DBSCAN is a fundamental spatial clustering algorithm with numerous practical applications. However, bottleneck of its O(n2) worst-case time complexity. To address this limitation, we propose new grid-based for exact in Euclidean space called GriT-DBSCAN, which based on the following two techniques. First, introduce grid tree to organize non-empty grids purpose efficient neighboring queries. Sec...

Terrestrial laser scanning (TLS) can provide accurate and detailed three-dimensional (3D) structure information of the forest understory. Segmenting individual trees from disordered, discrete, high-density TLS point clouds is premise for obtaining tree parameters understory, pest control fine modeling. In this study, we propose a bottom-up method to segment data based on density-based spatial c...

We show that DBSCAN can estimate the connected components of the λ-density level set {x : f(x) ≥ λ} given n i.i.d. samples from an unknown density f . We characterize the regularity of the level set boundaries using parameter β > 0 and analyze the estimation error under the Hausdorff metric. When the data lies in R we obtain a rate of Õ(n−1/(2β+D)), which matches known lower bounds up to logari...

In this contribution we provide an application of the technique of F–transform. We demonstrate that by using a simple density-based preprocessing, the applicability of F–transform in data analysis can be significantly improved. Despite of the fact that our procedure is demonstrated by a well-known DBSCAN algorithm and the technique of F–transform, the ideas are general enough to be applied for ...