Neural network models for the quaternion singular value decompositions
APPLIED MATHEMATICAL MODELLING(2024)
Abstract
We develop two neural network models for computing the quaternion singular value decomposition (QSVD), which can be shown to arise as gradient flows or Riemannian-gradient flows on the product of Stiefel manifold over the quaternion skew-field and their geometric and dynamical properties are investigated. Numerical experiments including color image compression indicate the feasibility and effectiveness of the proposed neural network models.
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Key words
Quaternion singular value decomposition,Quaternion neutral network,Asymptotic stability,Stiefel manifold
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