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Subspace clustering aims to find all clusters in all subspaces of a high-dimensional data space. We present a massively data-parallel approach that can be run on graphics processing units. It extends a previous density-based method that scales well with the number of dimensions. Its main computational bottleneck consists of (sequentially) generating a large number of minimal cluster candidates in each dimension and using hash collisions in order to find matches of such candidates across multiple dimensions. Our approach parallelizes this process by removing previous interdependencies between consecutive steps in the sequential generation process and by applying a very efficient parallel hashing scheme optimized for GPUs. This massive parallelization gives up to 70x speedup for
the bottleneck computation when it is replaced by our approach and run on current GPU hardware. We note that depending on data size and choice of parameters, the parallelized part of the algorithm can take different percentages of the overall runtime of the clustering process, and thus, the overall clustering speedup may vary significantly between different cases. However, even
in our ”worst-case” test, a small dataset where the computation makes up only a small fraction of the overall clustering time, our parallel approach still yields a speedup of more than 3x for the complete run of the clustering process. Our method could also be combined with parallelization of other parts of the clustering algorithm, with an even higher potential gain in processing speed.
Finding clusters in high dimensional data is a challenging research problem. Subspace clustering algorithms aim to find clusters in all possible subspaces of the dataset, where a subspace is a subset of dimensions of the data. But the exponential increase in the number of subspaces with the dimensionality of data renders most of the algorithms inefficient as well as ineffective. Moreover, these algorithms have ingrained data dependency in the clustering process, which means that parallelization becomes difficult and inefficient. SUBSCALE is a recent subspace clustering algorithm which is scalable with the dimensions and contains independent processing steps which can be exploited through parallelism. In this paper, we aim to leverage the computational power of widely available multi-core processors to improve the runtime performance of the SUBSCALE algorithm. The experimental evaluation shows linear speedup. Moreover, we develop an approach using graphics processing units (GPUs) for fine-grained data parallelism to accelerate the computation further. First tests of the GPU implementation show very promising results.