A density-sensitive hierarchical clustering method

We define a hierarchical clustering method: α-unchaining single linkage or SL(α). The input of this algorithm is a finite metric space and a certain parameter α. This method is sensitive to the density of the distribution and offers some solution to the so called chaining effect. We also define a modified version, SL∗(α), to treat the chaining through points or small blocks. We study the theoretical properties of these methods and offer some theoretical background for the treatment of chaining effects.