Equivalence of Non-Iterative Algorithms for Simultaneous Low Rank Approximations of Matrices

Equivalence of Non-Iterative Algorithms for Simultaneous Low Rank Approximations of Matrices
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DOI：
10.1109/cvpr.2006.112
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发表时间：
2006-06
期刊：
2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06)
影响因子：
--
通讯作者：
K. Inoue;K. Urahama
K. Inoue;K. Urahama
中科院分区：
其他
文献类型：
--
作者：
K. Inoue;K. Urahama

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近年来，一些研究者提出了四种求解矩阵同时低秩逼近的非迭代算法。在本文中，我们证明了这些算法是等价的，因为它们被简化为给定矩阵的行-行和列-列协方差矩阵的特征值问题。此外，我们还展示了非迭代算法与另一种算法之间的关系，该算法被认为是SLRAM的解析算法。实验结果表明，解析算法并不一定能给出SLRAM的最优解。
Recently four non-iterative algorithms for simultaneous low rank approximations of matrices (SLRAM) have been presented by several researchers. In this paper, we show that those algorithms are equivalent to each other because they are reduced to the eigenvalue problems of row-row and column-column covariance matrices of given matrices. Also, we show a relationship between the non-iterative algorithms and another algorithm which is claimed to be an analytical algorithm for the SLRAM. Experimental results show that the analytical algorithm does not necessarily give the optimal solution of the SLRAM.