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The DBSCAN method for spatial clustering has received significant attention due to its applicability in a variety of data analysis tasks. There are fast sequential algorithms for DBSCAN in Euclidean space that take $O(n\log n)$ work for two…
DBSCAN is a well-known density-based clustering algorithm to discover arbitrary shape clusters. While conceptually simple in serial, the algorithm is challenging to efficiently parallelize on manycore GPU architectures. Common pitfalls,…
DBSCAN is a fundamental spatial clustering algorithm with numerous practical applications. However, a bottleneck of the algorithm is in the worst case, the run time complexity is $O(n^2)$. To address this limitation, we propose a new…
This paper presents \pandora, a novel parallel algorithm for efficiently constructing dendrograms for single-linkage hierarchical clustering, including \hdbscan. Traditional dendrogram construction methods from a minimum spanning tree…
We study the classic Euclidean Minimum Spanning Tree (MST) problem in the Massively Parallel Computation (MPC) model. Given a set $X \subset \mathbb{R}^d$ of $n$ points, the goal is to produce a spanning tree for $X$ with weight within a…
HDBSCAN*, a state-of-the-art density-based hierarchical clustering method, produces a hierarchical organization of clusters in a dataset w.r.t. a parameter mpts. While the performance of HDBSCAN* is robust w.r.t. mpts in the sense that a…
We present a new algorithm for the widely used density-based clustering method DBscan. Our algorithm computes the DBscan-clustering in $O(n\log n)$ time in $\mathbb{R}^2$, irrespective of the scale parameter $\varepsilon$ (and assuming the…
Computing a Single-Linkage Dendrogram (SLD) is a key step in the classic single-linkage hierarchical clustering algorithm. Given an input edge-weighted tree $T$, the SLD of $T$ is a binary dendrogram that summarizes the $n-1$ clusterings…
Clustering is a fundamental task in machine learning. One of the most successful and broadly used algorithms is DBSCAN, a density-based clustering algorithm. DBSCAN requires $\epsilon$-nearest neighbor graphs of the input dataset, which are…
Clustering multidimensional points is a fundamental data mining task, with applications in many fields, such as astronomy, neuroscience, bioinformatics, and computer vision. The goal of clustering algorithms is to group similar objects…
This paper studies the hierarchical clustering problem, where the goal is to produce a dendrogram that represents clusters at varying scales of a data set. We propose the ParChain framework for designing parallel hierarchical agglomerative…
In this paper we present and evaluate a parallel algorithm for solving a minimum spanning tree (MST) problem for supercomputers with distributed memory. The algorithm relies on the relaxation of the message processing order requirement for…
HDBSCAN is a density-based clustering algorithm that constructs a cluster hierarchy tree and then uses a specific stability measure to extract flat clusters from the tree. We show how the application of an additional threshold value can…
We provide efficient constant factor approximation algorithms for the problems of finding a hierarchical clustering of a point set in any metric space, minimizing the sum of minimimum spanning tree lengths within each cluster, and in the…
Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition…
Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) finds meaningful patterns in spatial data by considering density and spatial proximity. As the clustering algorithm is inherently designed for static…
Neuromorphic computing, characterized by its event-driven computation and massive parallelism, is particularly effective for handling data-intensive tasks in low-power environments, such as computing the minimum spanning tree (MST) for…
Minimum Spanning Tree (MST) is an important graph algorithm that has wide ranging applications in the areas of computer networks, VLSI routing, wireless communications among others. Today virtually every computer is built out of multi-core…
Single-linkage clustering is a popular form of hierarchical agglomerative clustering (HAC) where the distance between two clusters is defined as the minimum distance between any pair of points across the two clusters. In single-linkage HAC,…
One of the main challenges for hierarchical clustering is how to appropriately identify the representative points in the lower level of the cluster tree, which are going to be utilized as the roots in the higher level of the cluster tree…