On the Generalized Likelihood Ratio Test and One-Class Classifiers

One-class classification (OCC) is the problem of deciding whether an observed sample belongs to a target class. We consider the problem of learning an OCC model that performs as the generalized likelihood ratio test (GLRT), given a dataset containing samples of the target class. The GLRT solves the same problem when the statistics of the target class are available. The GLRT is a well-known and provably optimal (under specific assumptions) classifier. To this end, we consider both the multilayer perceptron neural network (NN) and the support vector machine (SVM) models. They are trained as two-class classifiers using an artificial dataset for the alternative class, obtained by generating random samples, uniformly over the domain of the target-class dataset. We prove that, under suitable assumptions, the models converge (with a large dataset) to the GLRT. Moreover, we show that the one-class least squares SVM (OCLSSVM) with suitable kernels at convergence performs as the GLRT. Lastly, we prove that the widely used autoencoder (AE) classifier does not generally provide the GLRT.