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Medium noise of perpendicular double layer media is investigated in conjunction with transition irregularity. The noise is typically proportional to the square root of linear density, but it saturates at a particular density. This nonlinear noise behavior is explained by clusters consisting of several grains becoming minimum magnetic units. A simulation with a media model using Voronoi cells is carried out based on this result; it also gives good agreement with experimental results. Measured partial erasure quantitatively corresponds to the noise saturation. Clustering and partial erasure both suggest transition percolation; however, no supra-linear noise increase is usually observed. Noise characteristics in terms of percolation density suggest grain-clustering in perpendicular media.