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Exploring matrix manifolds, lie group theory, and their application to learning rotations

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Learning Image Rotations with Lie Groups & Riemannian Geometry

img1

Relevant concepts I explore include:

  • Skew-symmetric matrix manifolds
  • Lie group theory
  • Matrix exponential-based gradient updates in a Riemannian optimization approach
  • The applications to learning rotations

I attempt to implement the following Algorithm 1 in Python - as originally proposed in [1]:

algorithm1

[1]. R. Arora. On learning rotations. In Advances in Neural Information Processing Systems, pages 55–63, 2009.

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Exploring matrix manifolds, lie group theory, and their application to learning rotations

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