A density-sensitive hierarchical clustering method

We define a hierarchical clustering method: $\alpha$-unchaining single linkage or $SL(\alpha)$. The input of this algorithm is a finite metric space and a certain parameter $\alpha$. 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, $SL^*(\alpha)$, 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.