Geometric Gaussian Mixture Learning of Manifolds

Forschungsthema/Bereich

Artificial Intelligence, Machine Learning, Computational Mathematic

Typ der Abschlussarbeit

Bachelor / Master

Startzeitpunkt

-

Bewerbungsschluss

30.06.2028

Dauer der Arbeit

4 months(BSc) - 6 months(MSc)

Beschreibung

Preface

Sometimes you need a probabilistic representation of a deterministic manifold and for many reasons having them in Gaussian Mixtures is useful. Gaussian mixtures are fitted to data using expectation maximization. The algorithm is not guaranteed to converge to the optimum, is data hungry and quite slow.

Problem

Is it possible to have a Gaussian Mixture representation for a manifold without sampling and coupling it with an expectation maximization step?

Voraussetzung

Voraussetzungen an Studierende

• * Firm grasp over Linear/Multilinear Algebra and Analysis
• * PyTorch or an equivalent NumPy-like framework
• * Some exposition to Functional Analysis and Differential Geometry is advantageous

Studiengangsbereiche

• Ingenieurwissenschaften
  Informatik
  Mechanical Engineering
  Remote Sensing and Geoinformatics
  Information System Engineering and Management
  Computer Science
  Electrical Engineering and Information Technology
  Mechatronics and Information Technology
• Naturwissenschaften und Technik
  Mathematik
  Physik
  Technomathematik
  Computational and Data Sience
  Geophysics
  Wirtschaftsmathematik

Betreuung

Titel, Vorname, Name

Ali Darijani

Organisationseinheit

* Computer Science(IAR/IES) * Fraunhofer IOSB

E-Mail Adresse

ali.darijani@iosb.fraunhofer.de

Link zur eigenen Homepage/Personenseite

Website

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Senden Sie die oben genannten Bewerbungsunterlagen bitte per Mail an ali.darijani@iosb.fraunhofer.de


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