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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.