Density peak clustering using global and local consistency adjustable manifold distance

•The method applied a novel manifold distance to calculate local densities of DPC.•The used distance possesses global and local consistency adjustable characteristics.•The improved DPC is suitable for both manifold and Gaussian-like distributed clusters.•The method uses a compensation strategy for clusters with different density and size.•The method provides a feasible parameter tuning strategy and outperforms other ones.