  Agglomerative hierarchical clustering (AHC) is one of the popular clustering
approaches. Existing AHC methods, which are based on a distance measure, have
one key issue: it has difficulty in identifying adjacent clusters with varied
densities, regardless of the cluster extraction methods applied on the
resultant dendrogram. In this paper, we identify the root cause of this issue
and show that the use of a data-dependent kernel (instead of distance or
existing kernel) provides an effective means to address it. We analyse the
condition under which existing AHC methods fail to extract clusters
effectively; and the reason why the data-dependent kernel is an effective
remedy. This leads to a new approach to kernerlise existing hierarchical
clustering algorithms such as existing traditional AHC algorithms, HDBSCAN, GDL
and PHA. In each of these algorithms, our empirical evaluation shows that a
recently introduced Isolation Kernel produces a higher quality or purer
dendrogram than distance, Gaussian Kernel and adaptive Gaussian Kernel.
