Neural network models for the quaternion singular value decompositions

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.