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A novel clustering algorithm named local reachability density peaks clustering (LRDPC) which uses local reachability density to improve the performance of the density peaks clustering algorithm (DPC) is proposed in this paper. This algorithm enhances robustness by removing the cutoff distance dc which is a sensitive parameter from the DPC. In addition, a new allocation strategy is developed to eliminate the domino effect, which often occurs in DPC. The experimental results confirm that this algorithm is feasible and effective.