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

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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.