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

A Robust and Efficient Boundary Point Detection Method by Measuring Local Direction Dispersion