k-means-u* 算法：非局部跳转和贪婪重试改进了k-means++聚类
The k-means-u* algorithm: non-local jumps and greedy retries improve k-means++ clustering
摘要：
我们提出了一种新的聚类算法，称为k-means-u*，在许多情况下是能够显着提高聚类发现的k-means++，目前的事实标准聚类在欧几里得空间。首先，我们介绍了k-means-u算法，它从k-means++的结果开始，并试图通过标准k-means的运行交替的非局部“跳跃”序列来改进它。每次跳跃都将“最无用”的中心转移到具有最大局部误差的中心，偏移一个小的随机向量。只要误差减小，这就继续下去，并且通常会导致改进的解决方案。偶尔k-means-u会终止，尽管存在明显的剩余优化可能性。通过允许最后一次跳转的重试次数有限，通常可以达到更好的局部最小值。由此产生的算法称为k-means-u*，并且优于k-means++ wrt。解决方案的质量，这是经验证明使用各种数据集。通过构造，为k-means++建立的对数质量界也适用于k-means-u*。
英文摘要：
We present a new clustering algorithm called k-means-u* which in many cases is able to significantly improve the clusterings found by k-means++, the current de-facto standard for clustering in Euclidean spaces. First we introduce the k-means-u algorithm which starts from a result of k-means++ and attempts to improve it with a sequence of non-local "jumps" alternated by runs of standard k-means. Each jump transfers the "least useful" center towards the center with the largest local error, offset by a small random vector. This is continued as long as the error decreases and often leads to an improved solution. Occasionally k-means-u terminates despite obvious remaining optimization possibilities. By allowing a limited number of retries for the last jump it is frequently possible to reach better local minima. The resulting algorithm is called k-means-u* and dominates k-means++ wrt. solution quality which is demonstrated empirically using various data sets. By construction the logarithmic quality bound established for k-means++ holds for k-means-u* as well.
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。
