Post-Doctoral Position On “New Approach Beyond Riemannian Geometry For Machine Learning Algorithms...

Universities and Institutes of France

France

July 22, 2022

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
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