Fast Scalable k-means++ Algorithm with MapReduce

摘要

K-means++ is undoubtedly one of the most important initializing algorithms for k-means owing to its provable approximation guarantee to the optimal solution. However, due to its sequential nature, k-means++ requires a large number of iterations to complete the initialization and it becomes inefficient as the size of data increase. Even though scalable k-means++ can drastically reduce the iterations and can be easily applied to the MapReduce systems, but due to its sequential nature, it still requires two MapReduce jobs in each round. Moreover, it takes a large number of I/O cost and it is time-consuming. In this paper, we propose Oversampling and Refining (OnR) method which can improve efficiency of scalable k-means++ by using only one MapReduce job to obtain　Ω(k) centers in each round. Except for the oversampling factor £ of scalable k-means++, OnR uses another oversampling factor o to further increase the number of chosen centers. Oversampling is executed on the Mapper phase, and in Reducer phase, one Reducer is responsible for removing the oversampled centers generated from o and outputs a set of centers which is the same as the output of scalable k-means++. To reduce the expensive network cost caused by too large o, OnR estimates the global cost by the local clustering cost and uses it to remove some wrong points in Mapper phase. Extensive experiments on real data are conducted and the performance results indicate that OnR outperforms scalable k-means++ in the aspect of I/O cost and running time.