  One-class learning (OCL) comprises a set of techniques applied when
real-world problems have a single class of interest. The usual procedure for
OCL is learning a hypersphere that comprises instances of this class and,
ideally, repels unseen instances from any other classes. Besides, several OCL
algorithms for graphs have been proposed since graph representation learning
has succeeded in various fields. These methods may use a two-step strategy,
initially representing the graph and, in a second step, classifying its nodes.
On the other hand, end-to-end methods learn the node representations while
classifying the nodes in one learning process. We highlight three main gaps in
the literature on OCL for graphs: (i) non-customized representations for OCL;
(ii) the lack of constraints on hypersphere parameters learning; and (iii) the
methods' lack of interpretability and visualization. We propose One-cLass Graph
Autoencoder (OLGA). OLGA is end-to-end and learns the representations for the
graph nodes while encapsulating the interest instances by combining two loss
functions. We propose a new hypersphere loss function to encapsulate the
interest instances. OLGA combines this new hypersphere loss with the graph
autoencoder reconstruction loss to improve model learning. OLGA achieved
state-of-the-art results and outperformed six other methods with a
statistically significant difference from five methods. Moreover, OLGA learns
low-dimensional representations maintaining the classification performance with
an interpretable model representation learning and results.
