densitypeaks

Density peaks clustering, sometimes referred to as density peaks, is a clustering method introduced by Alex Rodriguez and Alessandro Laio in 2014. It identifies cluster centers as local maxima of data-point density that are also far from any point of higher density. Each data point is assigned two values: rho, a local density measure, and delta, the distance to the nearest point with higher density. By jointly considering rho and delta, cluster centers appear as points with high density and large separation.

To compute rho, a distance threshold or kernel is used. A common definition is the number of neighbors within a cutoff distance d_c, or a weighted sum of neighbors via exp(-(dist_ij/d_c)^2). Delta is defined as the minimum distance from a point to any other point with higher rho; for the point with the highest rho, delta is set to the maximum distance to any other point. Clusters are formed by designating as centers the points with large rho and delta, either through a manual threshold or via a decision graph of delta versus rho.

Once centers are identified, remaining points are assigned to the cluster of their nearest neighbor with higher density, effectively following the density gradient to a center. The method can detect clusters of arbitrary shapes and varying sizes and typically requires relatively few parameters.

Limitations include sensitivity to the chosen density definition and the cutoff parameter, as well as potential difficulty when density peaks are not well separated. The approach has quadratic computational cost in the number of points unless optimized. It has been applied in fields such as image segmentation, genomics, astronomy, and pattern recognition.

See also: clustering; density-based clustering; Rodriguez and Laio, 2014, Clustering by fast search and find of density peaks.