Efficient algorithm for low-rank matrix factorization with missing components and performance comparison of latest algorithms
Efficient algorithm for low-rank matrix factorization with missing components and performance comparison of latest algorithms
复制标题
DOI：
10.1109/iccv.2011.6126324
复制
发表时间：
2011-11
期刊：
影响因子：
--
通讯作者：
Takayuki Okatani;Takahiro Yoshida;K. Deguchi
中科院分区：
文献类型：
--
作者：
Takayuki Okatani;Takahiro Yoshida;K. Deguchi
本文研究了含有缺失分量的低阶矩阵因式分解的数值算法。我们首先提出了一种新的方法，在Wiberg方法中加入了一个阻尼因子来解决这个问题。该方法的特点是抑制了矩阵分解的模糊性，提高了算法的全局收敛能力和局部收敛速度。然后，我们给出了用来解决这个问题的最新方法的实验比较。目前还没有文献报道对最近提出的方法进行全面的比较。在我们的实验中，我们优先评估每种方法的全局收敛性能，即从随机初始值开始，方法达到全局最优的频率和速度。我们的结论是，通过一组基于牛顿族最小化的带阻尼因子的方法可以获得最好的性能，这些方法通过消除两个因式分解矩阵中的任何一个来减少问题。我们的方法属于这一组，对于不同类型的仿射结构，从具有非常高的缺失分量的运动数据中一致地显示出100%的全局收敛速度。
This paper examines numerical algorithms for factorization of a low-rank matrix with missing components. We first propose a new method that incorporates a damping factor into the Wiberg method to solve the problem. The new method is characterized by the way it constrains the ambiguity of the matrix factorization, which helps improve both the global convergence ability and the local convergence speed. We then present experimental comparisons with the latest methods used to solve the problem. No comprehensive comparison of the methods that have been proposed recently has yet been reported in literature. In our experiments, we prioritize the assessment of the global convergence performance of each method, that is, how often and how fast the method can reach the global optimum starting from random initial values. Our conclusion is that top performance is achieved by a group of methods based on Newton-family minimization with damping factor that reduce the problem by eliminating either of the two factored matrices. Our method, which belongs to this group, consistently shows a 100% global convergence rate for different types of affine structure from motion data with a very high population of missing components.