  This paper presents a randomized quaternion singular value decomposition
(QSVD) algorithm for low-rank matrix approximation problems, which are widely
used in color face recognition, video compression, and signal processing
problems. With quaternion normal distribution based random sampling, the
randomized QSVD algorithm projects a high-dimensional data to a low-dimensional
subspace and then identifies an approximate range subspace of the quaternion
matrix. The key statistical properties of quaternion Wishart distribution are
proposed and used to perform the approximation error analysis of the algorithm.
Theoretical results show that the randomized QSVD algorithm can trace dominant
singular value decomposition triplets of a quaternion matrix with acceptable
accuracy. Numerical experiments also indicate the rationality of proposed
theories. Applied to color face recognition problems, the randomized QSVD
algorithm obtains higher recognition accuracies and behaves more efficient than
the known Lanczos-based partial QSVD and a quaternion version of fast frequent
directions algorithm.
