更紧的Sketched Generalized Matrix Approximation界限
Tighter bound of Sketched Generalized Matrix Approximation
AI总结：
本文提出新的Sketching技术，通过减少原始数据矩阵尺寸，开发出更高效的矩阵近似算法，实现了更紧的近似界。
摘要：
广义矩阵近似在许多机器学习问题中起着基础性作用，如CUR分解、核近似和矩阵低秩近似。特别是在处理日益增大的数据集时，更高效的广义矩阵近似算法成为关键研究问题。本文发现新的Sketching技术，以减少原始数据矩阵的尺寸，开发出新的矩阵近似算法。我们的结果推导出比先前工作更紧的近似界：我们获得了(1+ε)的近似比，使用小的Sketched维度，这表明更高效的广义矩阵近似。
英文摘要：
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and larger dataset, more and more efficient generalized matrix approximation algorithems become a crucially important research issue. In this paper, we find new sketching techniques to reduce the size of the original data matrix to develop new matrix approximation algorithms. Our results derive a much tighter bound for the approximation than previous works: we obtain a $(1+ε)$ approximation ratio with small sketched dimensions which implies a more efficient generalized matrix approximation.
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。
