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Pre-Scaling Anisotropic Orthogonal Procrustes Analysis Based on Gradient Descent over Matrix Manifold

  • Peng ZhangEmail author
  • Zhou Sun
  • Chunbo Fan
  • Yi Ding
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9141)

Abstract

This paper proposes a pre-scaling extension of the Orthogonal Procrustes Analysis (OPA), where anisotropic scaling occurs before rigid motion. We propose an efficient algorithm to solve this problem based on gradient descent method over matrix manifold. We show that the proposed algorithm is monotonically convergent and provide an acceleration procedure. Its performance is validated through a series of numerical simulations.

Keywords

Procrustes analysis Gradient descent Stiefel manifold Pre-scaling 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Data Center, National Disaster Reduction Center of ChinaBeijingPeople’s Republic of China

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