Multidimensional Balance-Based Cluster Boundary Detection for High-Dimensional Data

The balance of neighborhood space around a central point is an important concept in cluster analysis. It can be used to effectively detect cluster boundary objects. The existing neighborhood analysis methods focus on the distribution of data, i.e., analyzing the characteristic of the neighborhood space from a single perspective, and could not obtain rich data characteristics. In this paper, we analyze the high-dimensional neighborhood space from multiple perspectives. By simulating each dimension of a data point's k nearest neighbors space (kNNs) as a lever, we apply the lever principle to compute the balance fulcrum of each dimension after proving its inevitability and uniqueness. Then, we model the distance between the projected coordinate of the data point and the balance fulcrum on each dimension and construct the DHBlan coefficient to measure the balance of the neighborhood space. Based on this theoretical model, we propose a simple yet effective cluster boundary detection algorithm called Lever. Experiments on both low- and high-dimensional data sets validate the effectiveness and efficiency of our proposed algorithm.