Multi-objective Clustering Algorithm Research Articles

Multi-Objective Automatic Clustering Algorithm Based on Evolutionary Multi-Tasking Optimization

Data mining technology is the process of extracting hidden knowledge and potentially useful information from a large number of incomplete, noisy, and random practical application data. The clustering algorithm based on multi-objective evolution has obvious advantages compared with the traditional single-objective method. In order to further improve the performance of evolutionary multi-objective clustering algorithms, this paper proposes a multi-objective automatic clustering model based on evolutionary multi-task optimization. Based on the multi-objective clustering algorithm that automatically determines the value of k, evolutionary multi-task optimization is introduced to deal with multiple clustering tasks simultaneously. A set of non-dominated solutions for clustering results is obtained by concurrently optimizing the overall deviation and connectivity index. Multi-task adjacency coding based on a locus adjacency graph was designed to encode the clustered data. Additionally, an evolutionary operator based on relevance learning was designed to facilitate the evolution of individuals within the population. It also facilitates information transfer between individuals with different tasks, effectively avoiding negative transfer. Finally, the proposed algorithm was applied to both artificial datasets and UCI datasets for testing. It was then compared with traditional clustering algorithms and other multi-objective clustering algorithms. The results verify the advantages of the proposed algorithm in clustering accuracy and algorithm convergence.

Multi-Objective Optimization Technology for Building Energy-Saving Renovation Strategy Based on Genetic Algorithm

Building energy-saving design is significant for the industry to achieve carbon reduction and sustainable development. Firstly, a multi-objective model for energy consumption, cost, and carbon emissions is established based on the three-dimensional perspectives of society, nature, and economy. Then, a polynomial operator is used to improve the non dominated sorting genetic algorithm to calculate the optimal solution set. The low computational efficiency caused by direct coupling of algorithms in traditional optimization processes is expected to be addressed. According to the results, for the Square1 dataset and Iris dataset, the algorithm proposed in this study improved the reverse distance and convergence metrics by more than 70% compared to support vector machine-genetic algorithm and multi-objective clustering algorithm, with values closer to 0. The solution solved by this algorithm had lower building costs, energy consumption, and carbon emissions, with values of 345200 yuan, 2374 KWh/year, and 26 tons, respectively. This validates the effectiveness of the multi-objective model and solving algorithm established in the study, which helps to obtain the optimal energy-saving design scheme and provides reference for low-carbon optimization of building.

An Improved Evolutionary Multi-Objective Clustering Algorithm Based on Autoencoder

Evolutionary multi-objective clustering (EMOC) algorithms have gained popularity recently, as they can obtain a set of clustering solutions in a single run by optimizing multiple objectives. Particularly, in one type of EMOC algorithm, the number of clusters k is taken as one of the multiple objectives to obtain a set of clustering solutions with different k. However, the numbers of clusters k and other objectives are not always in conflict, so it is impossible to obtain the clustering solutions with all different k in a single run. Therefore, evolutionary multi-objective k-clustering (EMO-KC) has recently been proposed to ensure this conflict. However, EMO-KC could not obtain good clustering accuracy on high-dimensional datasets. Moreover, EMO-KC’s validity is not ensured as one of its objectives (SSDexp, which is transformed from the sum of squared distances (SSD)) could not be effectively optimized and it could not avoid invalid solutions in its initialization. In this paper, an improved evolutionary multi-objective clustering algorithm based on autoencoder (AE-IEMOKC) is proposed to improve the accuracy and ensure the validity of EMO-KC. The proposed AE-IEMOKC is established by combining an autoencoder with an improved version of EMO-KC (IEMO-KC) for better accuracy, where IEMO-KC is improved based on EMO-KC by proposing a scaling factor to help effectively optimize the objective of SSDexp and introducing a valid initialization to avoid the invalid solutions. Experimental results on several datasets demonstrate the accuracy and validity of AE-IEMOKC. The results of this paper may provide some useful information for other EMOC algorithms to improve accuracy and convergence.

Ensemble CART surrogate-assisted automatic multi-objective rough fuzzy clustering algorithm for unsupervised image segmentation

Multi-objective clustering algorithms (MOCAs) are popular in unsupervised image segmentation due to their merit of meeting multiple segmentation requirements and the prospect of automatically estimating the number of clusters. However, most of them suffer from high time costs and are easily to be influenced by the uncertainty when handling real complex images. To address these issues, we propose an ensemble classification and regression tree (CART) surrogate-assisted automatic multi-objective rough fuzzy clustering (ECS-AMRFC) algorithm for unsupervised image segmentation. Firstly, a cluster medoid-based encoding scheme is employed to represent solutions with different number of clusters and meanwhile lessen the length of encoding. Then, we design an ensemble CART as the surrogate model to significantly reduce the computational burden. Moreover, a surrogate model management strategy is proposed to accelerate the optimization and enhance the quality of surrogate modeling. To handle the uncertainty in data, we extend the rough fuzzy clustering into MOCAs and construct three complementary objective functions to seek proper cluster medoids from multiple perspectives. In addition, the Gaussian kernel is introduced into the objective functions to handle image pixels that cannot separate linearly in the feature space. Finally, a kernelized rough fuzzy clustering validity index is defined to automatically select the optimal solution with no requirements of any prior knowledge. Experiments show that ECS-AMRFC not only identifies appropriate number of clusters on different kinds of images, but also obtains better segmentation results than state-of-the-art rough fuzzy clustering algorithms and automatic MOCAs.

Design of Log Analysis System Based on Multi-Object Clustering Algorithm

With the rapid development of the information age and the continuous expansion of data, all walks of life have begun to collect and analyze massive amounts of data to extract information that is valuable to them. Clustering technology in data mining is an important means of data analysis. Because different data sets have different distribution characteristics, traditional single-object clustering cannot adapt to the effective processing of different data sets, so multi-object clustering has gradually become a research hotspot. The purpose of this paper is the design of log analysis system based on a multi-objective clustering algorithm. This article first determines the main goals of the log analysis system and performs a detailed analysis of the system’s demanding functional analysis and demanding non-functionality respectively. The log analysis system is mainly divided into five modules for the detailed design of the log analysis system. After the system design is completed, various functional modules are completed through corresponding technologies, the entire log system is tested for attacks, and the system is further improved. Finally, the system can completely analyze the attack type through log analysis and carry out relevant early warnings to meet the needs of users. When the data set is 1.8MB, the convergence time of the K-medoid algorithm is 3678.49, and the convergence time of the algorithm in this paper is 2536.42. When the data reaches 165MB, the convergence time of the algorithm in this paper is 4326.28, and the convergence time of the K-medoid algorithm is 8184. This shows that as the scale of data continues to increase, the processing time difference changes and the processing speed of this algorithm has obvious advantages.

A reliable region information driven kriging-assisted multiobjective rough fuzzy clustering algorithm for color image segmentation

Multiobjective clustering algorithms (MOCAs) are becoming increasingly popular with the merit of segmenting images from multiple perspectives. The performances of MOCAs highly depend on their fitness functions. However, most existing MOCAs adopt one pair of complementary fitness functions, which always measure intra-class compactness and inter-class separation, respectively. This may result in insufficient ability to recognize and mine feature structures from complex images. Moreover, information within color images, such as region information and uncertain information, can barely receive enough attention in MOCAs. To resolve these problems, we propose a reliable region information driven Kriging-assisted multiobjective rough fuzzy clustering algorithm (RRI-KMRFC). Firstly, a reliability-based region information extraction strategy (RRIES) is designed to obtain reliable image information with satisfactory regional homogeneity and abundant image details. Secondly, the derived region information is used to construct three complementary fitness functions, focusing on rough intra-class compactness, rough inter-class separation, and regional consistency, respectively. Such fitness functions can effectively identify the clustering structure, maintain contour details, and characterize uncertain information from color images. To efficiently optimize the proposed functions, an incremental Kriging-assisted evolutionary framework is presented to decrease the expensive function evaluations in which an improved infill sampling strategy is devised to assist in finding unexplored areas in the decision space. Finally, a rough fuzzy clustering validity index with reliable region information is proposed to select the optimal trade-off solution. Experiments performed on Berkeley and Weizmann images confirm the effectiveness and robustness of RRI-KMRFC.

A Parallel Multiobjective PSO Weighted Average Clustering Algorithm Based on Apache Spark

Multiobjective clustering algorithm using particle swarm optimization has been applied successfully in some applications. However, existing algorithms are implemented on a single machine and cannot be directly parallelized on a cluster, which makes it difficult for existing algorithms to handle large-scale data. With the development of distributed parallel computing framework, data parallelism was proposed. However, the increase in parallelism will lead to the problem of unbalanced data distribution affecting the clustering effect. In this paper, we propose a parallel multiobjective PSO weighted average clustering algorithm based on apache Spark (Spark-MOPSO-Avg). First, the entire data set is divided into multiple partitions and cached in memory using the distributed parallel and memory-based computing of Apache Spark. The local fitness value of the particle is calculated in parallel according to the data in the partition. After the calculation is completed, only particle information is transmitted, and there is no need to transmit a large number of data objects between each node, reducing the communication of data in the network and thus effectively reducing the algorithm's running time. Second, a weighted average calculation of the local fitness values is performed to improve the problem of unbalanced data distribution affecting the results. Experimental results show that the Spark-MOPSO-Avg algorithm achieves lower information loss under data parallelism, losing about 1% to 9% accuracy, but can effectively reduce the algorithm time overhead. It shows good execution efficiency and parallel computing capability under the Spark distributed cluster.

Research on credit risk assessment of e-commerce enterprises based on improved multi-objective clustering algorithm

Research on credit risk assessment of e-commerce enterprises based on improved multi-objective clustering algorithm

Research on credit risk assessment of e-commerce enterprises based on improved multi-objective clustering algorithm

Research on credit risk assessment of e-commerce enterprises based on improved multi-objective clustering algorithm

Hierarchical Topology-Based Cluster Representation for Scalable Evolutionary Multiobjective Clustering.

Evolutionary multiobjective clustering (MOC) algorithms have shown promising potential to outperform conventional single-objective clustering algorithms, especially when the number of clusters k is not set before clustering. However, the computational burden becomes a tricky problem due to the extensive search space and fitness computational time of the evolving population, especially when the data size is large. This article proposes a new, hierarchical, topology-based cluster representation for scalable MOC, which can simplify the search procedure and decrease computational overhead. A coarse-to-fine-trained topological structure that fits the spatial distribution of the data is utilized to identify a set of seed points/nodes, then a tree-based graph is built to represent clusters. During optimization, a bipartite graph partitioning strategy incorporated with the graph nodes helps in performing a cluster ensemble operation to generate offspring solutions more effectively. For the determination of the final result, which is underexplored in the existing methods, the usage of a cluster ensemble strategy is also presented, whether k is provided or not. Comparison experiments are conducted on a series of different data distributions, revealing the superiority of the proposed algorithm in terms of both clustering performance and computing efficiency.

Enhanced Connectivity Validity Measure Based on Outlier Detection for Multi-Objective Metaheuristic Data Clustering Algorithms

Data clustering algorithms experience challenges in identifying data points that are either noise or outlier. Hence, this paper proposes an enhanced connectivity measure based on the outlier detection approach for multi-objective data clustering problems. The proposed algorithm aims to improve the quality of the solution by utilising the local outlier factor method (LOF) with the connectivity validity measure. This modification is applied to select the neighbour data point’s mechanism that can be modified to eliminate such outliers. The performance of the proposed approach is assessed by applying the multi-objective algorithms to eight real-life and seven synthetic two-dimensional datasets. The external validity is evaluated using the F-measure, while the performance assessment matrices are employed to assess the quality of Pareto-optimal sets like the coverage and overall non-dominant vector generation. Our experimental results proved that the proposed outlier detection method has enhanced the performance of the multi-objective data clustering algorithms.

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.

Evolutionary Multiobjective Clustering Algorithms With Ensemble for Patient Stratification.

Patient stratification has been studied widely to tackle subtype diagnosis problems for effective treatment. Due to the dimensionality curse and poor interpretability of data, there is always a long-lasting challenge in constructing a stratification model with high diagnostic ability and good generalization. To address these problems, this article proposes two novel evolutionary multiobjective clustering algorithms with ensemble (NSGA-II-ECFE and MOEA/D-ECFE) with four cluster validity indices used as the objective functions. First, an effective ensemble construction method is developed to enrich the ensemble diversity. After that, an ensemble clustering fitness evaluation (ECFE) method is proposed to evaluate the ensembles by measuring the consensus clustering under those four objective functions. To generate the consensus clustering, ECFE exploits the hybrid co-association matrix from the ensembles and then dynamically selects the suitable clustering algorithm on that matrix. Multiple experiments have been conducted to demonstrate the effectiveness of the proposed algorithm in comparison with seven clustering algorithms, twelve ensemble clustering approaches, and two multiobjective clustering algorithms on 55 synthetic datasets and 35 real patient stratification datasets. The experimental results demonstrate the competitive edges of the proposed algorithms over those compared methods. Furthermore, the proposed algorithm is applied to extend its advantages by identifying cancer subtypes from five cancer-related single-cell RNA-seq datasets.

Distributed clustering in peer to peer networks using multi-objective whale optimization

Multi-objective clustering algorithms have superiority over its single objective counterparts as they include additional knowledge on properties of data in the form of objectives to discover the underlying clusters present in various datasets. This paper proposes a distributed clustering algorithm using multi-objective whale optimization (DMOWOA) for peer to peer network. The algorithm minimizes two objective functions to perform clustering, namely : Total Euclidean Deviation and Total Symmetrical Deviation. Both objective values are shared using diffusion method of cooperation to obtain correct partitioning at each peer. A single solution from the non-dominated solutions is selected as final solution based on its minimum distance to origin in the normalized objective space. The proposed algorithm’s performance is evaluated on four synthetic and five real-life wireless sensor network datasets (Canada weather station dataset, Delhi air pollution content dataset, Intel laboratory dataset, Washington cook agronomy farm dataset and Thames river water quality dataset). The comparison is carried out with multi-objective distributed particle swarm optimization (DMOPSO), distributed K-Means (DK-Means) and other seven recently developed nature inspired multi-objective clustering techniques. The proposed algorithm in most of the cases outperforms the existing techniques in terms of statistical measures Minkowski Score, Dunn index and Silhouette index. The average rank of the proposed algorithm is also better in Kruskal–Wallis statistical test.

Multiobjective clustering algorithm for complex data in learning management systems

Learning Management Systems (LMS) is now an emergent technology where massive data are collected and requires handling. This data comes from different sources with multiple features which represents another complex paradigm. However, as part of business intelligence and decision support, this data needs to be classified and analyzed for the management, teachers, as well as students to make the appropriate decisions. Thus, one of the effective data analysis methods is clustering. However, LMS data encompasses multi-features, which are not sufficient to make appropriate decisions. Therefore, single feature clustering algorithms would not help LMS decision-makers. Consequently, multifeatured/multiobjective clustering algorithms could be one of the proposed solutions. Thus, looking at different multiobjective clustering algorithms as compared to the LMS nature of data, those algorithms do not satisfy the clustering purpose. In addition, the LMS data could be huge, complex, and sequential algorithms would not help as well. Thus, this paper is a step forward towards clustering LMS data for better decision making. The paper proposes a new clustering framework based upon distributed systems and a new multiobjective algorithm for the purpose of LMS clustering. The algorithm has been examined experimentally in order to answer some of the questions that help taking decision based upon LMS collected data.

Multi-objective clustering algorithm using particle swarm optimization with crowding distance (MCPSO-CD)

Clustering, an unsupervised method of grouping sets of data, is used as a solution technique in various fields to divide and restructure data to become more significant and transform them into more useful information. Generally, clustering is difficult and complex phenomenon, where the appropriate numbers of clusters are always unknown, comes with a large number of potential solutions, and as well the datasets are unsupervised. These problems can be addressed by the Multi-Objective Particle Swarm Optimization (MOPSO) approach, which is commonly used in addressing optimization problems. However, MOPSO algorithm produces a group of non-dominated solutions which make the selection of an “appropriate” Pareto optimal or non-dominated solution more difficult. According to the literature, crowding distance is one of the most efficient algorithms that was developed based on density measures to treat the problem of selection mechanism for archive updates. In an attempt to address this problem, the clustering-based method that utilizes crowding distance (CD) technique to balance the optimality of the objectives in Pareto optimal solution search is proposed. The approach is based on the dominance concept and crowding distances mechanism to guarantee survival of the best solution. Furthermore, we used the Pareto dominance concept after calculating the value of crowding degree for each solution. The proposed method was evaluated against five clustering approaches that have succeeded in optimization that comprises of K-means Clustering, MCPSO, IMCPSO, Spectral clustering, Birch, and average-link algorithms. The results of the evaluation show that the proposed approach exemplified the state-of-the-art method with significant differences in most of the datasets tested.

A Unified Multi-view Clustering Algorithm Using Multi-objective Optimization Coupled with Generative Model

There is a large body of works on multi-view clustering that exploit multiple representations (or views) of the same input data for better convergence. These multiple views can come from multiple modalities (image, audio, text) or different feature subsets. Obtaining one consensus partitioning after considering different views is usually a non-trivial task. Recently, multi-objective based multi-view clustering methods have suppressed the performance of single objective based multi-view clustering techniques. One key problem is that it is difficult to select a single solution from a set of alternative partitionings generated by multi-objective techniques on the final Pareto optimal front. In this article, we propose a novel multi-objective based multi-view clustering framework that overcomes the problem of selecting a single solution in multi-objective based techniques. In particular, our proposed framework has three major components as follows: (i) multi-view based multi-objective algorithm, Multiview-AMOSA, for initial clustering of data points; (ii) a generative model for generating a combined solution having probabilistic labels; and (iii) K -means algorithm for obtaining the final labels. As the first component, we have adopted a recently developed multi-view based multi-objective clustering algorithm to generate different possible consensus partitionings of a given dataset taking into account different views. A generative model is coupled with the first component to generate a single consensus partitioning after considering multiple solutions. It exploits the latent subsets of the non-dominated solutions obtained from the multi-objective clustering algorithm and combines them to produce a single probabilistic labeled solution. Finally, a simple clustering algorithm, namely K -means, is applied on the generated probabilistic labels to obtain the final cluster labels. Experimental validation of our proposed framework is carried out over several benchmark datasets belonging to three different domains; UCI datasets, multi-view datasets, search result clustering datasets, and patient stratification datasets. Experimental results show that our proposed framework achieves an improvement of around 2%--4% over different evaluation metrics in all the four domains in comparison to state-of-the art methods.

Research on Multi-objective clustering Optimization of Logistics Distribution Line

In order to improve the ability of logistics distribution line optimization, a multi-objective clustering algorithm based on particle clustering is proposed. The maximum density sparse detection and adaptive optimization method are used to schedule the logistics distribution route. The particle swarm optimization (PSO) algorithm is used to construct the multi-objective optimization model of the logistics distribution line. The global optimization characteristics of the particle swarm optimization algorithm are used to optimize the logistics distribution route. PSO adaptive clustering method is used to realize multi-objective optimization of logistics distribution path. The simulation results show that the method has better performance in the optimization control of logistics distribution line, improves the efficiency of logistics, reduces the loss of logistics line, and improves the throughput performance of logistics line.

Presenting the Hybrid Algorithm of Honeybee - Harmony in Clustering and Routing of Wireless Sensor Networks

Background: Wireless sensor networks are considered as one of the 21st century's most important technologies. Sensors in wireless sensor networks usually have limited and sometimes non-rechargeable batteries, which they are supposed to be preserved for months or even years. That's why the energy consumption in these networks is of a great importance. Objective: One way to improve energy consumption in a wireless sensor network is to use clustering. In clustered networks, one node is known as the cluster head and other nodes as normal members, which normal nodes send the collected data to the cluster head, and the cluster head sends the information to the base station either by a single step or by multiple steps. Method: Using clustering simplifies resource management and increases scalability, reliability, and the network lifetime. Although the cluster formation involves a time- overhead and how to choose the cluster head is another problem, but its advantages are more than its disadvantages. : The primary aim of this study is to offer a solution to reduce energy consumption in the sensor network. In this study, during the selection of cluster heads, Honeybee Algorithm is used and also for routing, Harmonic Search Algorithm is used. In this paper, the simulation is performed by using MATLAB software and the proposed method is compared with the Low Energy Adaptive Clustering Hierarchy (LEACH) and the multi-objective fuzzy clustering algorithm (MOFCA). Result and Conclusion: By simulations of this study, we conclude that this research has remarkably increased the network lifetime with respect to EECS, LEACH, and MOFCA algorithms. In view of the energy constraints of the wireless sensor network and the non-rechargeable batteries in most cases, providing such solutions and using metaheuristic algorithms can result in a significant reduction in energy consumption and, consequently, increase in the network lifetime.

Multi-objective clustering: a kernel based approach using Differential Evolution

ABSTRACTA multi-objective algorithm is always favoured over a single objective algorithm as it considers different aspects of a dataset in the form of various objectives. In this article, a multi-objective clustering algorithm has been proposed based on Differential Evolution. Here, three objectives have been considered to handle different complex datasets. In addition to this, a kernel function is hybridised with the objectives to evaluate the data on a hyperspace for reducing the impact of nonlinearity on cluster formation. Moreover, to get the best compromised solution from the Pareto front an effective fuzzy concept has been followed. Five metaheuristic approaches have been taken into consideration for performance comparison. These methodologies have been applied to twelve datasets and the result reveals the efficacy of the proposed model in data clustering.