PhD graduated
Team : LFI
Departure date : 03/16/2019

Supervision : Christophe MARSALA

Co-supervision : LESOT Marie-Jeanne

Regularization operators for fuzzy subspace clustering

Subspace clustering is a data mining task which consists in simultaneously identifiying groups of similar data and making this similarity, local to each of these clusters, explicit, for example by identifying characteristic features for each group. In this thesis, we consider a specific family of fuzzy subspace clustering models, which are based on the minimization of a cost function. We propose three desirable qualities of clustering, which are absent from the solutions computed by the previous models. We then propose simple penalty terms which we use to encode these properties in the original cost functions. relaxing the usual contraint according to which regularization terms should be differentiable: we propose to consider the framework of proximal optimisation. Indeed, when non-differentiable terms are considered, the standard techniques in fuzzy clustering cannot be applied to minimize the new cost functions. We thus propose a new, generic optimization algorithm, which extends the standard approach by combining alternate optimization and proximal gradient descent. We then instanciate this algorithm with operators minimizing the three previous penalty terms and show that the resulting algorithms posess the corresponding qualities.

Defence : 03/01/2019

Jury members :

M. Julien Velcin, Université de Lyon 2, [rapporteur]
M. Nicolas Labroche, Université de Tours, [rapporteur]
M. Carl Frélicot, Université de la Rochelle
M. Antoine Cornuéjols, AgroParisTech
M. Matthieu Cord, Université Sorbonne Université
Mme Marie-Jeanne Lesot, Université Sorbonne Université
M. Christophe Marsala, Université Sorbonne Université

Departure date : 03/16/2019

2016-2019 Publications