Fast k-means algorithm clustering

k-means has recently been recognized as one of the best algorithms for clustering unsupervised data. Since k-means depends mainly on distance calculation between all data points and the centers, the time cost will be high when the size of the dataset is large (for example more than 500millions of points). We propose a two stage algorithm to reduce the time cost of distance calculation for huge datasets. The first stage is a fast distance calculation using only a small portion of the data to produce the best possible location of the centers. The second stage is a slow distance calculation in which the initial centers used are taken from the first stage. The fast and slow stages represent the speed of the movement of the centers. In the slow stage, the whole dataset can be used to get the exact location of the centers. The time cost of the distance calculation for the fast stage is very low due to the small size of the training data chosen. The time cost of the distance calculation for the slow stage is also minimized due to small number of iterations. Different initial locations of the clusters have been used during the test of the proposed algorithms. For large datasets, experiments show that the 2-stage clustering method achieves better speed-up (1-9 times).Comment: 16 pages, Wimo2011; International Journal of Computer Networks & Communications (IJCNC) Vol.3, No.4, July 201

Embed and Conquer: Scalable Embeddings for Kernel k-Means on MapReduce

The kernel $k$-means is an effective method for data clustering which extends the commonly-used $k$-means algorithm to work on a similarity matrix over complex data structures. The kernel $k$-means algorithm is however computationally very complex as it requires the complete data matrix to be calculated and stored. Further, the kernelized nature of the kernel $k$-means algorithm hinders the parallelization of its computations on modern infrastructures for distributed computing. In this paper, we are defining a family of kernel-based low-dimensional embeddings that allows for scaling kernel $k$-means on MapReduce via an efficient and unified parallelization strategy. Afterwards, we propose two methods for low-dimensional embedding that adhere to our definition of the embedding family. Exploiting the proposed parallelization strategy, we present two scalable MapReduce algorithms for kernel $k$-means. We demonstrate the effectiveness and efficiency of the proposed algorithms through an empirical evaluation on benchmark data sets.Comment: Appears in Proceedings of the SIAM International Conference on Data Mining (SDM), 201