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A clustering method combining differential evolution with the k-means algorithm

PATTERN RECOGNITION LETTERS 2011年第12期32卷 1613-1621页

作者： kwedlo, Wojciech Bialystok Tech Univ Fac Comp Sci PL-15351 Bialystok Poland

The present paper considers the problem of partitioning a dataset into a known number of clusters using the sum of squared errors criterion (SSE). A new clustering method, called DE-kM, which combines differential evolution algorithm (DE) with the well known k-means procedure is described. In the method, the k-means algorithm is used to fine-tune each candidate solution obtained by mutation and crossover operators of DE. Additionally, a reordering procedure which allows the evolutionary algorithm to tackle the redundant representation problem is proposed. The performance of the DE-kM clustering method is compared to the performance of differential evolution, global k-means method, genetic k-means algorithm and two variants of the k-means algorithm. The experimental results show that if the number of clusters k is sufficiently large, DE-kM obtains solutions with lower SSE values than the other five algorithms. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Cluster analysis Differential evolution k-means algorithm

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Improved k-means algorithm based on density Canopy

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kNOWLEDGE-BASED SYSTEMS 2018年 145卷 289-297页

作者： Zhang, Geng Zhang, Chengchang Zhang, Huayu China Elect Power Res Inst Informat & Commun Dept Beijing Peoples R China Chongqing Univ Posts & Telecommun Coll Elect Engn Chongqing Peoples R China

In order to improve the accuracy and stability of k-means algorithm and solve the problem of determining the most appropriate number k of clusters and best initial seeds, an improved k-means algorithm based on density Canopy is proposed. Firstly, the density of sample data sets, the average sample distance in clusters and the distance between clusters are calculated, choosing the density maximum sampling point as the first cluster center and removing the density cluster from the data sets. Defining the product of sample density, the reciprocal of the average distance between the samples in the cluster, and the distance between the clusters as weight product, the other initial seeds is determined by the maximum weight product in the remaining data sets until the data sets is empty. The density Canopy is used as the preprocessing procedure of k-means and its result is used as the cluster number and initial clustering center of k-means algorithm. Finally, the new algorithm is tested on some well-known data sets from UCI machine learning repository and on some simulated data sets with different proportions of noise samples. The simulation results show that the improved k-means algorithm based on density Canopy achieves better clustering results and is insensitive to noisy data compared to the traditional k-means algorithm, the Canopy-based k-means algorithm, Semi-supervised k-means++ algorithm and k-means u* algorithm. The clustering accuracy of the proposed k-means algorithm based on density Canopy is improved by 30.7%, 6.1%, 5.3% and 3.7% on average on UCI data sets, and improved by 44.3%, 3.6%, 9.6% and 8.9% on the simulated data sets with noise signal respectively. With the increase of the noise ratio, the noise immunity of the new algorithm is more obvious, when the noise ratio reached 30%, the accuracy rate is improved 50% and 6% compared to the traditional k-means algorithm and the Canopy-based k-means algorithm. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Density Canopy k-means algorithm Weight product Optimal value k Initial seed

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An evolutionary technique based on k-means algorithm for optimal clustering in R^N

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INFORMATION SCIENCES 2002年第1-4期146卷 221-237页

作者： Bandyopadhyay, S Maulik, U Indian Stat Inst Inst Machine Intelligence Kolkata 700108 W Bengal India Kalyani Govt Engn Coll Dept Comp Sci & Engn Kalyani Nadia India

A genetic algorithm-based efficient clustering technique that utilizes the principles of k-means algorithm is described in this paper. The algorithm called kGA-clustering, while exploiting the searching capability of k-means, avoids its major limitation of getting stuck at locally optimal values. Its superiority over the k-means algorithm and another genetic algorithm-based clustering method, is extensively demonstrated for several artificial and real life data sets. A real life application of the kGA-clustering in classifying the pixels of a satellite image of a part of the city of Mumbai is provided. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： clustering genetic algorithms k-means algorithm satellite image classification

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Towards multicriteria clustering:: An extension of the k-means algorithm

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第2期158卷 390-398页

作者： De Smet, Y Guzmán, LM Free Univ Brussels Serv Math Gest B-1050 Brussels Belgium

The research within the multicriteria classification field is mainly focused on the assignment of actions to pre-defined classes. Nevertheless the building of multicriteria categories remains a theoretical question still not studied in detail. To tackle this problem, we propose an extension of the well-known k-means algorithm to the multicriteria framework. This extension relies on the definition of a multicriteria distance based on the preference structure defined by the decision maker. Thus, two alternatives will be similar if they are preferred, indifferent and incomparable to more or less the same actions. Armed with this multicriteria distance, we will be able to partition the set of alternatives into classes that are meaningful from a multicriteria perspective. Finally, the examples of the country risk problem and the diagnosis of firms will be treated to illustrate the applicability of this method. (C) 2003 Elsevier B.V. All rights reserved.

关键词： multiple criteria analysis clustering preference modeling k-means algorithm

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Analysis of athletes' stadium stress source based on improved layered k-means algorithm

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020年第4期39卷 5905-5914页

作者： Gong, Chen Northeast Elect Power Univ Sch Phys Educ Jilin 132012 Jilin Peoples R China

Most of the research on stressors is in the medical field, and there are few analysis of athletes' stressors, so it can not provide reference for the analysis of athletes' stressors. Based on this, this study combines machine learning algorithms to analyze the pressure source of athletes' stadium. In terms of data collection, it is mainly obtained through questionnaire survey and interview form, and it is used as experimental data after passing the test. In order to improve the performance of the algorithm, this paper combines the known k-means algorithm with the layering algorithm to form a new improved layered k-means algorithm. At the same time, this paper analyzes the performance of the improved hierarchical k-means algorithm through experimental comparison and compares the clustering results. In addition, the analysis system corresponding to the algorithm is constructed based on the actual situation, the algorithm is applied to practice, and the user preference model is constructed. Finally, this article helps athletes find stressors and find ways to reduce stressors through personalized recommendations. The research shows that the algorithm of this study is reliable and has certain practical effects and can provide theoretical reference for subsequent related research.

关键词： k-means algorithm athlete stress source machine learning

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Application of the k-means algorithm and the Gaussian Mixture Model (GMM) - African Vulture Optimization algorithm (AVOA) for the Resolution of Overlapping Energy-Dispersive X-Ray Fluorescence (EDXRF) Peaks

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ANALYTICAL LETTERS 2024年第16期57卷 2629-2643页

作者： Niu, Chuanle Li, Fang Ren, Shun Lu, Anxiang Beijing Acad Agr & Forestry Sci Inst Qual Stand & Testing Technol Beijing Peoples R China China Three Gorges Univ Coll Comp & Informat Technol Yichang Peoples R China Beijing Acad Agr & Forestry Sci Inst Qual Stand & Testing Technol Beijing 100097 Peoples R China

Limitations in instrument resolution mean that soil samples analysis using energy-dispersive X-ray fluorescence (EDXRF) often produced overlapping spectral peaks of heavy metals with similar energies. This overlapping of spectral peaks posed a significant problem in the quantitative analysis of heavy metals in soil samples. Therefore, it was necessary to decompose the overlapping peaks. In this paper, a new method for decomposing overlapping peaks was presented in the context of Gaussian Mixture Model (GMM) parameter estimation, combining the k-means algorithm and the African Vulture Optimization algorithm (AVOA). The data acquired from EDXRF instruments were preprocessed before being input to the k-means algorithm, which produces the output used to initialize the parameters of the GMM. Subsequently, AVOA was employed to optimize the GMM parameters based on a fitness function derived from the data. Ultimately, the optimized GMM parameters obtained through the AVOA process yield the optimal solution for the decomposition of overlapping peaks. This approach effectively addressed the challenge of peak overlap in the determination of heavy metals in soil by EDXRF. Soil samples were obtained from national standard samples, peach gardens, and vegetable-growing regions. The results showed that the maximum absolute errors for the peak channel and peak area were 1.46% and 6.37%, respectively. A comparison of the proposed model with others models indicated that the k-means-GMM-AVOA model exhibits the best performance in terms of speed, accuracy, and stability.

关键词： African vulture optimization algorithm (AVOA) energy-dispersive X-ray fluorescence (EDXRF) Gaussian mixture model (GMM) k-means algorithm

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HFSMOOk-means: An Improved k-means algorithm Using Hesitant Fuzzy Sets and Multi-objective Optimization

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2020年第8期45卷 6241-6257页

作者： Rezaei, kamran Rezaei, Hassan Univ Sistan & Baluchestan Fac Math Dept Comp Sci Zahedan Iran

Clustering is considered as one of the important methods in data mining. The performance of the k-means algorithm, as one of the most common clustering methods, is high sensitivity to the initial cluster centers. Hence, selecting appropriate initial cluster centers for implementing the algorithm improves clustering resulted from the algorithm. The present study aims to find suitable initial cluster centers for the k-means. In fact, the initial cluster centers should be selected in such a way that clusters with high separation and high density can be obtained. Therefore, in this paper, finding initial cluster centers is considered as a multi-objective optimization problem through maximizing the distance between the initial cluster centers, as well as the neighbor density of the initial cluster centers. Solving the above problem through using the MOPSO algorithm provided a set of initial cluster centers of the candidate. Then, the hesitant fuzzy sets were used to evaluate the clusters generated from initial cluster centers by considering separation, cohesion and silhouette index. After that, the concept of informational energy of hesitant fuzzy sets is used, by which non-dominated particles in the Pareto optimal set were ranked and the initial cluster centers were selected for starting the k-means algorithm. The proposed HFSMOOk-means method was compared with several clustering algorithms by considering common and widely used criteria. The results indicated the successful performance of HFSMOOk-means in the majority of the datasets compared to the other algorithms.

关键词： Clustering k-means algorithm Multi-objective optimization MOPSO Hesitant fuzzy sets

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Estimating wheat fractional vegetation cover using a density peak k-means algorithm based on hyperspectral image data

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Journal of Integrative Agriculture 2021年第11期20卷 2880-2891页

作者： LIU Da-zhong YANG Fei-fei LIU Sheng-ping Key Laboratory of Agricultural Information Service Technology Ministry of Agriculture and Rural Affairs/Intelligent Agriculture Research OfficeAgricultural Information InstituteChinese Academy of Agricultural SciencesBeijing 100081P.R.China

Fractional vegetation cover(FVC)is an important parameter to measure crop *** studies of crop growth monitoring,it is very important to extract FVC quickly and *** the most widely used FVC extraction method,the photographic method has the advantages of simple operation and high extraction ***,when soil moisture and acquisition times vary,the extraction results are less *** accommodate various conditions of FVC extraction,this study proposes a new FVC extraction method that extracts FVC from a normalized difference vegetation index(NDVI)greyscale image of wheat by using a density peak k-means(DPk-means)*** this study,Yangfumai 4(YF4)planted in pots and Yangmai 16(Y16)planted in the field were used as the research *** a hyperspectral imaging camera mounted on a tripod,ground hyperspectral images of winter wheat under different soil conditions(dry and wet)were collected at 1 m above the potted wheat *** aerial vehicle(UAV)hyperspectral images of winter wheat at various stages were collected at 50 m above the field wheat canopy by a UAV equipped with a hyperspectral *** pixel dichotomy method and DPk-means algorithm were used to classify vegetation pixels and non-vegetation pixels in NDVI greyscale images of wheat,and the extraction effects of the two methods were compared and *** results showed that extraction by pixel dichotomy was influenced by the acquisition conditions and its error distribution was relatively scattered,while the extraction effect of the DPk-means algorithm was less affected by the acquisition conditions and its error distribution was *** absolute values of error were 0.042 and 0.044,the root mean square errors(RMSE)were 0.028 and 0.030,and the fitting accuracy R2 of the FVC was 0.87 and 0.93,under dry and wet soil conditions and under various time conditions,*** study found that the DPk-means algorithm was capable of achieving more accur

关键词： fractional vegetation cover k-means algorithm NDVI vegetation index wheat

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MULTIMEDIA TOOLS AND APPLICATIONS 2022年第26期81卷 37007-37032页

作者： Gupta, Manoj kumar Chandra, Pravin Guru Gobind Singh Indraprastha Univ Univ Sch Informat & Commun Technol Sect 16C Delhi 110078 India Trinity Inst Innovat Profess Studies Greater Noida 201310 Uttar Pradesh India

Recently, Internet of Things (IoT) and multimedia are gaining popularity because of their usages in various applications. Numerous sensors and automated devices are generating huge volumes of data. Therefore, it is required to efficiently and effectively analyze this voluminous data. It can be achieved by using appropriate machine leaning techniques such as clustering. Among the clustering techniques, the k-means method/algorithm is one of the simplest, effective and commonly used methods. For making the cluster, it uses a measure of similarity/distance among the data observations. Nearby/similar data observations are placed within the same cluster whereas distant/dis-similar data observations are placed in other clusters. Hence, the similarity/distance metric plays a major role on the performance and accuracy of the k-means. Therefore, using an appropriate similarity/distance metric, the performance and accuracy of the k-means can be improved. k-means algorithm is majorly implemented using Euclidean distance metric. With the objective to explore the better and/or alternate similarity/distance metric(s) for k-means, a case study, based on empirical evaluation, of thirteen different similarity/distance metrics on six well-known datasets is performed and presented in this paper. By using the efficient and effective similarity / distance metrics, the performance and accuracy of the k-means algorithm can be improved which leads to formation of good clusters of various data observations or things or images etc. The results of the empirical study are analyzed and compared on the basis of widely used statistical clustering evaluation/validation measures. Based on the comparative results, these metrics are assigned with the ranks. Overall, the results demonstrate that Manhattan and Minkowski distance metrics gives better results for k-means algorithm.

关键词： Internet of things Data analytics and multimedia Similarity metrics Distance metrics k-means algorithm Clustering Machine learning

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A fast near-optimum block truncation coding method using a truncated k-means algorithm and inter-block correlation

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AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS 2011年第6期65卷 576-581页

作者： Yang, Yan Chen, Qiqiang Wan, Yi Lanzhou Univ Inst Signals & Informat Proc Lanzhou 730000 Peoples R China Lanzhou Jiaotong Univ Lanzhou 730070 Peoples R China

Block truncation coding (BTC) is an efficient image compression method which finds application in diverse fields. The basic problem can be viewed as a two-level quantization process. However, efficient ways for optimal threshold determination have not been discovered so far. We propose a fast BTC algorithm based on a truncated k-means algorithm, utilizing the image inter-block correlation and the fact that k-means algorithm converges very fast in this case. This produces near-optimum solution with significantly improved speed over other methods. Simulation results confirm such advantages. (C) 2010 Elsevier GmbH. All rights reserved.

关键词： Block truncation coding Quantization k-means algorithm Image content correlation

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