  Clustering analysis identifies samples as groups based on either their mutual
closeness or homogeneity. In order to detect clusters in arbitrary shapes, a
novel and generic solution based on boundary erosion is proposed. The clusters
are assumed to be separated by relatively sparse regions. The samples are
eroded sequentially according to their dynamic boundary densities. The erosion
starts from low density regions, invading inwards, until all the samples are
eroded out. By this manner, boundaries between different clusters become more
and more apparent. It therefore offers a natural and powerful way to separate
the clusters when the boundaries between them are hard to be drawn at once.
With the sequential order of being eroded, the sequential boundary levels are
produced, following which the clusters in arbitrary shapes are automatically
reconstructed. As demonstrated across various clustering tasks, it is able to
outperform most of the state-of-the-art algorithms and its performance is
nearly perfect in some scenarios.
