  In classification problems, supervised machine-learning methods outperform
traditional algorithms, thanks to the ability of neural networks to learn
complex patterns. However, in two-class classification tasks like anomaly or
fraud detection, unsupervised methods could do even better, because their
prediction is not limited to previously learned types of anomalies. An
intuitive approach of anomaly detection can be based on the distances from the
centers of mass of the two respective classes. Autoencoders, although trained
without supervision, can also detect anomalies: considering the center of mass
of the normal points, reconstructions have now radii, with largest radii most
likely indicating anomalous points. Of course, radii-based classification were
already possible without interposing an autoencoder. In any space, radial
classification can be operated, to some extent. In order to outperform it, we
proceed to radial deformations of data (i.e. centric compression or expansions
of axes) and autoencoder training. Any autoencoder that makes use of a data
center is here baptized a centric autoencoder (cAE). A special type is the cAE
trained with a uniformly compressed dataset, named the centripetal autoencoder
(cpAE). The new concept is studied here in relation with a schematic artificial
dataset, and the derived methods show consistent score improvements. But tested
on real banking data, our radial deformation supervised algorithms alone still
perform better that cAEs, as expected from most supervised methods;
nonetheless, in hybrid approaches, cAEs can be combined with a radial
deformation of space, improving its classification score. We expect that
centric autoencoders will become irreplaceable objects in anomaly live
detection based on geometry, thanks to their ability to stem naturally on
geometrical algorithms and to their native capability of detecting unknown
anomaly types.
