Performance of Johnson-Lindenstrauss transform for k-means and k-medians clustering
Performance of Johnson-Lindenstrauss transform for k-means and k-medians clustering
复制标题
DOI：
10.1145/3313276.3316350
复制
发表时间：
2018-11
期刊：
影响因子：
--
通讯作者：
K. Makarychev;Yury Makarychev;Ilya P. Razenshteyn
中科院分区：
文献类型：
--
作者：
K. Makarychev;Yury Makarychev;Ilya P. Razenshteyn
考虑一个欧几里得k均值或K-Medians聚类的实例。 ε2） - 更一般而言（1+ε），我们的成本保留了，我们的结果适用于任何尺寸降低。最佳的。此外，我们的结果适用于欧几里得k群集，对于k均值的任何常数p，我们的p-th功率提高了，我们的结果解决了科恩，老年，穆斯科，穆斯科和persu（stoc）（stoc）（stoc） 2015年）；对于K-Medians，它回答了Kannan提出的一个问题。
Consider an instance of Euclidean k-means or k-medians clustering. We show that the cost of the optimal solution is preserved up to a factor of (1+ε) under a projection onto a random O(log(k /ε) / ε2)-dimensional subspace. Further, the cost of every clustering is preserved within (1+ε). More generally, our result applies to any dimension reduction map satisfying a mild sub-Gaussian-tail condition. Our bound on the dimension is nearly optimal. Additionally, our result applies to Euclidean k-clustering with the distances raised to the p-th power for any constant p. For k-means, our result resolves an open problem posed by Cohen, Elder, Musco, Musco, and Persu (STOC 2015); for k-medians, it answers a question raised by Kannan.