Geometry, imaGes, learninG, and alGorithms

The research group Geometry, imaGes, learninG and alGorithms (G4) is a member of the Decision Support Models and Algorithms (MAAD) group. We are all part of the LIMOS lab, in the Cézeaux campus of Université Clermont Auvergne, near Clermont Ferrand, France.

Short summary

The research topics of this group are centered on n-dimensional data modeling and analysis, from both methodology and application points of view. The team's interdisciplinary skills result in projects that cover a wide range of scientific topics including Geometry, Data Mining, Machine Learning, Data Structures, and their interactions for several fields of application.

For a brief description of our main research areas, we mention:

  • Machine learning: We address several aspects of machine learning, from the design of kernel methods to manifold learning and deep learning. Current research include modeling and simulation of spatio-temporal variations and dynamics using manifolds, understanding of the GANs approaches and their link to Optimal Transport, Siamese network for multimodal learning and autoencoders or solving multiclass SVM at the cost of a binary one, and dealing with indefinite kernels or large datasets.
  • Clustering methods: We study fuzzy clustering algorithms, or semi-supervised clustering, also referred to as constrained clustering. Such methods use background knowledge in order to improve the accuracy of the solution.
  • Digital geometry: The field is closely related to many other topics such as geometry of numbers, computational geometry, discrete geometry, and combinatorics. We are especially interested in questions of separability from a lattice set and its complement, as well as the recognition of digital polytopes.
  • Geometric approximation: We resort to approximations to solve geometric problems that would be intractable otherwise. We can either approximate distances (e.g., approximate nearest neighbor searching) or the size of the solution (e.g., maximum independent set of a unit disk graph).
  • Computational geometry: We design algorithms and data structures for numerous geometric problems related to range searching, geometric graphs, and several other topics. We analyze that asymptotic complexity of these algorithms and also prove lower bounds for the complexity of the problems.
  • Image and video processing: We address both the methodological (definition of image analysis methods in n dimension) and the application points of view (tracking of ballistics in thermal videos of volcanoes, design of computer assisted maps for visually impaired people, …).

National collaborations include:

LITIS (Rouen), LMV (Clermont-Ferrand), INRIA Sophia-Antipolis, Creatis (Lyon), IMT (Toulouse), LIFL (Lille) and IGN (Paris).

International collaborations include:

  • Australia: Murdoch University and CSIRO
  • Belgium: Université Catholique de Louvain and the Royal Observatory of Belgium
  • Brazil: UDESC and UFRJ
  • Hong Kong: Hong Kong University of Science and Technology
  • Norway: University of Bergen
  • USA: University of California Los Angeles, Florida State University, Ohio State University, Rice University, and University of Maryland


  • January 2018: first public version of ACTIVmap website
  • June 2017: added teaching section
  • October 2016: creation of this web site
  • March 2016:
    • First weekly meetings
    • Video describing the research topics, produced by Innovergne