论文标题
低级近似值的随机四基因奇异值分解
Randomized Quaternion Singular Value Decomposition for Low-Rank Approximation
论文作者
论文摘要
本文提出了一个随机的四元素奇异值分解（QSVD）算法，用于低级矩阵近似问题，该算法被广泛用于颜色面部识别，视频压缩和信号处理问题中。通过基于四元正态分布的随机抽样，随机QSVD算法将高维数据投射到低维子空间，然后识别Quaternion矩阵的近似范围子空间。提出了四元基金Wishart分布的关键统计特性，并用于执行算法的近似误差分析。理论结果表明，随机QSVD算法可以以可接受的精度追踪四元矩阵的显性奇异值分解三联体。数值实验还表明了提出的理论的合理性。随机QSVD算法应用于颜色的面部识别问题，获得了更高的识别精度，并且比已知的基于Lanczos的部分QSVD和快速频繁方向算法的Quaternion版本更有效。
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.
