大规模网络聚集数据分析的分布式增量SVD算法
A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks
摘要：
在本文中，我们证明了一个矩阵的SVD可以有效地构造在一个分层的方法。证明了在输入矩阵$A$的秩已知的情况下，该算法可以恢复奇异值和左奇异向量。此外，分层算法可以用于恢复具有有界误差的$d$最大奇异值和左奇异向量。我们还表明，所提出的方法是稳定的，相对于roundancial错误或腐败的原始矩阵条目。数值实验验证了所提出的算法和并行费用分析。
英文摘要：
In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix $A$ is known. Further, the hierarchical algorithm can be used to recover the $d$ largest singular values and left singular vectors with bounded error. We also show that the proposed method is stable with respect to roundoff errors or corruption of the original matrix entries. Numerical experiments validate the proposed algorithms and parallel cost analysis.
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