聚类分析研究中的若干问题 Page 1 第27 卷第3 期 Vol. 27 No. 3 控制与决策 Control and
Decision 2012 年3 月 Mar. 2012 聚类分析研究中的若干问题 文章编号: 1001-0920 (2012) 03-0321-08 …

Standard SVM training has O (m3) time and O (m2) space complexities, where m is the
training set size. It is thus computationally infeasible on very large data sets. By observing …

In this paper, we show the existence of small coresets for the problems of computing k-
median and k-means clustering for points in low dimension. In other words, we show that …

In this manuscript, we offer a gentle review of submodularity and supermodularity and their
properties. We offer a plethora of submodular definitions; a full description of a number of …

The paradigm of coresets has recently emerged as a powerful tool for efficiently
approximating various extent measures of a point set P. Using this paradigm, one quickly …

The problem of maximizing a concave function f (x) in the unit simplex Δ can be solved
approximately by a simple greedy algorithm. For given k, the algorithm can find a point x (k) …

Geometric data summarization has become an essential tool in both geometric
approximation algorithms and where geometry intersects with big data problems. In linear or …

In optimization or machine learning problems we are given a set of items, usually points in
some metric space, and the goal is to minimize or maximize an objective function over some …

We present new approximation algorithms for the k-median and k-means clustering
problems. To this end, we obtain small coresets for k-median and k-means clustering in …

In this paper, we consider the problem of finding high dimensional power means: given a set
$ A $ of $ n $ points in $\R^ d $, find the point $ m $ that minimizes the sum of Euclidean …