Clustering via Boundary Erosion
This provides a novel solution for clustering in arbitrary shapes, which is a common challenge in data analysis, though it appears incremental in the broader field of clustering methods.
The paper tackles the problem of detecting clusters of arbitrary shapes by proposing a boundary erosion method that sequentially erodes samples from low-density regions to reveal cluster boundaries, achieving near-perfect performance in some scenarios and outperforming most state-of-the-art algorithms.
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.