  Subtype Discovery consists in finding interpretable and consistent sub-parts
of a dataset, which are also relevant to a certain supervised task. From a
mathematical point of view, this can be defined as a clustering task driven by
supervised learning in order to uncover subgroups in line with the supervised
prediction. In this paper, we propose a general Expectation-Maximization
ensemble framework entitled UCSL (Unsupervised Clustering driven by Supervised
Learning). Our method is generic, it can integrate any clustering method and
can be driven by both binary classification and regression. We propose to
construct a non-linear model by merging multiple linear estimators, one per
cluster. Each hyperplane is estimated so that it correctly discriminates - or
predict - only one cluster. We use SVC or Logistic Regression for
classification and SVR for regression. Furthermore, to perform cluster analysis
within a more suitable space, we also propose a dimension-reduction algorithm
that projects the data onto an orthonormal space relevant to the supervised
task. We analyze the robustness and generalization capability of our algorithm
using synthetic and experimental datasets. In particular, we validate its
ability to identify suitable consistent sub-types by conducting a
psychiatric-diseases cluster analysis with known ground-truth labels. The gain
of the proposed method over previous state-of-the-art techniques is about +1.9
points in terms of balanced accuracy. Finally, we make codes and examples
available in a scikit-learn-compatible Python package at
https://github.com/neurospin-projects/2021_rlouiset_ucsl
