One-class classification through mutual information minimization

In one-class classification problems, a model is synthesized by using only information coming from the nominal state of the data generating process. Many important applications can be cast in the one-class classification framework, such as anomaly and change in stationarity detection, and fault recognition. In this paper, we present a novel design methodology for one-class classifiers derived from graph-based entropy estimators. The entropic graph is used to generate a partition of the input nominal conditions, which corresponds to the classifier model. Here we propose a criterion based on mutual information minimization to learn such a partition. The α-Jensen difference is considered, which provides a convenient way for estimating the mutual information. The classifier incorporates also a fuzzy model, providing a confidence value for a generic test sample during operational modality, expressed as a membership degree of the sample to the nominal conditions class. The fuzzification mechanism is based only on topological properties of the entropic spanning graph vertices; as such, it allows to model clusters of arbitrary shapes. We show preliminary - yet very promising - results on both synthetic problems and real-world datasets for one-class classification.