矩阵的快速蒙特卡洛低秩近似
Fast Monte-Carlo Low Rank Approximations for Matrices
AI总结：
提出一种蒙特卡洛算法，通过迭代读取O(k)列或行来逼近m×n矩阵的k秩近似，保证每次迭代优于前一次，复杂度为O(kmn)。
摘要：
在许多应用中，需要用至多秩k的矩阵B来近似由m×n矩阵A给出的数据，其中k远小于m和n。最佳近似由奇异值分解给出，但对于非常大的m和n，该方法过于耗时。我们提出一种蒙特卡洛算法，用于迭代计算由m×n矩阵A构成的数据的k秩近似。每次迭代涉及读取A的O(k)列或行。我们算法的复杂度为O(kmn)。与其他已知算法不同，我们的算法保证每次迭代都比前一次迭代得到更好的k秩近似。我们相信该算法将在数据挖掘、数据存储和数据分析中具有许多应用。
英文摘要：
In many applications, it is of interest to approximate data, given by mxn matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time consuming for very large m and n. We present here a Monte Carlo algorithm for iteratively computing a k-rank approximation to the data consisting of mxn matrix A. Each iteration involves the reading of O(k) of columns or rows of A. The complexity of our algorithm is O(kmn). Our algorithm, distinguished from other known algorithms, guarantees that each iteration is a better k-rank approximation than the previous iteration. We believe that this algorithm will have many applications in data mining, data storage and data analysis.
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。
