otherwise, it keeps equal performance.