We are pleased to invite you to FIL Seminar that will be hold on April, 6.

*When*: April, 2, 3pm-4pm

*Where*: Campus de la Doua (more details TBA)

Name of BBB room: FIL-seminaires

PSW: FILNouveauxArrivants

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Semi-supervised Low-rank Approximations

tensor decomposition, sparse approximations, convex optimization, machine learning

Low-rank approximations are typically unsupervised machine learning problems, that aim at extracting meaningful patterns from tensor dataset. While these methods have countless applications in data science, in many cases a priori knowledge on the patterns to extract is discarded. In the recent years, I have looked at low-rank approximation models that allow some sort of supervision, to incorporate various kind of a priori information. In this talk, after a quick general introduction on semi-supervised low-rank approximations, I will zomm on a recent model called Dictionary-based low-rank approximation, where one looks for patterns that are sparse in a known basis.

**Speaker bio:**

Jérémy Cohen is a CNRS researcher affected to CREATIS, team Myriad since 2022. Before that, he was affected to IRISA, Rennes. He works on low-rank factorizations in data mining, with a strong focus on tensor decompositions, nonnegative matrix factorization, dictionary-based representations, data fusion and numerical optimization. He was previously a post-doctoral researcher at the University of Mons, Belgium. From 2013 to 2016, he was a PhD student under the supervision of Pierre Comon at Gipsa-lab, Grenoble.

He studied at Ecole Centrale de Lyon from 2010 to 2013 with major in Mathematical engineering, with double degrees in Mathematics (bachelor) and Telecommunications (master with INSA Lyon).

He studied at Ecole Centrale de Lyon from 2010 to 2013 with major in Mathematical engineering, with double degrees in Mathematics (bachelor) and Telecommunications (master with INSA Lyon).

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**Talk by: **Théo Pierron (LIRIS)

Graph coloring via automatic discharging

graph coloring, discharging method, automatic proof, linear programming

Graph coloring is one of the most studied problems in graph theory. It originated in the 19th century with a well-known question: are four colors sufficient to color differently regions sharing a same border? About a century later, the question was finally solved by the so-called Four Color Theorem. At the core of its proof is a powerful tool, named the « discharging method », whose major downside is that it often requires lengthy case analyses. For the Four Color Theorem, this analysis is given to a computer for verification. This provided one of the first occurrences of a computer assisted proof.

Nowadays, using computers is more common to obtain some proofs, especially to deal with large verifications. However, it is still quite uncommon for a computer to actively look for a proof. We present here a Linear Programming approach to automatically look for a discharging proof and apply it to make some progress towards Wegner’s conjecture for distance-2 coloring of planar graphs. More precisely, we show that 12 colors are sufficient to color at distance 2 every planar graph with maximum degree 4.

After studying at ENS Rennes, Théo Pierron did a PhD at LaBRI in Bordeaux. He then went to Masaryk University (Brno, CZ) for a one-year postdoc before being hired as associate professor at LIRIS in 2020. His work involves graph theory and algorithmics. Hde is also interested in most areas of discrete mathematics.

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Amaury Habrard, Mathieu Lefort, Hamamache Kheddouci, Jean-Michel Muller