论文标题
混合DEIM和利用基于CUR指数选择的方法
A hybrid DEIM and leverage scores based method for CUR index selection
论文作者
论文摘要
离散的经验插值方法（DEIM）可用作制定验证分解的指数选择策略。原始DEIM算法的一个显着缺点是可以选择的列或行索引数量仅限于输入单数矢量的数量。我们提出了一种新的Deim变体，我们称之为L-Deim，这是确定性杠杆分数和Deim强度的组合。此方法允许选择大于可用单数矢量数量的许多索引。由于Deim需要单数向量作为输入矩阵，因此L-Deim在计算排名$ K $ -SVD近似值时在大数据问题中特别有吸引力，即使对于中等小$ k $，由于使用较低的SVD近似值，而不是全等级$ K $ SVD。我们从经验上证明了L-DEIM的性能，尽管它的效率可能与原始Deim相当，甚至比某些最先进的方法获得了可比的结果。
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.
