ADR Awareness Centre

The technical report presents popular methods for mapping data into a low-dimensional manifold (nonlinear dimensionality reduction).

The conference paper gives in the first section a brief and easy understandable introduction into the basics of Riemannian geometry.

The technical report gives a compact introduction into the basic definitions and theorems of Riemannian geometry, Lie groups & Lie algebras and symmetric spaces.

The conference paper provides a brief introduction into manifolds from a computer vision perspective. Important manifolds for this research field, like symmetric positive definite matrices and affine transformation matrices, are presented.

This book provides an introduction to the theory of manifolds in an easy readable way. Key concepts of manifolds, angent spaces and Lie group / Lie algebra are presented.

Recent progress in the Computer Vision and Natural Language Processing communities have made it possible to connect Vision and Language together in a variety of different tasks which lie at the intersection of Vision, Language, and Embodied AI.