Related papers: Towards Metric DBSCAN: Exact, Approximate, and Str…
DBSCAN* and HDBSCAN* are well established density based clustering algorithms. However, obtaining the clusters of very large datasets is infeasible, limiting their use in real world applications. By exploiting the geometry of Euclidean…
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…
The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…
Interactive visualization of embedding projections is a useful technique for understanding data and evaluating machine learning models. Labeling data within these visualizations is critical for interpretation, as labels provide an overview…
Recent advancements in neutron and X-ray sources, instrumentation and data collection modes have significantly increased the experimental data size (which could easily contain 10$^{8}$ -- 10$^{10}$ data points), so that conventional…
Clustering is an unsupervised technique for grouping data points by similarity. While explainability methods exist for supervised machine learning, they are not directly applicable to clustering, making it challenging to understand cluster…
Incremental K-means and DBSCAN are two very important and popular clustering techniques for today's large dynamic databases (Data warehouses, WWW and so on) where data are changed at random fashion. The performance of the incremental…
This paper presents new parallel algorithms for generating Euclidean minimum spanning trees and spatial clustering hierarchies (known as HDBSCAN$^*$). Our approach is based on generating a well-separated pair decomposition followed by using…
Density-based clustering algorithms are widely used for discovering clusters in pattern recognition and machine learning since they can deal with non-hyperspherical clusters and are robustness to handle outliers. However, the runtime of…
We consider the $k$-means clustering problem in the dynamic streaming setting, where points from a discrete Euclidean space $\{1, 2, \ldots, \Delta\}^d$ can be dynamically inserted to or deleted from the dataset. For this problem, we…
This paper tries to present a more unified view of clustering, by identifying the relationships between five different clustering algorithms. Some of the results are not new, but they are presented in a cleaner, simpler and more concise…
Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high…
Density-based clustering is the task of discovering high-density regions of entities (clusters) that are separated from each other by contiguous regions of low-density. DBSCAN is, arguably, the most popular density-based clustering…
General Purpose computing on Graphical Processing Units (GPGPU) has resulted in unprecedented levels of speedup over its CPU counterparts, allowing programmers to harness the computational power of GPU shader cores to accelerate other…
Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…
The problem of automatically clustering data is an age old problem. People have created numerous algorithms to tackle this problem. The execution time of any of this algorithm grows with the number of input points and the number of cluster…
We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…
Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, whose number, orientations, and dimensions are all unknown. In practice one may have access to…
In recent years, data streaming has gained prominence due to advances in technologies that enable many applications to generate continuous flows of data. This increases the need to develop algorithms that are able to efficiently process…
This paper studies density-based clustering of point sets. These methods use dense regions of points to detect clusters of arbitrary shapes. In particular, we study variants of density peaks clustering, a popular type of algorithm that has…