Clusters Of Different Densities Research Articles

Fast conformational clustering of extensive molecular dynamics simulation data.

We present an unsupervised data processing workflow that is specifically designed to obtain a fast conformational clustering of long molecular dynamics simulation trajectories. In this approach, we combine two dimensionality reduction algorithms (cc_analysis and encodermap) with a density-based spatial clustering algorithm (hierarchical density-based spatial clustering of applications with noise). The proposed scheme benefits from the strengths of the three algorithms while avoiding most of the drawbacks of the individual methods. Here, the cc_analysis algorithm is applied for the first time to molecular simulation data. The encodermap algorithm complements cc_analysis by providing an efficient way to process and assign large amounts of data to clusters. The main goal of the procedure is to maximize the number of assigned frames of a given trajectory while keeping a clear conformational identity of the clusters that are found. In practice, we achieve this by using an iterative clustering approach and a tunable root-mean-square-deviation-based criterion in the final cluster assignment. This allows us to find clusters of different densities and different degrees of structural identity. With the help of four protein systems, we illustrate the capability and performance of this clustering workflow: wild-type and thermostable mutant of the Trp-cage protein (TC5b and TC10b), NTL9, and Protein B. Each of these test systems poses their individual challenges to the scheme, which, in total, give a nice overview of the advantages and potential difficulties that can arise when using the proposed method.

Adaptive Density-Based Spatial Clustering of Applications with Noise (ADBSCAN) for Clusters of Different Densities

Finding clusters based on density represents a significant class of clustering algorithms. These methods can discover clusters of various shapes and sizes. The most studied algorithm in this class is the Density-Based Spatial Clustering of Applications with Noise (DBSCAN). It identifies clusters by grouping the densely connected objects into one group and discarding the noise objects. It requires two input parameters: <i>epsilon</i> (fixed neighborhood radius) and <i>MinPts</i> (the lowest number of objects in <i>epsilon</i>). However, it can’t handle clusters of various densities since it uses a global value for epsilon. This article proposes an adaptation of the DBSCAN method so it can discover clusters of varied densities besides reducing the required number of input parameters to only one. Only user input in the proposed method is the <i>MinPts</i>. <i>Epsilon</i> on the other hand, is computed automatically based on statistical information of the dataset. The proposed method finds the core distance for each object in the dataset, takes the average of these distances as the first value of <i>epsilon</i>, and finds the clusters satisfying this density level. The remaining unclustered objects will be clustered using a new value of <i>epsilon</i> that equals the average core distances of unclustered objects. This process continues until all objects have been clustered or the remaining unclustered objects are less than 0.006 of the dataset’s size. The proposed method requires <i>MinPts</i> only as an input parameter because <i>epsilon</i> is computed from data. Benchmark datasets were used to evaluate the effectiveness of the proposed method that produced promising results. Practical experiments demonstrate that the outstanding ability of the proposed method to detect clusters of different densities even if there is no separation between them. The accuracy of the method ranges from 92% to 100% for the experimented datasets.

A varied density-based clustering algorithm

Discovering clusters of different sizes, shapes, and densities is a challenging duty. DBSCAN can find clusters of different shapes and sizes. But it has trouble finding clusters of different densities because it depends on a global value for its parameter Eps. Several methods have been proposed to tackle this problem, each method has its drawbacks. This paper introduces a new stand-alone method to discover clusters of different densities. The proposed method depends on the k-nearest neighbors to compute the local density of each object as the sum of distances to its k1-nearest neighbors, where 0 < k1 < k, it starts from any object. This object is called a cluster initiator. Any object that is reachable from a cluster initiator and has a local density similar to the local density of the cluster initiator is assigned the same cluster. So, the method requires a threshold for similarity, which will be called SR (Similarity Ratio). The proposed method discovers clusters of different densities, shapes, and sizes. The experimental results show the superior ability of the proposed method to detect clusters of different densities even with no discernible separations between them.

An Improved Clustering Algorithm for Multi-Density Data

The clustering method divides a dataset into groups with similar data using similarity metrics. However, discovering clusters in different densities, shapes and distinct sizes is still a challenging task. In this regard, experts and researchers opt to use the DBSCAN algorithm as it uses density-based clustering techniques that define clusters of different sizes and shapes. However, it is misapplied to clusters of different densities due to its global attributes that generate a single density. Furthermore, most existing algorithms are unsupervised methods, where available prior knowledge is useless. To address these problems, this research suggests the use of a clustering algorithm that is semi-supervised. This allows the algorithm to use existing knowledge to generate pairwise constraints for clustering multi-density data. The proposed algorithm consists of two stages: first, it divides the dataset into different sets based on their density level and then applies the semi-supervised DBSCAN algorithm to each partition. Evaluation of the results shows the algorithm performing effectively and efficiently in comparison to unsupervised clustering algorithms.

RFDPC: Density Peaks Clustering Algorithm Based on Resultant Force

Density peaks clustering (DPC) is an efficient and effective algorithm due to its outstanding performance in discovering clusters with varying densities. However, the quality of this method is highly dependent on the cutoff distance. To improve the performance of DPC, the gravitation-based clustering (GDPC) algorithm is proposed. However, it cannot identify the clusters of varying densities. We developed a novel density peaks clustering algorithm based on the magnitude and direction of the resultant force acting on a data point (RFDPC). RFDPC is based on the idea that the resultant forces acting on the data points in the same cluster are more likely to point towards the cluster center. The cluster centers are selected based on the force directional factor and distance in the decision graph. Experimental results indicate superior performance of the proposed algorithm in detecting clusters of different densities, irregular shapes, and numbers of clusters.

An Extended DBSCAN Clustering Algorithm

Finding clusters of different densities is a challenging task. DBSCAN “Density-Based Spatial Clustering of Applications with Noise” method has trouble discovering clusters of various densities since it uses a fixed radius. This article proposes an extended DBSCAN for finding clusters of different densities. The proposed method uses a dynamic radius and assigns a regional density value for each object, then counts the objects of similar density within the radius. If the neighborhood size ≥ MinPts, then the object is a core, and a cluster can grow from it, otherwise, the object is assigned noise temporarily. Two objects are similar in local density if their similarity ≥ threshold. The proposed method can discover clusters of any density from the data effectively. The method requires three parameters; MinPts, Eps (distance to the kth neighbor), and similarity threshold. The practical results show the superior ability of the suggested method to detect clusters of different densities even with no discernible separations between them.

KR-DBSCAN: A density-based clustering algorithm based on reverse nearest neighbor and influence space

Density-based clustering is one of the most commonly used analysis methods in data mining and machine learning, with the advantage of locating non-ball-shaped clusters without specifying the number of clusters in advance. However, it has notable shortcomings, such as an inability to distinguish adjacent clusters of different densities. We propose a density-based clustering algorithm, KR-DBSCAN, which is based on the reverse nearest neighbor and influence space. The core objects are identified according to the reverse nearest neighborhood, and their influence spaces are determined by calculating the k-nearest neighborhood and reverse nearest neighborhood for each data object under the Euclidean distance metric. In particular, a new cluster expansion condition is defined using the reverse nearest neighborhood and its influence space, and when the core objects are within their influence spaces, they are added to the cluster by breadth-first traversal. As a result, adjacent clusters with different densities are effectively distinguished, and the computational load is substantially reduced. Boundary objects and noise objects are identified, also using k-nearest neighbors. KR-DBSCAN is experimentally validated on the UCI dataset and some synthetic datasets.

A Multi-Density Clustering Algorithm Based on Similarity for Dataset With Density Variation

Clustering has been widely used in the fields of knowledge discovery, pattern recognition and artificial intelligence. However, discovering clusters in spatial databases is still a challenging task, especially when the shape, size, and density of clusters vary a lot. Existing algorithms have sensitive parameters, clusters must be separated far enough from each other and rich prior knowledge about datasets is required. In this paper, we propose algorithm DENSS, which performs clustering on the basis of the similarity of neighbour distribution and the number of shared neighbors for two objects. Algorithm DENSS can mine clusters that differ in densities, and within a cluster the local densities are reasonably homogeneous. Adjacent objects are separated into different clusters by significant change in densities. To verify the effectiveness of the algorithm DENSS, synthetic and real-world datasets are used for testing, and it has been compared with seven clustering algorithms. Experimental results show that the proposed algorithm has a relatively high efficiency, robustness and effectiveness, and is remarkably superior to the seven algorithms. This algorithm is universal and can rapidly and efficiently identify the clusters of different densities, shapes and sizes even in the presence of noise and outliers for any object feature types.

A holarchic approach for multi-scale distributed energy system optimisation

The benefits of decentralised energy systems can be realised through the optimal siting of distributed energy systems and the design of highly interlinked district heating networks within existing electrical and gas networks. The problem is often formulated as a Mixed Integer Linear Programming (MILP) problem. MILP formulations are efficient and reliable, however the computational burden increases drastically with the number of integer variables, making detailed optimisation infeasible at large urban scales. To tackle complex problems at large scale the development of an efficient and robust simplification method is required. This paper presents an aggregation schema to facilitate the optimisation of urban energy systems at city scale.Currently, spatial and/or temporal aggregation are commonly employed when modelling energy systems at spatio-temporal resolutions from plant scheduling up to national scenarios. This paper argues for solving different scales separately using a bottom-up approach, while keeping track of the error made by reducing the resolution when moving from building to urban scale. Novel modelling formulations and optimisation techniques are presented. They enable drastic reduction of the computational time (by up to a factor of 100) required to find an optimal solution in reasonable time without sacrificing the quality of the results (no more than 1% loss in accuracy).A density-based clustering algorithm enables intelligent division of a large city-scale problem into sub-optimisation problems by creating clusters of different density. In each cluster, the trade-off between centralised and decentralised energy systems and the associated district heating network design is evaluated. A solution is selected based on a local optimisation of the network costs. Demand profiles of each building are assigned appropriately, then at an upper level the energy optimisation problem is solved considering the network losses at lower levels. This method enables large-scale modelling of urban energy systems while taking into account building-scale levels of detail. The clustering method enables assessment of the potential of district heating networks on city scale based on building characteristics and available urban energy systems.

Point Clustering via Voting Maximization

In this paper, we propose an unsupervised point clustering framework. The goal is to cluster N given points into K clusters, so that similarities between objects in the same group are high while the similarities between objects in different groups are low. The point similarity is defined by a voting measure that takes into account the point distances. Using the voting formulation, the problem of clustering is reduced to the maximization of the sum of votes between the points of the same cluster. We have shown that the resulting clustering based on voting maximization has advantages concerning the cluster's compactness, working well for clusters of different densities and/or sizes. In addition, the proposed scheme is able to detect outliers. Experimental results and comparisons to existing methods on real and synthetic datasets demonstrate the high performance and robustness of the proposed scheme.

An efficient and scalable density-based clustering algorithm for datasets with complex structures

As a research branch of data mining, clustering, as an unsupervised learning scheme, focuses on assigning objects in the dataset into several groups, called clusters, without any prior knowledge. Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is one of the most widely used clustering algorithms for spatial datasets, which can detect any shapes of clusters and can automatically identify noise points. However, there are several troublesome limitations of DBSCAN: (1) the performance of the algorithm depends on two specified parameters, ε and MinPts in which ε represents the maximum radius of a neighborhood from the observing point and MinPts means the minimum number of data points contained in such a neighborhood. (2) The time consumption for searching the nearest neighbors of each object is intolerable in the cluster expansion. (3) Selecting different starting points results in quite different consequences. (4) DBSCAN is unable to identify adjacent clusters of various densities. In addition to these restrictions about DBSCAN mentioned above, the identification of border points is often ignored. In our paper, we successfully solve the above problems. Firstly, we improve the traditional locality sensitive hashing method to implement fast query of nearest neighbors. Secondly, several definitions are redefined on the basis of the influence space of each object, which takes the nearest neighbors and the reverse nearest neighbors into account. The influence space is proved to be sensitive to local density changes to successfully reduce the amount of parameters and identify adjacent clusters of different densities. Moreover, this new relationship based on the influence space makes the insensitivity to the ordering of inputting points possible. Finally, a new concept—core density reachable based on the influence space is put forward which aims to distinguish between border objects and noisy objects. Several experiments are performed which demonstrate that the performance of our proposed algorithm is better than the traditional DBSCAN algorithm and the improved algorithm IS-DBSCAN.

Strong effect of the cluster environment on the size of protoplanetary discs?

Context. Most stars are born in clusters, thus the protoplanetary discs surrounding the newly formed stars might be influenced by this environment. Isolated star-disc encounters have previously been studied, and it was shown that very close encounters are necessary to completely destroy discs. However, relatively distant encounters are still able to change the disc size considerably. Aims. We quantify the importance of disc-size reduction that is due to stellar encounters in an entire stellar population. Methods. We modelled young, massive clusters of different densities using the code Nbody6 to determine the statistics of stellar encounter parameters. In a second step, we used these parameters to investigate the effect of the environments on the disc size. For this purpose, we performed a numerical experiment with an artificial initial disc size of 105 AU. Results. We quantify to which degree the disc size is more sensitive to the cluster environment than to the disc mass or frequency. We show that in all investigated clusters a large portion of discs is significantly reduced in size. After 5 Myr, the fraction of discs smaller than 1000 AU in ONC-like clusters with an average number density of 60pc$^3$, the fraction of discs smaller than 1000 AU is 65%, while discs smaller than 100 AU make up 15%. These fractions increase to 84% and 39% for discs in denser clusters like IC 348 (500pc$^3$). Even in clusters with a density four times lower than in the ONC (15pc$^3$), about 43% of all discs are reduced to sizes below 1 000 AU and roughly 9% to sizes below 100 AU. Conclusions. For any disc in the ONC that initially was larger than 1 000 AU, the probability to be truncated to smaller disc sizes as a result of stellar encounters is quite high. Thus, among other effects, encounters are important in shaping discs and potentially forming planetary systems in stellar clusters.

Multi-Density based Incremental Clustering

Clustering is the task of grouping a set of objects in such a way that objects in the same group are more similar to each other than to those in other groups . It is a common technique for statistical data analysis, used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, and bioinformatics. A major difficulty in design of modern clustering algorithms is that, new datasets are dynamically added to the existing large database and it is not efficient to perform data clustering on the entire database every time a new dataset is added to the database. The new data added dynamically to the existing database is called incremental data. DBSCAN is widely used density based clustering algorithm. However it is known that DBSCAN fails to identify clusters of different densities. This paper presents a simple and efficient algorithm that identifies clusters of different densities and arbitrary shapes with automatic Eps estimation. Eps is estimated by using distance curve and difference of slopes and DBSCAN is applied on the data for each estimated Eps, resulting in multi-density clusters. Then by making use of formed clusters, incrementally updated data is clustered.

Mapping Large Spatial Flow Data with Hierarchical Clustering

AbstractIt is challenging to map large spatial flow data due to the problem of occlusion and cluttered display, where hundreds of thousands of flows overlap and intersect each other. Existing flow mapping approaches often aggregate flows using predetermined high‐level geographic units (e.g. states) or bundling partial flow lines that are close in space, both of which cause a significant loss or distortion of information and may miss major patterns. In this research, we developed a flow clustering method that extracts clusters of similar flows to avoid the cluttering problem, reveal abstracted flow patterns, and meanwhile preserves data resolution as much as possible. Specifically, our method extends the traditional hierarchical clustering method to aggregate and map large flow data. The new method considers both origins and destinations in determining the similarity of two flows, which ensures that a flow cluster represents flows from similar origins to similar destinations and thus minimizes information loss during aggregation. With the spatial index and search algorithm, the new method is scalable to large flow data sets. As a hierarchical method, it generalizes flows to different hierarchical levels and has the potential to support multi‐resolution flow mapping. Different distance definitions can be incorporated to adapt to uneven spatial distribution of flows and detect flow clusters of different densities. To assess the quality and fidelity of flow clusters and flow maps, we carry out a case study to analyze a data set of 243,850 taxi trips within an urban area.

An Iterative Detection and Removal Method for Detecting Spatial Clusters of Different Densities

AbstractA fundamental element of exploratory spatial data analysis is the discovery of clusters in a spatial point dataset. When clusters with distinctly different local densities exist, the determination of suitable density level is still an unsolved problem. On that account, an iterative detection and removal method is proposed in this study. In each step of the novel method, there are two stages. In the detection stage, density level is statistically modeled as a significance level controlled by the number and support domain of the points in the dataset, and then a hypothesis test is used to detect the high‐density points. In the removal stage, the Delaunay triangulation network is used to construct clusters and support domains for the identified high‐density points, and then the high‐density points and their support domains are removed from the dataset. The detection and removal operation are iteratively implemented until no high‐density points can be detected. Experiments and comparisons show that the proposed method, on the one hand, outperforms four state‐of‐the‐art methods for detecting clusters of complex shapes and diverse densities, and on the other hand, no user‐specified parameters are required. In addition, the support domains of clusters are very useful for spatial analysis.

Enhancing density-based clustering: Parameter reduction and outlier detection

Clustering is a widely used unsupervised data mining technique. It allows to identify structures in collections of objects by grouping them into classes, named clusters, in such a way that similarity of objects within any cluster is maximized and similarity of objects belonging to different clusters is minimized. In density-based clustering, a cluster is defined as a connected dense component and grows in the direction driven by the density. The basic structure of density-based clustering presents some common drawbacks: (i) parameters have to be set; (ii) the behavior of the algorithm is sensitive to the density of the starting object; and (iii) adjacent clusters of different densities could not be properly identified. In this paper, we address all the above problems. Our method, based on the concept of space stratification, efficiently identifies the different densities in the dataset and, accordingly, ranks the objects of the original space. Next, it exploits such a knowledge by projecting the original data into a space with one more dimension. It performs a density based clustering taking into account the reverse-nearest-neighbor of the objects. Our method also reduces the number of input parameters by giving a guideline to set them in a suitable way. Experimental results indicate that our algorithm is able to deal with clusters of different densities and outperforms the most popular algorithms DBSCAN and OPTICS in all the standard benchmark datasets.

Automated Hierarchical Density Shaving: A Robust Automated Clustering and Visualization Framework for Large Biological Data Sets

A key application of clustering data obtained from sources such as microarrays, protein mass spectroscopy, and phylogenetic profiles is the detection of functionally related genes. Typically, only a small number of functionally related genes cluster into one or more groups, and the rest need to be ignored. For such situations, we present Automated Hierarchical Density Shaving (Auto-HDS), a framework that consists of a fast hierarchical density-based clustering algorithm and an unsupervised model selection strategy. Auto-HDS can automatically select clusters of different densities, present them in a compact hierarchy, and rank individual clusters using an innovative stability criteria. Our framework also provides a simple yet powerful 2D visualization of the hierarchy of clusters that is useful for further interactive exploration. We present results on Gasch and Lee microarray data sets to show the effectiveness of our methods. Additional results on other biological data are included in the supplemental material.

Do binaries in clusters form in the same way as in the field?

We examine the dynamical destruction of binary systems in star clusters of different densities. We find that at high densities (10^4 - 10^5 Msun pc^-3) almost all binaries with separations > 10^3 AU are destroyed after a few crossing times. At low densities (order(10^2) Msun pc^-3) many binaries with separations > 10^3 AU are destroyed, and no binaries with separations > 10^4 AU survive after a few crossing times. Therefore the binary separations in clusters can be used as a tracer of the dynamical age and past density of a cluster. We argue that the central region of the Orion Nebula Cluster was around 100 times denser in the past with a half-mass radius of only 0.1 - 0.2 pc as (a) it is expanding, (b) it has very few binaries with separations > 10^3 AU, and (c) it is well-mixed and therefore dynamically old. We also examine the origin of the field binary population. Binaries with separations < 10^2 AU are not significantly modified in any cluster, therefore at these separations the field reflects the sum of all star formation. Binaries with separations in the range 10^2 - 10^4 AU are progressively more and more heavily affected by dynamical disruption in increasingly dense clusters. If most star formation is clustered, these binaries must be over-produced relative to the field. Finally, no binary with a separation > 10^4 AU can survive in any cluster and so must be produced by isolated star formation, but only if all isolated star formation produces extremely wide binaries.

DECODE: a new method for discovering clusters of different densities in spatial data

When clusters with different densities and noise lie in a spatial point set, the major obstacle to classifying these data is the determination of the thresholds for classification, which may form a series of bins for allocating each point to different clusters. Much of the previous work has adopted a model-based approach, but is either incapable of estimating the thresholds in an automatic way, or limited to only two point processes, i.e. noise and clusters with the same density. In this paper, we present a new density-based cluster method (DECODE), in which a spatial data set is presumed to consist of different point processes and clusters with different densities belong to different point processes. DECODE is based upon a reversible jump Markov Chain Monte Carlo (MCMC) strategy and divided into three steps. The first step is to map each point in the data to its mth nearest distance, which is referred to as the distance between a point and its mth nearest neighbor. In the second step, classification thresholds are determined via a reversible jump MCMC strategy. In the third step, clusters are formed by spatially connecting the points whose mth nearest distances fall into a particular bin defined by the thresholds. Four experiments, including two simulated data sets and two seismic data sets, are used to evaluate the algorithm. Results on simulated data show that our approach is capable of discovering the clusters automatically. Results on seismic data suggest that the clustered earthquakes, identified by DECODE, either imply the epicenters of forthcoming strong earthquakes or indicate the areas with the most intensive seismicity, this is consistent with the tectonic states and estimated stress distribution in the associated areas. The comparison between DECODE and other state-of-the-art methods, such as DBSCAN, OPTICS and Wavelet Cluster, illustrates the contribution of our approach: although DECODE can be computationally expensive, it is capable of identifying the number of point processes and simultaneously estimating the classification thresholds with little prior knowledge.

Hypersonic Swizzle Sticks: Protostellar Turbulence, Outflows and Fossil Outflow Cavities

The expected lifetimes for molecular clouds has become a topic of considerable debate as numerical simulations have shown that MHD turbulence, the nominal means of support for clouds against self-gravity, will decay on short timescales. Thus it appears that either molecular clouds are transient features or they are resupplied with turbulent energy through some means. Jets and molecular outflows are recognized as a ubiquitous phenomena associated with star formation. Stars however form not isolation but in clusters of different density and composion. The ubiquity and high density of outflows from young stars in clusters make them an intriguing candidate for the source of turbulence energy in molecular clouds. In this contribution we present new studies, both observational and theoretical, which address the issue of jet/outflow interactions and their abilityto drive turbulent flows in molecular clouds. Our studies focus on scales associated with young star forming clusters. In particular we first show that direct collisions between active outflows are not effective at stirring the ambient medium. We then show that fossil cavities from “extinct” outflows may provide the missing link in terms of transferring momentum and energy to the cloud.