Perturbation-based classifier

Abstract

The Bayes classifier depends on the conditional densities and the prior probabilities. Among many density functions, the Gaussian density has received more attention mainly motivated by its analytical tractability. The parameters of the Bayes classifier for the Gaussian distribution data are generally unknown, and approximations are calculated for the mean vector ${\hat{{\varvec{\mu }}}}$ and the covariance matrix ${\hat{\varSigma }}$. When a pattern is inserted in the training set of the class $\omega _i$, the values of the parameters $\hat{{\varvec{\mu }}}_{{\varvec{i}}}$ and ${\hat{\varSigma }}_{i}$ change by an amount given by $\varDelta \hat{{\varvec{\mu }}}_{{\varvec{i}}}$ and $\varDelta {\hat{\varSigma }}_i$, respectively. The insertion of one pattern can cause a perturbation, so we claim that this perturbation can be used for supervised classification purposes. Based on this assumption, we propose a supervised classifier called Perturbation-based Classifier PerC that assigns the class of the query pattern as the one that presents the smallest perturbation among all the classes after the insertion of this query pattern in the classes. The rationale is that the addition of a pattern that belongs to one specific class should not alter much the distribution of that class. PerC only uses the perturbations ($\varDelta \hat{{\varvec{\mu }}}_{{\varvec{i}}}$ and $\varDelta {\hat{\varSigma }}_i$) to evaluate the class of a query pattern; so, it is a parameter-free classifier. The proposed method was assessed on 21 datasets from the UCI Machine Learning Repository, and its results were compared with classifiers from the literature. Results have shown that PerC obtains very competitive recognition rates.