  Previously in 2014, we proposed the Nearest Descent (ND) method, capable of
generating an efficient Graph, called the in-tree (IT). Due to some beautiful
and effective features, this IT structure proves well suited for data
clustering. Although there exist some redundant edges in IT, they usually have
salient features and thus it is not hard to remove them.
  Subsequently, in order to prevent the seemingly redundant edges from
occurring, we proposed the Nearest Neighbor Descent (NND) by adding the
"Neighborhood" constraint on ND. Consequently, clusters automatically emerged,
without the additional requirement of removing the redundant edges. However,
NND proved still not perfect, since it brought in a new yet worse problem, the
"over-partitioning" problem.
  Now, in this paper, we propose a method, called the Hierarchical Nearest
Neighbor Descent (H-NND), which overcomes the over-partitioning problem of NND
via using the hierarchical strategy. Specifically, H-NND uses ND to effectively
merge the over-segmented sub-graphs or clusters that NND produces. Like ND,
H-NND also generates the IT structure, in which the redundant edges once again
appear. This seemingly comes back to the situation that ND faces. However,
compared with ND, the redundant edges in the IT structure generated by H-NND
generally become more salient, thus being much easier and more reliable to be
identified even by the simplest edge-removing method which takes the edge
length as the only measure. In other words, the IT structure constructed by
H-NND becomes more fitted for data clustering. We prove this on several
clustering datasets of varying shapes, dimensions and attributes. Besides,
compared with ND, H-NND generally takes less computation time to construct the
IT data structure for the input data.
