  One-class classifiers offer valuable tools to assess the presence of outliers
in data. In this paper, we propose a design methodology for one-class
classifiers based on entropic spanning graphs. Our approach takes into account
the possibility to process also non-numeric data by means of an embedding
procedure. The spanning graph is learned on the embedded input data and the
outcoming partition of vertices defines the classifier. The final partition is
derived by exploiting a criterion based on mutual information minimization.
Here, we compute the mutual information by using a convenient formulation
provided in terms of the $\alpha$-Jensen difference. Once training is
completed, in order to associate a confidence level with the classifier
decision, a graph-based fuzzy model is constructed. The fuzzification process
is based only on topological information of the vertices of the entropic
spanning graph. As such, the proposed one-class classifier is suitable also for
data characterized by complex geometric structures. We provide experiments on
well-known benchmarks containing both feature vectors and labeled graphs. In
addition, we apply the method to the protein solubility recognition problem by
considering several representations for the input samples. Experimental results
demonstrate the effectiveness and versatility of the proposed method with
respect to other state-of-the-art approaches.
