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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 the subset of dimensions of the data. But 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, thus, 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, firstly, the computational power of widely available multi-core processors to improve the runtime performance of the SUBSCALE algorithm. The experimental evaluation has shown linear speedup. Secondly, we are developing 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.