  In this paper, we propose a physically inspired graph-theoretical clustering
method, which first makes the data points organized into an attractive graph,
called In-Tree, via a physically inspired rule, called Nearest Descent (ND). In
particular, the rule of ND works to select the nearest node in the descending
direction of potential as the parent node of each node, which is in essence
different from the classical Gradient Descent or Steepest Descent. The
constructed In-Tree proves a very good candidate for clustering due to its
particular features and properties. In the In-Tree, the original clustering
problem is reduced to a problem of removing a very few of undesired edges from
this graph. Pleasingly, the undesired edges in In-Tree are so distinguishable
that they can be easily determined in either automatic or interactive way,
which is in stark contrast to the cases in the widely used Minimal Spanning
Tree and k-nearest-neighbor graph. The cluster number in the proposed method
can be easily determined based on some intermediate plots, and the cluster
assignment for each node is easily made by quickly searching its root node in
each sub-graph (also an In-Tree). The proposed method is extensively evaluated
on both synthetic and real-world datasets. Overall, the proposed clustering
method is a density-based one, but shows significant differences and advantages
in comparison to the traditional ones. The proposed method is simple yet
efficient and reliable, and is applicable to various datasets with diverse
shapes, attributes and any high dimensionality
