基于DEIM和杠杆分数的混合CUR指数选择方法
A hybrid DEIM and leverage scores based method for CUR index selection
摘要：
离散经验插值方法（DEIM）可以用作用于制定CUR因子分解的索引选择策略。原始DEIM算法的一个显著缺点是，可以选择的列或行索引的数量限于输入奇异向量的数量。我们提出了一种新的DEIM变体，我们称之为L-DEIM，结合了确定性杠杆分数和DEIM的强度。该方法允许选择数量大于可用奇异向量的数量的索引。由于DEIM需要奇异向量作为输入矩阵，因此L-DEIM例如在计算秩- $k$ -SVD近似时的大数据问题中特别有吸引力，即使对于适度小的$k$，SVD近似也是昂贵的，因为它使用较低秩SVD近似而不是满秩- $k$ SVD。我们经验证明的L-DEIM，尽管它的效率，可能会达到可比的结果，原来的DEIM，甚至更好的近似比一些国家的最先进的方法的性能。
英文摘要：
The discrete empirical interpolation method (DEIM) may be used as an index selection strategy for formulating a CUR factorization. A notable drawback of the original DEIM algorithm is that the number of column or row indices that can be selected is limited to the number of input singular vectors. We propose a new variant of DEIM, which we call L-DEIM, a combination of the strength of deterministic leverage scores and DEIM. This method allows for the selection of a number of indices greater than the number of available singular vectors. Since DEIM requires singular vectors as input matrices, L-DEIM is particularly attractive for example in big data problems when computing a rank-$k$-SVD approximation is expensive even for moderately small $k$ since it uses a lower-rank SVD approximation instead of the full rank-$k$ SVD. We empirically demonstrate the performance of L-DEIM, which despite its efficiency, may achieve comparable results to the original DEIM and even better approximations than some state-of-the-art methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
