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Weight selection in W-k-means algorithm with an application in color image segmentation

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2011年第2期62卷 668-676页

作者： Hung, Wen-Liang Chang, Yen-Chang Lee, E. Stanley Natl Hsinchu Univ Educ Dept Appl Math Hsinchu 30013 Taiwan Kansas State Univ Dept Ind & Mfg Syst Engn Manhattan KS 66506 USA

In this paper, a weight selection procedure in the W-k-means algorithm is proposed based on the statistical variation viewpoint. This approach can solve the W-k-means algorithm's problem that the clustering quality is greatly affected by the initial value of weight. After the statistics of data, the weights of data are designed to provide more information for the character of W-k-means algorithm so as to improve the precision. Furthermore, the corresponding computational complexity is analyzed as well. We compare the clustering results of the W-k-means algorithm with the different initialization methods. Results from color image segmentation illustrate that the proposed procedure produces better segmentation than the random initialization according to Liu and Yang's (1994) evaluation function. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Coefficient of variation Color image segmentation Entropy k-means algorithm W-k-means algorithm

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Fast modified global k-means algorithm for incremental cluster construction

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PATTERN RECOGNITION 2011年第4期44卷 866-876页

作者： Bagirov, Adil M. Ugon, Julien Webb, Dean Univ Ballarat Ctr Informat & Appl Optimizat Grad Sch Informat Technol & Math Sci Ballarat Vic 3353 Australia

The k-means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and are inefficient for solving clustering problems in large datasets. Recently, incremental approaches have been developed to resolve difficulties with the choice of starting points. The global k-means and the modified global k-means algorithms are based on such an approach. They iteratively add one cluster center at a time. Numerical experiments show that these algorithms considerably improve the k-means algorithm. However, they require storing the whole affinity matrix or computing this matrix at each iteration. This makes both algorithms time consuming and memory demanding for clustering even moderately large datasets. In this paper, a new version of the modified global k-means algorithm is proposed. We introduce an auxiliary cluster function to generate a set of starting points lying in different parts of the dataset. We exploit information gathered in previous iterations of the incremental algorithm to eliminate the need of computing or storing the whole affinity matrix and thereby to reduce computational effort and memory usage. Results of numerical experiments on six standard datasets demonstrate that the new algorithm is more efficient than the global and the modified global k-means algorithms. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Minimum sum-of-squares clustering Nonsmooth optimization k-means algorithm Global k-means algorithm

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An improved k-means algorithm for underwater image background segmentation

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MULTIMEDIA TOOLS AND APPLICATIONS 2021年第14期80卷 21059-21083页

作者： Chen, Wei He, Cenyu Ji, Chunlin Zhang, Meiying Chen, Siyu Nanjing Inst Technol Coll Innovat & Entrepreneurship Ind Ctr Nanjing 211167 Peoples R China Shenzhen Kuang Chi Space Technol Co Ltd Shenzhen 518000 Peoples R China Shenzhen Kuang Chi Inst Adv Technol Shenzhen 518000 Peoples R China Tech Univ Munich Dept Elect & Comp Engn D-80333 Munich Germany

Conventional algorithms fail to obtain satisfactory background segmentation results for underwater images. In this study, an improved k-means algorithm was developed for underwater image background segmentation to address the issue of improper k value determination and minimize the impact of initial centroid position of grayscale image during the gray level quantization of the conventional k-means algorithm. A total of 100 underwater images taken by an underwater robot were sampled to test the aforementioned algorithm in respect of background segmentation validity and time cost. The k value and initial centroid position of grayscale image were optimized. The results were compared to the other three existing algorithms, including the conventional k-means algorithm, the improved Otsu algorithm, and the Canny operator edge extraction method. The experimental results showed that the improved k-means underwater background segmentation algorithm could effectively segment the background of underwater images with a low color cast, low contrast, and blurred edges. Although its cost in time was higher than that of the other three algorithms, it none the less proved more efficient than the time-consuming manual segmentation method. The algorithm proposed in this paper could potentially be used in underwater environments for underwater background segmentation.

关键词： Underwater image Image segmentation Background segmentation k-means algorithm

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A new algorithm for initial cluster centers in k-means algorithm

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PATTERN RECOGNITION LETTERS 2011年第14期32卷 1701-1705页

作者： Erisoglu, Murat Calis, Nazif Sakallioglu, Sadullah Cukurova Univ Fac Sci & Letters Dept Stat TR-01300 Adana Turkey

Clustering is one of the widely used knowledge discovery techniques to reveal structures in a dataset that can be extremely useful to the analyst. In iterative clustering algorithms the procedure adopted for choosing initial cluster centers is extremely important as it has a direct impact on the formation of final clusters. Since clusters are separated groups in a feature space, it is desirable to select initial centers which are well separated. In this paper, we have proposed an algorithm to compute initial cluster centers for k-means algorithm. The algorithm is applied to several different datasets in different dimension for illustrative purposes. It is observed that the newly proposed algorithm has good performance to obtain the initial cluster centers for the k-means algorithm. (C) 2011 Elsevier B.V. All rights reserved.

关键词： k-means algorithm Initial cluster centers Rand index Error percentage Wilks' lambda test statistic

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Comments on "Modified k-means algorithm for vector quantizer design"

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2000年第11期9卷 1964-1967页

作者： Paliwal, kk Ramasubramanian, V Griffith Univ Sch Microelect Engn Brisbane Qld 4111 Australia Tata Inst Fundamental Res Bombay 400005 Maharashtra India

Recently a modified k-means algorithm for vector quantization design has been proposed where the codevector updating step is as follows: new codevector = current codevector + scale factor (new centroid - current codevector), This algorithm uses a fixed value for the scale factor. In this paper, we propose the use of a variable scale factor which is a function of the iteration number. For the vector quantization of image data, we show that it offers faster convergence than the modified k-means algorithm with a fixed scale factor, without affecting the optimality of the codebook.

关键词： faster convergence k-means algorithm vector quantization

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An empirical comparison of four initialization methods for the k-means algorithm

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PATTERN RECOGNITION LETTERS 1999年第10期20卷 1027-1040页

作者： Peña, JM Lozano, JA Larrañaga, P Univ Basque Country Dept Comp Sci & Artificial Intelligence Intelligent Syst Grp E-20080 San Sebastian Spain

In this paper, we aim to compare empirically four initialization methods for the k-means algorithm: random, Forgy, MacQueen and kaufman. Although this algorithm is known for its robustness, it is widely reported in the literature that its performance depends upon two key points: initial clustering and instance order. We conduct a series of experiments to draw up tin terms of mean, maximum, minimum and standard deviation) the probability distribution of the square-error values of the final clusters returned by the k-means algorithm independently on any initial clustering and on any instance order when each of the four initialization methods is used. The results of our experiments illustrate that the random and the kaufman initialization methods outperform the rest of the compared methods as they make the k-means more effective and more independent on initial clustering and on instance order. In addition, we compare the convergence speed of the k-means algorithm when using each of the four initialization methods. Our results suggest that the kaufman initialization method induces to the k-means algorithm a more desirable behaviour with respect to the convergence speed than the random initialization method. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： k-means algorithm k-means initialization partitional clustering genetic algorithms

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Behavioral analysis of electricity consumption characteristics for customer groups using the k-means algorithm

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SYSTEMS AND SOFT COMPUTING 2024年 6卷

作者： Wu, Ruobing Yunnan Power Grid Co Informat Ctr Kunming 650217 Yunnan Peoples R China

In the fierce competition of the electricity market, how to consolidate and develop customers is particularly important. Aiming to analyze the electricity consumption characteristics of customer groups, this paper used a k-means algorithm and optimized it. The number of clusters was determined by the Davies-Bouldin index (DBI). An improved Harris Hawks optimization (IHHO) algorithm was designed to realize the initial cluster center selection. Based on data such as electricity purchase and average electricity price, electricity customer groups were clustered using the IHHO-k-means algorithm. The IHHO-k-means algorithm achieved the best clustering effect on Iris, Wine, and Glass datasets compared with the traditional k-means and PSO-k-means algorithms. Taking Iris as an example, the optimal value of the IHHO-k-means algorithm was 96.538, with an accuracy rate of 0.932, precision and recall rates of 0.941 and 0.793, respectively, an F-measure of 0.861, and an area under the curve (AUC) value of 0.851. In the customer dataset, the number of clusters determined by DBI was 4. The power customers were divided into four groups with different characteristics of electricity consumption, and their electricity consumption behaviors were analyzed. The results prove the reliability of the IHHO-k-means algorithm in analyzing electricity consumption characteristics of customer groups, and it can be applied in practice.

关键词： k-means algorithm Electricity consumption characteristic Behavior analysis Yunnan power grid Electricity customer

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A NEAR-OPTIMAL INITIAL SEED VALUE SELECTION IN k-means algorithm USING A GENETIC algorithm

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PATTERN RECOGNITION LETTERS 1993年第10期14卷 763-769页

作者： BABU, GP MURTY, MN INDIAN INST SCI DEPT COMP SCI & AUTOMAT BANGALORE 560012 KARNATAKA INDIA

The k-means algorithm for clustering is very much dependent on the initial seed values. We use a genetic al to find a near-optimal partitioning of the given data set by selecting proper initial seed values in the k-means algorithm. Results obtained are very encouraging and in most of the cases, on data sets having well separated clusters, the proposed scheme reached a global minimum.

关键词： CLUSTERING SEED VALUES OPTIMAL PARTITION GENETIC algorithmS k-means algorithm

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On k-means algorithm with the use of Mahalanobis distances

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STATISTICS & PROBABILITY LETTERS 2014年第1期84卷 88-95页

作者： Melnykoy, Igor Melnykov, Volodymyr Nazarbayev Univ Astana 010000 Kazakhstan Univ Alabama Tuscaloosa AL 35487 USA

The k-means algorithm is commonly used with the Euclidean metric. While the use of Mahalanobis distances seems to be a straightforward extension of the algorithm, the initial estimation of covariance matrices can be complicated. We propose a novel approach for initializing covariance matrices. (C) 2013 Elsevier B.V. All rights reserved.

关键词： k-means algorithm Mahalanobis distance Initialization

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A method for correcting InSAR interferogram errors using GNSS data and the k-means algorithm

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EARTH PLANETS AND SPACE 2024年第1期76卷 1-19页

作者： Yan, Huineng Dai, Wujiao Xu, Wenbin Shi, Qiang Sun, kai Lu, Zhigang Wang, Rui Cent South Univ Sch Geosci & Info Phys Changsha 410083 Hunan Peoples R China Gannan Univ Sci & Technol Sch Resources & Civil Engn Ganzhou 341000 Jiangxi Peoples R China Ganzhou Key Lab Remote Sensing Resource & Environm Ganzhou 341000 Jiangxi Peoples R China Jiangsu Ocean Univ Sch Marine Technol & Geomatics Lianyungang 222005 Jiangsu Peoples R China

Correcting interferometric synthetic aperture radar (InSAR) interferograms using Global Navigation Satellite System (GNSS) data can effectively improve their accuracy. However, most of the existing correction methods utilize the difference between GNSS and InSAR data for surface fitting;these methods can effectively correct overall long-wavelength errors, but they are insufficient for multiple medium-wavelength errors in localized areas. Based on this, we propose a method for correcting InSAR interferograms using GNSS data and the k-means spatial clustering algorithm, which is capable of obtaining correction information with high accuracy, thus improving the overall and localized area error correction effects and contributing to obtaining high-precision InSAR deformation time series. In an application involving the Central Valley of Southern California (CVSC), the experimental results show that the proposed correction method can effectively compensate for the deficiency of surface fitting in capturing error details and suppress the effect of low-quality interferograms. At the nine GNSS validation sites that are not included in the modeling process, the errors in the ascending track 137A and descending track 144D are mostly less than 15 mm, and the average root mean square error values are 11.8 mm and 8.0 mm, respectively. Overall, the correction method not only realizes effective interferogram error correction, but also has the advantages of high accuracy, high efficiency, ease of promotion, and can effectively address large-scale and high-precision deformation monitoring scenarios.

关键词： InSAR GNSS Error correction k-means algorithm Interferogram quality High-precision deformation time series

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