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# 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, both from a methodological and an applicative point of view. The staff has interdisciplinary skills, and the projects developed in the group cover a wide range of scientific topics, at the boundaries of Computer Science and Geometry, Data Mining and Machine Learning, or data structures and applications.

Our research field include:

**Machine Learning**: several aspects are addressed, 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, dealing with indefinite kernels or large datasets.

* **Clustering methods**, using 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**, strongly related with many other topics going from geometry of numbers to computational geometry, discrete geometry, combinatorics or inverse problems. For instance, we are especially interested nowadays in questions of separability from a lattice set and its complementary on the grid.

* **Computational geometry** and geometric approximation, where we 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). Current works include the search of dramatic improvements to the complexity of several approximation problems such as polytope membership, nearest neighbor searching, epsilon-kernel, and diameter of a point set, using a hierarchy of Macbeath regions

* **Image and Video Processing**, addressed from both a methodological (definition of image analysis methods in nD) and applicative points of view (tracking of ballistics in thermal videos of volcanoes, design of computer assisted maps for visually impaired people,…)

International collaborations include Hong Kong University of Science and Technology (Hong Kong), University of Bergen (Norway), UCLA, FSU, OSU, Houston Rice and Maryland Universities (USA) Murdoch University and CSIRO (Australia), UCL and the Royal Observatory of Belgium (Belgium) or UDESC (Brazil). Among all national partners are LITIS (Rouen), LMV (Clermont-Ferrand) and Creatis (Lyon) labs.

## News

**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