论文标题
基于切线空间的流形的快速交替预测
Fast Alternating Projections on Manifolds Based on Tangent Spaces
论文作者
论文摘要
在本文中，我们研究了基于切线空间的非倾向流形的交替预测。主要的动机是，对歧管的投影可能很昂贵。我们建议使用歧管中点的切线空间，以将投影近似于歧管上，以降低计算成本。我们表明，通过基于切线空间的两个非区域歧管上的交替投影生成的序列，线性收敛到两个歧管的相交点，其中收敛点接近最佳解决方案。给出了非负低等级矩阵近似值和低等级图像Quaternion矩阵（颜色图像）近似的数值示例，以证明所提出的方法的性能优于计算时间的经典交替投影方法的性能。
In this paper, we study alternating projections on nontangential manifolds based on the tangent spaces. The main motivation is that the projection of a point onto a manifold can be computational expensive. We propose to use the tangent space of the point in the manifold to approximate the projection onto the manifold in order to reduce the computational cost. We show that the sequence generated by alternating projections on two nontangential manifolds based on tangent spaces, converges linearly to a point in the intersection of the two manifolds where the convergent point is close to the optimal solution. Numerical examples for nonnegative low rank matrix approximation and low rank image quaternion matrix (color image) approximation, are given to demonstrate that the performance of the proposed method is better than that of the classical alternating projection method in terms of computational time.
