Evolutionary Clustering Research Articles

Multiobjective Deep Clustering and its Applications in Single-cell RNA-seq Data

Single-cell RNA sequencing is a transformative technology that enables us to study the heterogeneity of the tissue at the cellular level. Clustering is used as the key computational approach to group cells under the transcriptome profiles from single-cell RNA-seq data. However, accurate identification of distinct cell types is facing the challenge of high dimensionality, and it could cause uninformative clusters when clustering is directly applied on the original transcriptome. To address such challenge, an evolutionary multiobjective deep clustering (EMDC) algorithm is proposed to identify single-cell RNA-seq data in this study. First, EMDC removes redundant and irrelevant genes by applying the differential gene expression analysis to identify differentially expressed genes across biological conditions. After that, a deep autoencoder is proposed to project the high-dimensional data into different low-dimensional nonlinear embedding subspaces under different bottleneck layers. Then, the basic clustering algorithm is applied in those nonlinear embedding subspaces to generate some basic clustering results to produce the cluster ensemble. To lessen the unnecessary cost produced by those clusterings in the ensemble, the multiobjective evolutionary optimization is designed to prune the basic clustering results in the ensemble, unleashing its cell type discovery performance under three objective functions. Multiple experiments have been conducted on 30 synthetic single-cell RNA-seq datasets and six real single-cell RNA-seq datasets, which reveal that EMDC outperforms eight other clustering methods and three multiobjective optimization algorithms in cell type identification. In addition, we have conducted extensive comparisons to effectively demonstrate the impact of each component in our proposed EMDC.

Energy Efficient Clustering Protocol for FANETS Using Moth Flame Optimization

FANET (flying ad-hoc networks) is currently a trending research topic. Unmanned aerial vehicles (UAVs) have two significant challenges: short flight times and inefficient routing due to low battery power and high mobility. Due to these topological restrictions, FANETS routing is considered more complicated than MANETs or VANETs. Clustering approaches based on artificial intelligence (AI) approaches can be used to solve complex routing issues when static and dynamic routings fail. Evolutionary algorithm-based clustering techniques, such as moth flame optimization, and ant colony optimization, can be used to solve these kinds of problems with routes. Moth flame optimization gives excellent coverage while consuming little energy and requiring a minimum number of cluster heads (CHs) for routing. This paper employs a moth flame optimization algorithm for network building and node deployment. Then, we employ a variation of the K-Means Density clustering approach to choosing the cluster head. Choosing the right cluster heads increases the cluster’s lifespan and reduces routing traffic. Moreover, it lowers the number of routing overheads. This step is followed by MRCQ image-based compression techniques to reduce the amount of data that must be transmitted. Finally, the reference point group mobility model is used to send data by the most optimal path. Particle swarm optimization (PSO), ant colony optimization (ACO), and grey wolf optimization (GWO) were put to the test against our proposed EECP-MFO. Several metrics are used to gauge the efficiency of our proposed method, including the number of clusters, cluster construction time, cluster lifespan, consistency of cluster heads, and energy consumption. This paper demonstrates that our proposed algorithm performance is superior to the current state-of-the-art approaches using experimental results.

RecMem: Time Aware Recommender Systems Based on Memetic Evolutionary Clustering Algorithm.

Nowadays, the recommendation is an important task in the decision-making process about the selection of items especially when item space is large, diverse, and constantly updating. As a challenge in the recent systems, the preference and interest of users change over time, and existing recommender systems do not evolve optimal clustering with sufficient accuracy over time. Moreover, the behavior history of the users is determined by their neighbours. The purpose of the time parameter for this system is to extend the time-based priority. This paper has been carried out a time-aware recommender systems based on memetic evolutionary clustering algorithm called RecMem for recommendations. In this system, clusters that evolve over time using the memetic evolutionary algorithm and extract the best clusters at every timestamp, and improve the memetic algorithm using the chaos criterion. The system provides appropriate suggestions to the user based on optimum clustering. The system uses optimal evolutionary clustering using item attributes for the cold-start item problem and demographic information for the cold start user problem. The results show that the proposed method has an accuracy of approximately 0.95, which is more effective than existing systems.

A Feature Similarity Machine Learning Model for DDoS Attack Detection in Modern Network Environments for Industry 4.0

• A new traffic attribute-pattern similarity function SWATHI for similarity computation between network traffic attribute patterns and evolutionary feature clustering of traffic attribute patterns to carry feature transformation-based dimensionality reduction. • A Gaussian based network traffic similarity function for similarity computation between network traffic instances. • A machine learning model SWASTHIKA which considers network traffic data obtained after feature transformation for detection of low rate and high-rate network attacks. Recent advancements in artificial intelligence and machine learning technologies have laid the flagstone for the fourth industrial revolution, Industry 4.0. The industry 4.0 is at a very high momentum when compared to previous revolutions witnessed by humans in a way which was never anticipated. Cyber Physical Systems and Cloud computing are the basis for Industry 4.0. An ongoing research challenge in cloud computing is the immediate need to address security and data availability challenges coined in modern networking environments. For instance, DDoS attacks in cloud are continuously throwing new challenges to network community which makes detection of these attacks, an ongoing research challenge with respect to cloud security. At the outset, the research reported in this work has addressed three important contributions (i) A new gaussian based traffic attribute-pattern similarity function for evolutionary feature clustering to achieve feature transformation-based dimensionality reduction, (ii) A Gaussian based network traffic similarity function for similarity computation between network traffic instances and (iii) A machine learning model SWASTHIKA which uses feature transformation traffic for detection of low rate and high-rate network attacks. For experimental study, the most recent benchmark dataset namely IoT DoS and DDoS attack dataset available at IEEE Dataport is considered as this dataset has highly non-linear traffic instances which are like the real-world traffic. The performance evaluation of the proposed machine learning model SWASTHIKA is done by considering various classifier evaluation parameters such as accuracy, precision, detection rate, and F-Score. The experiment results proved that the attack detection rate of SWASTHIKA is significantly better compared to state of art machine learning classifiers.

Broad learning approach to Surrogate-Assisted Multi-Objective evolutionary fuzzy clustering algorithm based on reference points for color image segmentation

For some real-world problems, the objective function evaluation is time-consuming and computationally expensive in multi-objective evolutionary algorithms. Surrogate-assistance approaches can be used to estimate the objective function and solve the computationally expensive problem. Taking advantages of the flatted structure and incremental learning, broad learning system (BLS) has shown a great improvement of time efficiency on the premise of ensuring the performance on the classification and regression problems. In this paper, BLS is adopted to design a BLS surrogate-assisted evolutionary framework to boost the time efficiency of clustering-based image segmentation. A BLS-assisted multi-objective evolutionary fuzzy clustering algorithm with reference points (BLS-MOEFC) is proposed. Firstly, two fuzzy clustering objective functions integrating image region information are constructed as the optimized fitness functions for obtaining satisfactory segmentation quality. Secondly, in order to improve the optimization efficiency and reduce the computational time cost, a BLS surrogate model-assisted multi-objective evolutionary framework with reference points is designed to optimize the constructed objective functions. Thirdly, an adaptively updating strategy of parameters and a model update mechanism based on the non-dominated sorting are adopted to improve the prediction accuracy of the BLS surrogate model. Finally, a novel fuzzy clustering validity index integrating region information is designed to select an optimal solution from the final set of non-dominated solutions. Experimental results on Berkeley and Weizmann images show that the proposed algorithm behaves well in the segmentation performance and time cost.

Partitioning of Transportation Networks by Efficient Evolutionary Clustering and Density Peaks

Road traffic congestion has became a major problem in most countries because it affects sustainable mobility. Partitioning a transport network into homogeneous areas can be very useful for monitoring traffic as congestion is spatially correlated in adjacent roads, and it propagates at different speeds as a function of time. Spectral clustering has been successfully applied for the partitioning of transportation networks based on the spatial characteristics of congestion at a specific time. However, this type of classification is not suitable for data that change over time. Evolutionary spectral clustering represents a state-of-the-art algorithm for grouping objects evolving over time. However, the disadvantages of this algorithm are the cubic time complexity and the high memory demand, which make it insufficient to handle a large number of data sets. In this paper, we propose an efficient evolutionary spectral clustering algorithm that solves the drawbacks of evolutionary spectral clustering by reducing the size of the eigenvalue problem. This algorithm is applied in a dynamic environment to partition a transportation network into connected homogeneous regions that evolve with time. The number of clusters is selected automatically by using a density peak algorithm adopted for the classification of traffic congestion based on the sparse snake similarity matrix. Experiments on the real network of Amsterdam city demonstrate the superiority of the proposed algorithm in robustness and effectiveness.

A multi-objective model for optimizing the redundancy allocation, component supplier selection, and reliable activities for multi-state systems

This paper presents a multi-objective availability-redundancy allocation optimization model for a hyper-system. The hyper-system consists of B systems with shared resources. The structure of the systems is series-parallel subsystems consisting of multi-failure and multi-state components. The components may be purchased from different suppliers based on their price and discounts. It is assumed that technical and organizational activities continuously affect the components' failure rates and the subsystems' working conditions before starting the system's mission horizon. The model aims to find the optimal number and the type of the subsystems' components for all systems from each supplier and the level of the technical and organizational activities. The problem is classified as an NP-hard class of problems; thus, four multi-objective meta-heuristics are adapted to solve the proposed model. These four meta-heuristics are non-dominated sorting genetic algorithm type II (NSGA-II) and type III (NSGA-III), non-dominated ranking genetic algorithm (NRGA), and multi-objective evolutionary algorithm based on decomposition (MOEA/D). The parameters of all algorithms are calibrated using response surface methodology. Moreover, a method based on a sequential combination of multi-objective evolutionary algorithms and data clustering is used on the Pareto solutions to yield a smaller and more manageable set of prospective solutions. The results showed the superiority of the NSGA-III and the MOEA/D algorithms to solve the presented model.

Sequencing Independent Molecular Typing of Staphylococcus aureus Isolates: Approach for Infection Control and Clonal Characterization.

ABSTRACTStaphylococcus aureus is a major bacterial human pathogen that causes a wide variety of clinical manifestations. The main aim of the presented study was to determine and optimize a novel sequencing independent approach that enables molecular typing of S. aureus isolates and elucidates the transmission of emergent clones between patients. In total, 987 S. aureus isolates including both methicillin-resistant S. aureus (MRSA) and methicillin-sensitive S. aureus (MSSA) isolates were used to evaluate the novel typing approach combining high-resolution melting (HRM) analysis of multilocus sequence typing (MLST) genes (mini-MLST) and spa gene (spa-HRM). The novel approach’s discriminatory ability was evaluated by whole-genome sequencing (WGS). The clonal relatedness of tested isolates was set by the BURP and BURST approach using spa and MLST data, respectively. Mini-MLST classified the S. aureus isolates into 38 clusters, followed by spa-HRM classifying the isolates into 101 clusters. The WGS proved HRM-based methods to effectively differentiate between related S. aureus isolates. Visualizing evolutionary relationships among different spa-types provided by the BURP algorithm showed comparable results to MLST/mini-MLST clonal clusters. We proved that the combination of mini-MLST and spa-HRM is rapid, reproducible, and cost-efficient. In addition to high discriminatory ability, the correlation between spa evolutionary relationships and mini-MLST clustering allows the variability in population structure to be monitored.IMPORTANCE Rapid and cost-effective molecular typing tools for Staphylococcus aureus epidemiological applications such as transmission tracking, source attribution and outbreak investigations are highly desirable. High-resolution melting based methods are effective alternative to those based on sequencing. Their good reproducibility and easy performance allow prospective typing of large set of isolates while reaching great discriminatory power. In this study, we established a new epidemiological approach to S. aureus typing. This scheme has the potential to greatly improve epidemiological investigations of S. aureus.

Research on the Trust Mechanism of Individual Consumers in Rural Financial Markets Based on the Dynamic CGE Model

In order to obtain the complete equilibrium state of rural financial market and ensure the stable development of rural financial consumer market, this paper introduces CGE model and analyzes the dynamic trust mechanism of individual consumers in rural financial market. In this paper, the single variable evolutionary fuzzy clustering algorithm is used to analyze the orthogonal eigenvector solutions of individual consumers; the big data of individual consumers under the mode of perceived trust is automatically clustered, so as to obtain the fuzzy analogy function of individual consumers in the rural financial market; and finally the prediction value of consumer trust is obtained. The results show that trust, customer satisfaction, and service quality are positively correlated. Under the same sample expectation constraints, the dynamic CGE model is more robust, and the individual consumer trust mechanism of rural financial market in the study area has higher advantages.

Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows.

We explore the transport mechanisms of heat in two- and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the spectral clustering of trajectories of massless fluid tracers that are advected in the flow. Coherent sets result from trajectories that stay closely together under the dynamics of the turbulent flow. For longer times, they are always destroyed by the intrinsic turbulent dispersion of material transport. Here, this constraint is overcome by the application of evolutionary clustering algorithms that add a time memory to the coherent set detection and allows individual trajectories to leak in or out of evolving clusters. Evolutionary clustering thus also opens the possibility to monitor the splits and mergers of coherent sets. These rare dynamic events leave clear footprints in the evolving eigenvalue spectrum of the Laplacian matrix of the trajectory network in both convection flows. The Lagrangian trajectories reveal the individual pathways of convective heat transfer across the fluid layer. We identify the long-term coherent sets as those fluid flow regions that contribute least to heat transfer. Thus, our evolutionary framework defines a complementary perspective on the slow dynamics of turbulent superstructure patterns in convection flows that were recently discussed in the Eulerian frame of reference. The presented framework might be well suited for studies in natural flows, which are typically based on sparse information from drifters and probes.

An Overview of Investigations Concerning Agglomerations in Regional Economy

The concentration of organisations in a city or region allows companies to receive benefits without additional costs and increase their productivity. It has been empirically proven that urbanisation and localisation effects of agglomerations contribute to economic growth and development, and therefore should be taken into account in regional and urban policies. The article considers the factors of agglomeration formation, their specific development and impact on the economy of regions and cities. The paper examines studies on the territorial distribution of companies and the population, including creative capital, showing the connection with innovative systems and knowledge capital. The research demonstrates how international trade, market competition, the transport system development and many other factors affect agglomerations. The study of agglomeration processes intersects with other fields of science, such as evolutionary economics, cluster organisation, specialisation and diversification, demography of firms. To cover the topic, works in the field of agglomeration processes were systematised by using time-domain, terminological and geographical analysis, as well by studying definitions and typology, based on data obtained from Google Scholar and Web of Science for 1959–2018. It is revealed that agglomerations are considered in such scientific fields as economics, geography, regional urban planning, urban studies, management and regional studies. The key terms are agglomeration economy (economics), localisation, urbanisation, agglomeration forces, agglomerative and deglomerative factors. These works are geographically distributed, and most of them are conducted in the USA (mainly at the University of California), Great Britain (London School of Economics and Law) and China (Chinese Academy of Sciences and Peking University). The presented research review will serve as a starting point for a more in-depth study of agglomeration processes in various fields of economics.

An Evolutionary Algorithm-Based Vehicular Clustering Technique for VANETs

Many precious lives are lost world-wide due to road accidents. To counter this issue, the ultimate solution is Vehicular ad hoc networks (VANETs). Due to the high mobility of vehicles and varying network topology in VANETs, efficient communication among the vehicular nodes is of extreme importance. To enhance communication proficiency in VANETs, clustering is a renowned procedure. Therefore, a clustering algorithm based on Moth-Flame Optimization (MFO), titled AMONET, is projected which can effectively work in high mobility nodes scenario of VANETs. AMONET is based on bio inspired procedure and creates optimized clusters for reliable and efficient communication. Our algorithm is assessed experimentally with well-known procedures such as Ant Colony Optimization (ACO), Comprehensive Learning Particle Swarm Optimization (CLPSO) and Multi Objective Particle Swarm Optimization (MOPSO). Several experiments are conducted to measure the comparative efficiency of these procedures. The average cumulative results for all the grid sizes are 27.1% for AMONET while 36.3% for ACO, 54.9% for CLPSO and 58.7% for MOPSO. The results signify that AMONET produces near ideal results, covers the entire network and generates least number of clusters. It is an efficient technique to accomplish vehicular clustering with the purpose of improving the network’s overall performance and consequently reducing the routing cost of the vehicular network.

Research on Dynamic Community Detection Method Based on an Improved Pity Beetle Algorithm

In the last decade, community detection in dynamic networks has received increasing attention, because it can not only uncover the community structure of the network at any time but also reveal the regularity of dynamic networks evolution. Although methods based on the framework of evolutionary clustering are promising for dynamic community detection, there is still room for further improvement in the snapshot quality and the temporal cost. In this study, a dynamic community detection algorithm based on optional pathway guide pity beetle algorithm (DYN-OPGPBA), which is a novel dynamic community detection method based on the framework of evolutionary clustering, is proposed. We propose an improved PBA for community detection of the network at the first time step, including a discrete search strategy based on adjacent nodes, a closeness-based community modification strategy and a crowded community split strategy. Compared with many representative static community detection methods, the proposed method has some superior detection accuracy. A neighbour vector competition-based individual update strategy and an external population size restriction mechanism are also proposed for community detection at subsequent time steps. Results show that DYN-OPGPBA has a better balance between snapshot quality and temporal cost than two representative dynamic community detection methods.

An Empirical Study of Cluster-Based MOEA/D Bare Bones PSO for Data Clustering †

Previously, cluster-based multi or many objective function techniques were proposed to reduce the Pareto set. Recently, researchers proposed such techniques to find better solutions in the objective space to solve engineering problems. In this work, we applied a cluster-based approach for solution selection in a multiobjective evolutionary algorithm based on decomposition with bare bones particle swarm optimization for data clustering and investigated its clustering performance. In our previous work, we found that MOEA/D with BBPSO performed the best on 10 datasets. Here, we extend this work applying a cluster-based approach tested on 13 UCI datasets. We compared with six multiobjective evolutionary clustering algorithms from the existing literature and ten from our previous work. The proposed technique was found to perform well on datasets highly overlapping clusters, such as CMC and Sonar. So far, we found only one work that used cluster-based MOEA for clustering data, the hierarchical topology multiobjective clustering algorithm. All other cluster-based MOEA found were used to solve other problems that are not data clustering problems. By clustering Pareto solutions and evaluating new candidates against the found cluster representatives, local search is introduced in the solution selection process within the objective space, which can be effective on datasets with highly overlapping clusters. This is an added layer of search control in the objective space. The results are found to be promising, prompting different areas of future research which are discussed, including the study of its effects with an increasing number of clusters as well as with other objective functions.

EvolveCluster: an evolutionary clustering algorithm for streaming data

Data has become an integral part of our society in the past years, arriving faster and in larger quantities than before. Traditional clustering algorithms rely on the availability of entire datasets to model them correctly and efficiently. Such requirements are not possible in the data stream clustering scenario, where data arrives and needs to be analyzed continuously. This paper proposes a novel evolutionary clustering algorithm, entitled EvolveCluster, capable of modeling evolving data streams. We compare EvolveCluster against two other evolutionary clustering algorithms, PivotBiCluster and Split-Merge Evolutionary Clustering, by conducting experiments on three different datasets. Furthermore, we perform additional experiments on EvolveCluster to further evaluate its capabilities on clustering evolving data streams. Our results show that EvolveCluster manages to capture evolving data stream behaviors and adapts accordingly.

A novel cluster detection of COVID-19 patients and medical disease conditions using improved evolutionary clustering algorithm star

With the increasing number of samples, the manual clustering of COVID-19 and medical disease data samples becomes time-consuming and requires highly skilled labour. Recently, several algorithms have been used for clustering medical datasets deterministically; however, these definitions have not been effective in grouping and analysing medical diseases. The use of evolutionary clustering algorithms may help to effectively cluster these diseases. On this presumption, we improved the current evolutionary clustering algorithm star (ECA*), called iECA*, in three manners: (i) utilising the elbow method to find the correct number of clusters; (ii) cleaning and processing data as part of iECA* to apply it to multivariate and domain-theory datasets; (iii) using iECA* for real-world applications in clustering COVID-19 and medical disease datasets. Experiments were conducted to examine the performance of iECA* against state-of-the-art algorithms using performance and validation measures (validation measures, statistical benchmarking, and performance ranking framework). The results demonstrate three primary findings. First, iECA* was more effective than other algorithms in grouping the chosen medical disease datasets according to the cluster validation criteria. Second, iECA* exhibited the lower execution time and memory consumption for clustering all the datasets, compared to the current clustering methods analysed. Third, an operational framework was proposed to rate the effectiveness of iECA* against other algorithms in the datasets analysed, and the results indicated that iECA* exhibited the best performance in clustering all medical datasets. Further research is required on real-world multi-dimensional data containing complex knowledge fields for experimental verification of iECA* compared to evolutionary algorithms.

Understanding the Angular Momentum Evolution of T Tauri and Herbig Ae/Be Stars

Abstract We investigate a sample of six Herbig Ae/Be stars belonging to the Orion OB1 association, as well as 73 low-mass objects, members of the σ Orionis cluster, in order to explore the angular momentum evolution at early stages of evolution, and its possible connection with main-sequence Ap/Bp magnetic stars. Using FIES and HECTOCHELLE spectra, we obtain projected rotational velocities through two independent methods. Individual masses, radii, and ages are computed using evolutionary models, distance, and cluster extinction. Under the assumption that similar physical processes operate in both T Tauri and Herbig Ae/Be stars, we construct snapshots of the protostar’s rotation against mass during the first 10 Myr with the aid of a rotational model that includes a variable disk lifetime, changes in the stellar moment of inertia, a dipolar magnetic field with variable strength, and angular momentum loss through stellar winds powered by accretion. We use these snapshots, as well as the rotational data, to infer a plausible scenario for the angular momentum evolution. We find that magnetic field strengths of a few kilo-Gauss at 3 Myr are required to match the rotational velocities of both groups of stars. Models with masses between 2 M ⊙ and 3 M ⊙ display larger angular momentum values by a factor of ∼3, in comparison to stars of similar spectral types on the main sequence. Even though some quantitative estimates on this dramatic decrease with age for Ap/Bp magnetic main-sequence stars are presented, the results obtained for the angular momentum evolution do not explain their low rotation rates.

Coarse–fine surrogate model driven multiobjective evolutionary fuzzy clustering algorithm with dual memberships for noisy image segmentation

To improve the segmentation performance and boost evolutionary efficiency of multiobjective evolutionary clustering algorithms on noisy images, this paper proposes a coarse–fine surrogate model driven multiobjective evolutionary fuzzy clustering algorithm with dual membership functions (CFS-MOEFC). The existing fuzzy clustering validity-based fitness functions generally consider one single fuzzy membership function, which cannot fully process the uncertainty in an image. Moreover, most existing fitness functions used in image segmentation only utilize one type of spatial information derived from the image, which cannot behave robust on images with uncertain types of noise. To deal with the above problems, dual fuzzy membership functions are first designed by utilizing the local and non-local image spatial information. Then, the designed dual membership functions and the two kinds of spatial information are both used to construct spatial information-motivated fitness functions for image segmentation. To promote the time efficiency, the coarse–fine surrogate model is employed to assist the evolutionary optimization process, such as approximating the fitness functions instead of real function evaluations and evolving satisfactory cluster centers for CFS-MOEFC. Besides, a dual memberships-driven cluster validity index combining the local and non-local spatial information is designed for selecting an optimal solution from the final non-dominated solution set of CFS-MOEFC. Experiments on Berkeley and Magnetic Resonance (MR) images indicate that CFS-MOEFC greatly improves the segmentation accuracy on images with multiple types of noise, preserves more significant detailed image information, and behaves well on time cost comparing with state-of-the-art methods.

Evolutionary Clustering and Analysis of User Behaviour in Online Forums

In this paper we cluster and analyse temporal user behaviour in online communities. We adapt a simple unsupervised clustering algorithm to an evolutionary setting where we cluster users into prototypical behavioural roles based on features derived from their ego-centric reply-graphs. We then analyse changes in the role membership of the users over time, the change in role composition of forums over time and examine the differences between forums in terms of role composition. We perform this analysis on 200 forums from a popular national bulletin board and 14 enterprise technical support forums.

A density-based evolutionary clustering algorithm for intelligent development

Inspired by the clustering mechanism of human cognitive development, this paper proposes a density-based evolutionary clustering algorithm based on incremental data (DBEC). The DBEC algorithm is developed from a zero sample state without prior knowledge, and the control parameter can evolve as the number of samples increases, which simulates the human cognitive development process structurally. Furthermore, we propose conservative, robust, and radical DBEC algorithms based on different combinations of strategies. These three types of DBEC algorithms have different characteristics, and can find various clustering attributes of the samples to be clustered. Finally, we analyse the performance of three types of DBEC algorithms and compare their result with those of other popular clustering algorithms on the datasets in the experiment. The results show the effectiveness of DBEC algorithms.