Description
Organisation/Company: Université Grenoble Alpes
Research Field: Mathematics › Applied mathematics
Researcher Profile: Recognised Researcher (R2) Leading Researcher
(R4)
Application Deadline: 22/07/2022 21:00 - Europe/Athens
Location: France › Saint Martin d'Hères
Type Of Contract: Temporary
Job Status: Full-time
Hours Per Week: 35
Offer Starting Date: 01/10/2022
The recruited person will conduct research in the field of geometric machine
learning. Efficiently dealing with high-dimensional data is currently a major
issue in many applications of machine learning. The AMELIORATE project aims at
contributing to solve this problem by exploiting the structures and geometric
properties that might be contained in the data. Indeed, in many cases, data
actually belong to a lower dimensional subspace (often a manifold) of the
global ambient space. The geometrical structure can be leveraged to achieve
machine learning tasks. In recent works, such a geometrical machine learning
approach has obtained competitive results in various applications – e.g.,
electroencephalography, hyperspectral, computer vision.
This success relies on employing a well-chosen Riemannian geometry – in
particular, the resulting Riemannian distance. However, the Riemannian
distance can only be found for a small number of manifolds – mainly for
covariance matrices and subspaces. This drastically limits the potential
applications of this approach. For instance, the Riemannian distance on the
Stiefel manifold – rectangular orthogonal matrices – is unknown. It is quite
unfortunate as it is encountered in many situations. The objective of the
AMELIORATE project is to overcome this issue and propose efficient geometrical
machine learning algorithms, especially on the Stiefel manifold. To do so, we
will provide original solutions based on new objects beyond Riemannian
geometry.
Three different tasks will be considered in the project. The first one will
consist in studying a new alternative geometry fot the Stiefel manifold, and
propose the associated Fréchet mean. This will allow us to develop well-
adapted machine learning methods on this manifold. The second task will focus
on extending R-barycenters' theory based on divergences.
The corresponding obtained means will be studied and resulting geometrical
machine learning algorithms will be obtained and tested. The third task will
explore higher order approximations of the Riemannian exponential and
logarithm, the connected metric and resulting Fréchet mean and machine
learning algorithms. The classification/clustering algorithms to be developped
in the AMELIORATE project will be tested and validated on simulated datasets.
Application to real dataset could be considered but may be a long term
perspective. Great care will be taken to make avalaible to the community the
developed algorithms by mean of a toolbox.
Main activities :
- scientific research (reading, reflexion, discussions and interactions with
colleagues)
- Visit labs of the research collaboration
- Coding (algorithms to be tested on simulated datasets)
- Writing scientific articles (journals and conferences)
- Attend seminars, workshop and conferences
Offer Requirements
REQUIRED EDUCATION LEVEL
Mathematics: PhD or equivalent
Skills/Qualifications
Solid background in mathematics (differential geometry, probability and
statistics)
Computing/Coding in julia language
Autonomy
Ability to interact and work with other researchers
Spirit of synthesis and fluency in scientific speech
Specific Requirements
PhD in mathematics, probability, statistics or data science.
Experience in the public research domain would be appreciated.
Contact Information
Organisation/Company: Université Grenoble Alpes
Department: MSPRI
Organisation Type: Higher Education Institute
Website: https: // edu.univ-grenoble-alpes.fr/
Country: France
City: Saint-Martin-d'Hères
State/Province: France
Postal Code: 38400
Street: 621 avenue centrale
