A novel SVM+NDA model for classification with an application to face recognition

Support vector machine (SVM) is a powerful classification methodology, where the support vectors fully describe the decision surface by incorporating local information. On the other hand, nonparametric discriminant analysis (NDA) is an improvement over LDA where the normality assumption is relaxed. NDA also detects the dominant normal directions to the decision plane. This paper introduces a novel SVM+NDA model which can be viewed as an extension to the SVM by incorporating some partially global information, especially, discriminatory information in the normal direction to the decision boundary. This can also be considered as an extension to the NDA where the support vectors improve the choice of k-nearest neighbors on the decision boundary by incorporating local information. Being an extension to both SVM and NDA, it can deal with heteroscedastic and non-normal data. It also avoids the small sample size problem. Moreover, it can be reduced to the classical SVM model, so that existing softwares can be used. A kernel extension of the model, called KSVM+KNDA is also proposed to deal with nonlinear problems. We have carried an extensive comparison of the SVM+NDA to the LDA, SVM, heteroscedastic LDA (HLDA), NDA and the combined SVM and LDA on artificial, real and face recognition data sets. Results for KSVM+KNDA have also been presented. These comparisons demonstrate the advantages and superiority of our proposed model.

► We present a novel SVM+NDA model which combines the well-known SVM and NDA models.
► The SVM+NDA is improvement to the SVM and NDA in terms of classification performance.
► The SVM+NDA outperforms other models in terms of classification and face recognition.
► A kernel version of the SVM+NDA is proposed to deal with nonlinearly separable data.
► The SVM+NDA (Kernel) can deal with heteroscedasticity, non-normality and SSS problem.