Hierarchical Density Estimates for Data Clustering, Visualization, and Outlier Detection

Abstract

An integrated framework for density-based cluster analysis, outlier detection, and data visualization is introduced in this article. The main module consists of an algorithm to compute hierarchical estimates of the level sets of a density, following Hartigan's classic model of density-contour clusters and trees. Such an algorithm generalizes and improves existing density-based clustering techniques with respect to different aspects. It provides as a result a complete clustering hierarchy composed of all possible density-based clusters following the nonparametric model adopted, for an infinite range of density thresholds. The resulting hierarchy can be easily processed so as to provide multiple ways for data visualization and exploration. It can also be further postprocessed so that: (i) a normalized score of "outlierness" can be assigned to each data object, which unifies both the global and local perspectives of outliers into a single definition; and (ii) a "flat" (i.e., nonhierarchical) clustering solution composed of clusters extracted from local cuts through the cluster tree (possibly corresponding to different density thresholds) can be obtained, either in an unsupervised or in a semisupervised way. In the unsupervised scenario, the algorithm corresponding to this postprocessing module provides a global, optimal solution to the formal problem of maximizing the overall stability of the extracted clusters. If partially labeled objects or instance-level constraints are provided by the user, the algorithm can solve the problem by considering both constraints violations/satisfactions and cluster stability criteria. An asymptotic complexity analysis, both in terms of running time and memory space, is described. Experiments are reported that involve a variety of synthetic and real datasets, including comparisons with state-of-the-art, density-based clustering and (global and local) outlier detection methods.

hdbscan: Hierarchical density based clustering

“…HDBSCAN: Hierarchical Density-Based Spatial Clustering of Applications with Noise (Campello, Moulavi, and Sander 2013), (Campello et al 2015). Performs DBSCAN over varying epsilon values and integrates the result to find a clustering that gives the best stability over epsilon.…”

“…This allows HDBSCAN to find clusters of varying densities (unlike DBSCAN), and be more robust to parameter selection. The library also includes support for Robust Single Linkage clustering (Chaudhuri et al 2014), (Chaudhuri and Dasgupta 2010), GLOSH outlier detection (Campello et al 2015), and tools for visualizing and exploring cluster structures. Finally support for prediction and soft clustering is also available.…”

Efficient Computation of Multiple Density-Based Clustering Hierarchies

“…The authors of HDBSCAN* [5], [6] deem G mpts a conceptual graph as it does not need to be explicitly stored; edge weights can be computed on demand, when needed.…”

“…It generalizes and improves several aspects of previous algorithms, and allows for a comprehensive framework for cluster analysis, visualization, and unsupervised outlier detection [6]. It requires a single parameter mpts, a smoothing factor that can implicitly influence which clusters are detectable in the cluster hierarchy.…”

“…Density-based clustering, in particular, is a popular clustering paradigm that defines clusters as high-density regions in the data space, separated by lowdensity regions. Algorithms in this class, such as DBSCAN [10], DENCLUE [14], OPTICS [2] and HDBSCAN* [6], stand out for their ability to find clusters of arbitrary shapes and to differentiate between cluster points and noise.…”