Boundary points pose a significant challenge for machine learning tasks, including classification, clustering, and dimensionality reduction. Due to the similarity of features, boundary areas can result in mixed-up classes or clusters, leading to a crowding problem in dimensionality reduction. To address this challenge, numerous boundary point detection methods have been developed, but they are insufficiently to accurately and efficiently identify the boundary points in non-convex structures and high-dimensional manifolds. In this work, we propose a robust and efficient method for detecting boundary points using Local Direction Dispersion (LoDD). LoDD considers that internal points are surrounded by neighboring points in all directions, while neighboring points of a boundary point tend to be distributed only in a certain directional range. LoDD adopts a density-independent K-Nearest Neighbors (KNN) method to determine neighboring points, and defines a statistic-based metric using the eigenvalues of the covariance matrix of KNN coordinates to measure the centrality of a query point. We demonstrated the validity of LoDD on five synthetic datasets (2-D and 3-D) and ten real-world benchmarks, and tested its clustering performance by equipping with two typical clustering methods, K-means and Ncut. Our results show that LoDD achieves promising and robust detection accuracy in a time-efficient manner.

提出了一种使用本地方向分散 (LoDD) 方法来检测边界点的鲁棒且高效的方法，该方法在非凸结构和高维流形中能够准确地识别边界点，并在多个数据集上展示了良好的聚类性能。

通过测量局部方向离散度的方法实现鲁棒高效的边界点检测