  The new financial European regulations such as PSD2 are changing the retail
banking services. Noticeably, the monitoring of the personal expenses is now
opened to other institutions than retail banks. Nonetheless, the retail banks
are looking to leverage the user-device authentication on the mobile banking
applications to enhance the personal financial advertisement. To address the
profiling of the authentication, we rely on tensor decomposition, a higher
dimensional analogue of matrix decomposition. We use Paratuck2, which expresses
a tensor as a multiplication of matrices and diagonal tensors, because of the
imbalance between the number of users and devices. We highlight why Paratuck2
is more appropriate in this case than the popular CP tensor decomposition,
which decomposes a tensor as a sum of rank-one tensors. However, the
computation of Paratuck2 is computational intensive. We propose a new
APproximate HEssian-based Newton resolution algorithm, APHEN, capable of
solving Paratuck2 more accurately and faster than the other popular approaches
based on alternating least square or gradient descent. The results of Paratuck2
are used for the predictions of users' authentication with neural networks. We
apply our method for the concrete case of targeting clients for financial
advertising campaigns based on the authentication events generated by mobile
banking applications.
