Density-based Clustering Analysis Research Articles

A new local indicator of spatial autocorrelation identifies clusters of high rendaku frequency in Japanese place names

AbstractThe methods of spatial statistics have been successfully applied to the study of linguistic variation, especially for detecting the existence of spatial patterns in the geographical distribution of linguistic features. However, the use of local indicators of spatial autocorrelation for detecting spatial clusters have been limited to continuous variables, and we propose to apply the new method of Anselin and Li (2019) for categorical variables to linguistic data. We illustrate this method with the case of Japanese rendaku, or sequential voicing, whose dialectal variation is still poorly documented. Focusing on regional differences in the frequency of rendaku, we examined the occurrence of rendaku for four lexemes in 4,921 place names from all Japan. A statistical analysis of local spatial association and an unsupervised density-based cluster analysis revealed the existence of two cluster areas of high rendaku frequency centered around Wakayama and Fukushima-Yamagata prefectures. This suggests that rendaku is more frequent in those dialects, and we recommend that further studies in the dialectal variation of rendaku start by looking at those areas.

Comparing Perceptual Effects of Perspectival Convergence in Architectural Images

Abstract This paper examines the correlation between vertical perspectival convergences in architectural images and their perception by monitoring the eye movements of subjects using eye tracking. Participants viewed images of buildings rendered in one of two variants, either with parallel or convergent vertical lines. In order to quantify differences of perception, a number of analyses were conducted, including density-based cluster analysis to determine areas of heightened visual regard, Voronoi subdivision which allowed for comparison of overall fixation areas, comparisons of fixation durations, image preference tests, and verbal comparisons. Eye-tracking recordings were analyzed in the aggregate in order to examine cumulative viewing behaviors. The study found that while differences in viewing behavior were evident within discrete image counterparts and various forms of analyses, perceptual trends regularly converged toward an even balance across testing stimuli. Attentional propensities tended to be guided by image features over the effects of mere perspectival registration.

New Coronae and Stellar Associations Revealed by a Clustering Analysis of the Solar Neighborhood

We present the results of a density-based clustering analysis of the 6D XYZ Galactic positions and UVW-space velocities of nearby (≤200 pc) Gaia Early Data Release 3 stars with radial velocities using HDBSCAN, in opposition to previous studies (Kounkel & Covey 2019; Meingast et al. 2021) that only included positions and tangential velocities. Among the 241 recovered clusters, we identify more than 50 known associations, 32 new candidate stellar streams aged 100 Myr to 3 Gyr, nine extensions of known Theia groups uncovered by Kounkel & Covey, and eight newly recognized coronae around nearby open clusters. Three confirmed exoplanet-hosting stars and three more TESS transiting exoplanet candidates are part of the new groups discovered here, including TOI–1807 and TOI–2076 from Hedges et al. (2021) that were suspected to belong to a yet unidentified moving group. The new groups presented here were not previously recognized because of their older ages, low spatial density, and projection effects that spread out the tangential velocities of their nearby comoving members. Several newly identified structures reach distances within 60 pc of the Sun, providing new grounds for the identification of isolated planetary-mass objects. The nearest member of the newly recognized corona of Volans–Carina is V419 Hya, a known young debris disk star at a distance of 22 pc. This study outlines the importance of further characterization of young associations in the immediate solar neighborhood, which will provide new laboratories for the precise age calibration of nearby stars, exoplanets, and substellar objects.

Accurate Prediction for Protein–Peptide Binding Based on High-Temperature Molecular Dynamics Simulations

The structural characterization of protein-peptide interactions is fundamental to elucidating biological processes and designing peptide drugs. Molecular dynamics (MD) simulations are extensively used to study biomolecular systems. However, simulating the protein-peptide binding process is usually quite expensive. Based on our previous studies, herein, we propose a simple and effective method to predict the binding site and pose of the peptide simultaneously using high-temperature (high-T) MD simulations with the RSFF2C force field. Thousands of binding events (nonspecific or specific) can be sampled during microseconds of high-T MD. From density-based clustering analysis, the structures of all of the 12 complexes (nine with linear peptides and three with cyclic peptides) can be successfully predicted with root-mean-square deviation (RMSD) < 2.5 Å. By directly simulating the process of the ligand binding onto the receptor, our method approaches experimental precision for the first time, significantly surpassing previous protein-peptide docking methods in terms of accuracy.

Massive young stellar objects in the Local Group spiral galaxy M 33 identified using machine learning

ABSTRACT We present a supervised machine learning classification of stellar populations in the Local Group spiral galaxy M 33. The Probabilistic Random Forest (PRF) methodology, previously applied to populations in NGC 6822, utilizes both near and far-IR classification features. It classifies sources into nine target classes: young stellar objects (YSOs), oxygen, and carbon-rich asymptotic giant branch stars, red giant branch, and red super-giant stars, active galactic nuclei, blue stars (e.g. O-, B-, and A-type main sequence stars), Wolf–Rayet stars, and Galactic foreground stars. Across 100 classification runs the PRF classified 162 746 sources with an average estimated accuracy of ∼86 per cent, based on confusion matrices. We identified 4985 YSOs across the disc of M 33, applying a density-based clustering analysis to identify 68 star forming regions (SFRs) primarily in the galaxy’s spiral arms. SFR counterparts to known H ii regions were recovered with ∼91 per cent of SFRs spatially coincident with giant molecular clouds identified in the literature. Using photometric measurements, as well as SFRs in NGC 6822 with an established evolutionary sequence as a benchmark, we employed a novel approach combining ratios of [Hα]/[24 μm] and [250 μm]/[500 μm] to estimate the relative evolutionary status of all M 33 SFRs. Masses were estimated for each YSO ranging from 6–27M⊙. Using these masses, we estimate star formation rates based on direct YSO counts of 0.63M⊙ yr−1 in M 33’s SFRs, 0.79 ± 0.16M⊙ yr−1 in its centre and 1.42 ± 0.16M⊙ yr−1 globally.

An Adaptive Clustering-Based Algorithm for Automatic Path Planning of Heterogeneous UAVs

Due to the high maneuverability and strong adaptability, autonomous unmanned aerial vehicles (UAVs) are of high interest to many civilian and military organizations around the world. Automatic path planning which autonomously finds a good enough path that covers the whole area of interest, is an essential aspect of UAV autonomy. In this study, we focus on the automatic path planning of heterogeneous UAVs with different flight and scan capabilities, and try to present an efficient algorithm to produce appropriate paths for UAVs. First, models of heterogeneous UAVs are built, and the automatic path planning is abstracted as a multi-constraint optimization problem and solved by a linear programming formulation. Then, inspired by the density-based clustering analysis and symbiotic interaction behaviours of organisms, an adaptive clustering-based algorithm with a symbiotic organisms search-based optimization strategy is proposed to efficiently settle the path planning problem and generate feasible paths for heterogeneous UAVs with a view to minimizing the time consumption of the search tasks. Experiments on randomly generated regions are conducted to evaluate the performance of the proposed approach in terms of task completion time, execution time and deviation ratio.

Separation of Spacecraft Noise From Geomagnetic Field Observations Through Density-Based Cluster Analysis and Compressive Sensing.

The use of magnetometers for space exploration is inhibited by magnetic noise generated by spacecraft electrical systems. Mechanical booms are traditionally used to extend magnetometers away from noise sources. If a spacecraft is equipped with multiple magnetometers, signal processing algorithms can be used to compare magnetometer measurements and remove stray magnetic noise signals. We propose the use of density‐based cluster analysis to identify spacecraft noise signals and compressive sensing to separate spacecraft noise from geomagnetic field data. This method assumes no prior knowledge of the number, location, or amplitude of noise signals, but assumes that they have minimal overlapping spectral properties. We demonstrate the validity of this algorithm by separating high latitude magnetic perturbations recorded by the low‐Earth orbiting satellite, SWARM, from noise signals in simulation and in a laboratory experiment using a mock CubeSat apparatus. In the case of more noise sources than magnetometers, this problem is an instance of underdetermined blind source separation (UBSS). This work presents a UBSS signal processing algorithm to remove spacecraft noise and minimize the need for a mechanical boom.

Geospatial analysis of reported activity locations to identify sites for tuberculosis screening

Mobile screening units can help close tuberculosis case detection gaps. Placing screening units where people at high risk for undiagnosed tuberculosis preferentially spend time could make screening more resource-effective. We conducted a case–control study in Lima, Peru to identify locations where people with tuberculosis were more likely to spend time than community controls. We surveyed participants about activity locations over the past 6 months. We used density-based clustering to assess how patient and control activity locations differed, and logistic regression to compare location-based exposures. We included 109 tuberculosis patients and 79 controls. In density-based clustering analysis, the two groups had similar patterns of living locations, but their work locations clustered in distinct areas. Both groups were similarly likely to use public transit, but patients predominantly used buses and were less likely to use rapid transit (adjusted odds ratio [aOR] 0.31, 95% confidence interval [CI] 0.10–0.96) or taxis (aOR 0.42, 95% CI 0.21–0.85). Patients were more likely to have spent time in prison (aOR 11.55, 95% CI 1.48–90.13). Placing mobile screening units at bus terminals serving locations where tuberculosis patients have worked and within and around prisons could help reach people with undiagnosed tuberculosis.

The Mathematical Model of Marine Engine Room Equipment Based on Machine Learning

This study is aimed at reducing the occurrence of oil spill accidents in the engine room of ships and carries out risk prevention for the equipment of the port ships, thereby reducing pollution to the marine ecological environment. Firstly, the concepts and principles of cluster analysis and ship automatic identification system are expounded. Secondly, the data information collected by the ship’s automatic identification system (AIS) is combined with density-based cluster analysis. The accident area and extent at different stages of the ship’s engine room equipment are classified. Finally, cluster analysis is used to evaluate the risk of equipment of the port ship engine room. The results show that there are 43000 ship operation information points in port a, the average operating speed of ships is 9 kilometers, and the fastest operation speed is 16.9 kilometers. In addition, many ship routes in port a need to take risk prevention measures to minimize the impact between ships and reduce the risk of oil leakage in the engine room. The proposed cabin model can easily and quickly analyze the orientation information of the ship and classify all the data into different types according to the surrounding information points. AIS can realize the information transfer between ships and between ship and shore. Information such as the position, speed, and direction of the ship needs to be accurately known to ensure safety at sea. These data need to relate to some terminals and networks to form a maritime monitoring network. The ship AIS based on cluster analysis can cluster the areas where the ship’s speed and direction change significantly in the port area, effectively preventing accidents. Scientific risk prevention measures can effectively reduce the oil leakage risk of ship engine room equipment, improve the working efficiency of marine engines, and provide a strong foundation for the entire marine ecological environment protection.

Single-Pulsed SERS with Density-Based Clustering Analysis.

We developed a new method for obtaining surface-enhanced Raman scattering (SERS) spectra with extremely high sensitivity and spectral resolution. In this method, thousands of SERS spectra are acquired, followed by a data selection procedure based on density-based spatial clustering of applications with noise (DBSCAN). Each spectrum is recorded by exposure to a single nanosecond laser pulse to avoid the effect of time averaging. The reconstructed spectrum consists of the data that belong to the clusters. The method was applied to a crystal violet aqueous solution with a concentration of 10-7 mol/L. The results suggest that several minor Raman peaks were successfully recovered, which cannot be detected in conventional SERS measurements. Moreover, the method is also effective for separately observing Raman peaks that overlap with other neighboring peaks. This method extends the possibilities of SERS and will contribute to future high-resolution spectroscopy in condensed phases.

Information mining of customers preferences for product specifications determination using big sales data

Product competitiveness is highly influenced by its related design specifications. Information retrieval of customers preferences for the specification determination is essential to product design and development. Big sales data is an emerging resource for mining customers preferences on product specifications. In this work, information entropy is used for customers preferences information quantification on product specifications firstly. Then, a method of information mining for customers preferences estimation is developed by using big sales data. On this basis, a density-based clustering analysis is carried out on customers preferences as a decision support tool for the determination and selection of product design specifications. A case study related to electric bicycle specifications determination using big sales data is reported to illustrate and validate the proposed method.

Flow Measurement-Based Self-Adaptive Line Segment Clustering Model for Leakage Detection in Water Distribution Networks

Leakage detection of water distribution networks (WDNs) plays a key role in water management. Current leakage detection methods mostly have high requirements for the installation of sensors in WDN. So, there needs an efficient and convenient method when dealing with a new WDN. In this article, a novel, timely, and accurate leakage detection model is proposed, called self-adaptive line segment clustering (SALICT), which only asks for flow measurement data of WDN, reducing the demand for sensors. The proposed method focuses on the identification phase of leakage detection to improve the sensitivity to leakage. To achieve this, SALICT efficiently fuses a density-based clustering analysis method and a line segment clustering model. Furthermore, a series of auxiliary decision functions are introduced and designed to adaptively select parameters, obtain cluster centers, and detect leakage data according to data distribution characteristics. Notably, the proposed method can detect leakages in real-time after learning from historical data. Besides that, the proposed method has the potential to be easily used in different types of WDN. Experimental results show that the proposed method can achieve a high leakage identification ratio and low false alarm ratio and has low time consumption in various water use scenarios.

Airborne Lidar Survey, Density-Based Clustering, and Ancient Maya Settlement in the Upper Usumacinta River Region of Mexico and Guatemala

We present results from the archaeological analysis of 331 km2 of high-resolution airborne lidar data collected in the Upper Usumacinta River basin of Mexico and Guatemala. Multiple visualizations of the DEM and multi-spectral data from four lidar transects crossing the Classic period (AD 350–900) Maya kingdoms centered on the sites of Piedras Negras, La Mar, and Lacanja Tzeltal permitted the identification of ancient settlement and associated features of agricultural infrastructure. HDBSCAN (hierarchical density-based clustering of applications with noise) cluster analysis was applied to the distribution of ancient structures to define urban, peri-urban, sub-urban, and rural settlement zones. Interpretations of these remotely sensed data are informed by decades of ground-based archaeological survey and excavations, as well as a rich historical record drawn from inscribed stone monuments. Our results demonstrate that these neighboring kingdoms in three adjacent valleys exhibit divergent patterns of structure clustering and low-density urbanism, distributions of agricultural infrastructure, and economic practices during the Classic period. Beyond meeting basic subsistence needs, agricultural production in multiple areas permitted surpluses likely for the purposes of tribute, taxation, and marketing. More broadly, this research highlights the strengths of HDBSCAN to the archaeological study of settlement distributions when compared to more commonly applied methods of density-based cluster analysis.

Super-resolution microscopy reveals the arrangement of inner membrane protein complexes in mammalian mitochondria.

The mitochondrial inner membrane is a protein-rich environment containing large multimeric complexes, including complexes of the mitochondrial electron transport chain, mitochondrial translocases and quality control machineries. Although the inner membrane is highly proteinaceous, with 40-60% of all mitochondrial proteins localised to this compartment, little is known about the spatial distribution and organisation of complexes in this environment. We set out to survey the arrangement of inner membrane complexes using stochastic optical reconstruction microscopy (STORM). We reveal that subunits of the TIM23 complex, TIM23 and TIM44 (also known as TIMM23 and TIMM44, respectively), and the complex IV subunit COXIV, form organised clusters and show properties distinct from the outer membrane protein TOM20 (also known as TOMM20). Density based cluster analysis indicated a bimodal distribution of TIM44 that is distinct from TIM23, suggesting distinct TIM23 subcomplexes. COXIV is arranged in larger clusters that are disrupted upon disruption of complex IV assembly. Thus, STORM super-resolution microscopy is a powerful tool for examining the nanoscale distribution of mitochondrial inner membrane complexes, providing a 'visual' approach for obtaining pivotal information on how mitochondrial complexes exist in a cellular context.

Marker-Less UAV-LiDAR Strip Alignment in Plantation Forests Based on Topological Persistence Analysis of Clustered Canopy Cover

A holistic strategy is established for automated UAV-LiDAR strip adjustment for plantation forests, based on hierarchical density-based clustering analysis of the canopy cover. The method involves three key stages: keypoint extraction, feature similarity and correspondence, and rigid transformation estimation. Initially, the HDBSCAN algorithm is used to cluster the scanned canopy cover, and the keypoints are marked using topological persistence analysis of the individual clusters. Afterward, the feature similarity is calculated by considering the linear and angular relationships between each point and the pointset centroid. The one-to-one feature correspondence is retrieved by solving the assignment problem on the similarity score function using the Kuhn–Munkres algorithm, generating a set of matching pairs. Finally, 3D rigid transformation parameters are determined by permutations over all conceivable pair combinations within the correspondences, whereas the best pair combination is that which yields the maximum count of matched points achieving distance residuals within the specified tolerance. Experimental data covering eighteen subtropical forest plots acquired from the GreenValley and Riegl UAV-LiDAR platforms in two scan modes are used to validate the method. The results are extremely promising for redwood and poplar tree species from both the Velodyne and Riegl UAV-LiDAR datasets. The minimal mean distance residuals of 31 cm and 36 cm are achieved for the coniferous and deciduous plots of the Velodyne data, respectively, whereas their corresponding values are 32 cm and 38 cm for the Riegl plots. Moreover, the method achieves both higher matching percentages and lower mean distance residuals by up to 28% and 14 cm, respectively, compared to the baseline method, except in the case of plots with extremely low tree height. Nevertheless, the mean planimetric distance residual achieved by the proposed method is lower by 13 cm.

Underdetermined mixing matrix estimation based on joint density-based clustering algorithms

In underdetermined blind source separation (UBSS), the estimation of the mixing matrix is crucial because it directly affects the performance of UBSS. To improve the estimation accuracy, this paper proposes a joint clustering analysis method based on density based spatial clustering of applications with noise (DBSCAN) and clustering by fast search and find of density peaks (CFSFDP). In the reprocessing, the observed signals in the time domain are transformed into sparse signals in the frequency domain through a short time Fourier transform (STFT), and single-source-point (SSP) detection is used to enhance the linear clustering characteristic of signals. In addition, to facilitate the use of density-based clustering analysis, mirroring mapping is used to transform the linear clustering into compact clustering on the positive half unit circle (or sphere). For the estimation of the underdetermined mixing matrix (UMM), the DBSCAN algorithm is first used to search for high-density data points, and automatically find the number of clusters and the cluster centers; then, the CFSFDP algorithm is used to search the density peaks of the data clusters, so as to further modify the cluster centers. Because each cluster center corresponds to a column vector of the mixing matrix, the proposed algorithm can estimate the UMM through cluster analysis. The simulation results show that the proposed algorithm can not only improve the estimation accuracy of the UMM, but also provide a more robust estimator. In addition, the joint clustering method also makes up for the shortcomings of the CFSFDP algorithm that requires human intervention.

Potential increase in oil and gas well leakage due to earthquakes

Earthquakes occurring naturally or induced by human activities can damage surface and subsurface infrastructure. Oil and gas wells represent a category of subsurface infrastructure that can act as leakage pathways connecting oil and gas reservoirs, groundwater aquifers, and the atmosphere. The integrity of these wells can be compromised through a wide range of processes and contribute to groundwater contamination, greenhouse gas emissions, and air quality degradation. We estimate the increase in such subsurface leakage potential due to seismic activity through geospatial analysis of 579,378 oil and gas well and 196,315 earthquake (magnitudes greater than 1.0) locations in Oklahoma, California, and British Columbia. We perform density-based clustering analysis and point density mapping using ArcGIS. We combine the well and earthquake point density maps to identify hot spots of joint high well and earthquake densities. We find that oil and gas wells and earthquakes are clustered in space, with densities reaching ∼60 wells per km2 and ∼40 earthquakes per km2 in California. There are at least two hot spots where these clusters overlap in each state/province. In Oklahoma and British Columbia, the hot spots are more correlated with earthquake densities; while, in California, the hot spots are more correlated with well densities. Our findings indicate the need to investigate the role of earthquakes on wellbore leakage through additional analysis of earthquake characteristics, wellbore attributes, improved data collection, and empirical field studies for all oil and gas wells, including those that are abandoned. In particular, large scale geospatial analysis establishing the scope of the problem and empirical field studies focusing on identified hot spots are needed to understand potential environmental impacts of earthquakes, especially those induced by oil and gas activities.

Hierarchical density-based cluster analysis framework for atom probe tomography data

Atom probe tomography (APT) has enabled the direct visualization of solute clusters. However one of the main analysis methods used by the APT community, i.e. the maximum separation method, often suffers from subjective parametric selection and limited applicability. To address the need for more robust and versatile analysis tools, a framework based on hierarchical density-based cluster analysis is implemented. Cluster analysis begins with the HDBSCAN algorithm to conservatively segment the datasets into regions containing clusters and a matrix or noise region. The stability of each cluster and the probability that an atom belongs to a cluster are quantified. Each clustered region is further analyzed by the DeBaCl algorithm to separate and refine clusters present in the sub-volumes. Finally, the k-nearest neighbor algorithm may be used to re-assign matrix atoms to clusters, based on their probability values. Four mandatory parameters are required for this cluster analysis approach. However, the selection of an appropriate value for only one of these parameters, i.e. a rough estimate of the minimum cluster size, is essential. The improved performance of the method was evaluated by analyzing four synthetic APT datasets and comparing the outcome with the commonly-used maximum separation method. Codes and data are made available through GitHub.

Abstract 2191: Quantitative cell-level spatial analysis of tumor metabolism

Abstract Sub-populations of tumor cells exhibit distinct responses to treatment. This cell-level heterogeneity can lead to growth of resistant populations, and tumor recurrence. Many cancer therapies alter tumor cell metabolism, and the metabolic microenvironment can further contribute to tumor heterogeneity and drug response. However, the relationship between the spatial diversity of tumor cell metabolism and treatment response requires further characterization. Two-photon fluorescence lifetime microscopy (FLIM) monitors cellular metabolism by measuring NAD(P)H and FAD autofluorescence, and enables single-cell resolution of metabolic heterogeneity within 3D samples. Previous studies have shown that FLIM predicts treatment response of 2D and 3D cultures in vitro, and in vivo tumors. Additionally, these studies demonstrated responsive cells have lower post-treatment NAD(P)H mean lifetime (NAD(P)H τm) than non-responsive cells. Thus, these published FLIM data were used to develop an algorithm to quantify the spatial distribution of cellular metabolism in response to treatment. Density-based clustering analysis defined sub-populations in organoids based on NAD(P)H τm. Accuracy of cluster analysis classification was first evaluated on 2D co-culture images of two cell lines plated at varying proportions. Following this validation, metabolic sub-populations and their spatial distributions were characterized in control and drug-treated 3D tumor organoids of human squamous cell carcinoma (FaDu). Descriptive spatial metrics were developed using graph-based network analysis integrated with standard image analysis to establish local (sub-population level) and global (organoid level) spatial relationships. High classification accuracy (94.7%) of cell lines was achieved in 2D breast carcinoma co-cultures. In all FaDu 3D organoids, metabolic sub-populations were largely segregated into clusters of identical metabolic phenotype, with ≥78% of cell neighbors belonging to the same sub-population. Clustering density was greater in populations with low NAD(P)H τm (responsive), exhibiting shorter intercellular distances than high NAD(P)H τm (non-responsive) populations (p &amp;lt;0.05). Additionally, responsive and non-responsive cell sub-populations displayed similar organization relative to both adjacent sub-populations and organoid centers. Geographically weighted principal component analysis demonstrates variability of each metabolic and spatial parameter as a function of cell location. This analysis is under refinement for use with in vivo FaDu xenograft images. This algorithm to quantify spatial distributions of metabolic sub-populations within tumors could enhance our understanding of tumor progression and therapeutic resistance. Citation Format: Tiffany M. Heaster, Bennett A. Landman, Melissa C. Skala. Quantitative cell-level spatial analysis of tumor metabolism [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 2191.

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

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.