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Pseudo-orthogonality for graph 1-Laplacian eigenvectors and applications to higher Cheeger constants and data clustering

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Frontiers of Mathematics in China 2022年第4期17卷 591-623页

作者： Antonio Corbo ESPOSITO Gianpaolo PISCITELLI Dipartimento di Ingegneria Elettrica e dell’Informazione“M.Scarano” Universitàdegli Studi di Cassino e del Lazio MeridionaleVia G.Di Biasio n.4303043Cassino(FR)Italy

The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data.This is an NP-hard problem that can be relaxed in the spectral graph theory,where the optimal cuts of a graph are related to the eigenvalues of graph 1-Laplacian.In this paper,we first give new notations to describe the paths,among critical eigenvectors of the graph 1-Laplacian,realizing sets with prescribed genus.We introduce the pseudo-orthogonality to characterize m_(3)(G),a special eigenvalue for the graph 1-Laplacian.Furthermore,we use it to give an upper bound for the third graph Cheeger constant h_(3)(G),that is,h_(3)(G)≤m_(3)(G).This is a first step for proving that the k-th Cheeger constant is the minimum of the 1-Laplacian Raylegh quotient among vectors that are pseudo-orthogonal to the vectors realizing the previous k−1 Cheeger constants.Eventually,we apply these results to give a method and a numerical algorithm to compute m3(G),based on a generalized inverse power method.

关键词： Graph 1-Laplacian graph Cheeger constants pseudo-orthogonality critical values data clustering

Power Incomplete data clustering Based on Fuzzy Fusion Algorithm

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Energy Engineering 2023年第1期120卷 245-261页

作者： Yutian Hong Yuping Yan Guangdong Electric Power Information Technology Co. Ltd.Guangzhou520000China Guangdong Power Grid Co. Ltd.Guangzhou520000China

With the rapid development of the economy,the scale of the power grid is expanding.The number of power equipment that constitutes the power grid has been very large,which makes the state data of power equipment grow explosively.These multi-source heterogeneous data have data differences,which lead to data variation in the process of transmission and preservation,thus forming the bad information of incomplete data.Therefore,the research on data integrity has become an urgent task.This paper is based on the characteristics of random chance and the Spatio-temporal difference of the system.According to the characteristics and data sources of the massive data generated by power equipment,the fuzzy mining model of power equipment data is established,and the data is divided into numerical and non-numerical data based on numerical data.Take the text data of power equipment defects as the mining material.Then,the Apriori algorithm based on an array is used to mine deeply.The strong association rules in incomplete data of power equipment are obtained and analyzed.From the change trend of NRMSE metrics and classification accuracy,most of the filling methods combined with the two frameworks in this method usually show a relatively stable filling trend,and will not fluctuate greatly with the growth of the missing rate.The experimental results show that the proposed algorithm model can effectively improve the filling effect of the existing filling methods on most data sets,and the filling effect fluctuates greatly with the increase of the missing rate,that is,with the increase of the missing rate,the improvement effect of the model for the existing filling methods is higher than 4.3%.Through the incomplete data clustering technology studied in this paper,a more innovative state assessment of smart grid reliability operation is carried out,which has good research value and reference significance.

关键词： Power system equipment parameter incomplete data fuzzy analysis data clustering

Harmony Search Algorithm Based on Dual-Memory Dynamic Search and Its Application on data clustering

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Complex System Modeling and Simulation 2023年第4期3卷 261-281页

作者： Jinglin Wang Haibin Ouyang Zhiyu Zhou Steven Li School of Mechanical and Electric Engineering Guangzhou UniversityGuangzhou 510006China Graduate School of Business and Law RMIT UniversityMelbourne 3000Australia

Harmony Search(HS)algorithm is highly effective in solving a wide range of real-world engineering optimization problems.However,it still has the problems such as being prone to local optima,low optimization accuracy,and low search efficiency.To address the limitations of the HS algorithm,a novel approach called the Dual-Memory Dynamic Search Harmony Search(DMDS-HS)algorithm is introduced.The main innovations of this algorithm are as follows:Firstly,a dual-memory structure is introduced to rank and hierarchically organize the harmonies in the harmony memory,creating an effective and selectable trust region to reduce approach blind searching.Furthermore,the trust region is dynamically adjusted to improve the convergence of the algorithm while maintaining its global search capability.Secondly,to boost the algorithm’s convergence speed,a phased dynamic convergence domain concept is introduced to strategically devise a global random search strategy.Lastly,the algorithm constructs an adaptive parameter adjustment strategy to adjust the usage probability of the algorithm’s search strategies,which aim to rationalize the abilities of exploration and exploitation of the algorithm.The results tested on the Computational Experiment Competition on 2017(CEC2017)test function set show that DMDS-HS outperforms the other nine HS algorithms and the other four state-of-the-art algorithms in terms of diversity,freedom from local optima,and solution accuracy.In addition,applying DMDS-HS to data clustering problems,the results show that it exhibits clustering performance that exceeds the other seven classical clustering algorithms,which verifies the effectiveness and reliability of DMDS-HS in solving complex data clustering problems.

关键词： harmony search dual-memory dynamic search optimization data clustering

A new algorithm based on metaheuristics for data clustering

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2010年第12期11卷 921-926页

作者： Tsutomu SHOHDOHJI Fumihiko YANO Yoshiaki TOYODA Department of Computer and Information Engineering Faculty of EngineeringNippon Institute of Technology Division of Integrated Sciences J.F.Oberlin University Aoyama Gakuin University

This paper presents a new algorithm for clustering a large amount of data.We improved the ant colony clustering algorithm that uses an ant’s swarm intelligence,and tried to overcome the weakness of the classical cluster analysis methods.In our proposed algorithm,improvements in the efficiency of an agent operation were achieved,and a new function "cluster condensation" was added.Our proposed algorithm is a processing method by which a cluster size is reduced by uniting similar objects and incorporating them into the cluster condensation.Compared with classical cluster analysis methods,the number of steps required to complete the clustering can be suppressed to 1% or less by performing this procedure,and the dispersion of the result can also be reduced.Moreover,our clustering algorithm has the advantage of being possible even in a small-field cluster condensation.In addition,the number of objects that exist in the field decreases because the cluster condenses;therefore,it becomes possible to add an object to a space that has become empty.In other words,first,the majority of data is put on standby.They are then clustered,gradually adding parts of the standby data to the clustering data.The method can be adopted for a large amount of data.Numerical experiments confirmed that our proposed algorithm can theoretically applied to an unrestricted volume of data.

关键词： Metaheuristics Ant colony clustering data clustering Swarm intelligence

A Novel Hybrid data clustering Algorithm Based on Artificial Bee Colony Algorithm and K-Means

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Chinese Journal of Electronics 2015年第4期24卷 694-701页

作者： TRAN Dang Cong WU Zhijian WANG Zelin DENG Changshou State Key Laboratory of Software Engineering School of Computer Wuhan University Vietnam Academy of Science and Technology School of Information Science and Technology Jiujiang University

To improve the performance of K-means clustering algorithm, this paper presents a new hybrid approach of Enhanced artificial bee colony algorithm and Kmeans(EABCK). In EABCK, the original artificial bee colony algorithm(called ABC) is enhanced by a new mutation operation and guided by the global best solution(called EABC). Then, the best solution is updated by Kmeans in each iteration for data clustering. In the experiments, a set of benchmark functions was used to evaluate the performance of EABC with other comparative ABC variants. To evaluate the performance of EABCK on data clustering, eleven benchmark datasets were utilized. The experimental results show that EABC and EABCK outperform other comparative ABC variants and data clustering algorithms, respectively.

关键词： data clustering K-means Artificial bee colony Mutation operation

Architecture of Integrated data clustering Machine

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Computer Aided Drafting,Design and Manufacturing 2009年第2期19卷 43-48页

作者： ARIF Iqbal School of Computer Science & Engineering Beijing University of Aeronautics and Astronautics

data clustering is a significant information retrieval technique in today＇s data intensive society. Over the last few decades a vast variety of huge number of data clustering algorithms have been designed and implemented for all most all data types. The quality of results of cluster analysis mainly depends on the clustering algorithm used in the analysis. Architecture of a versatile, less user dependent, dynamic and scalable data clustering machine is presented. The machine selects for analysis, the best available data clustering algorithm on the basis of the credentials of the data and previously used domain knowledge. The domain knowledge is updated on completion of each session of data analysis.

关键词： data mining data clustering data clustering algorithms architecture framework

Optimal data clustering by Using Artificial Immune Network with Elitist Learning

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Optimal Data Clustering by Using Artificial Immune Network w...

An Evolutionary Multi-Layer Extreme Learning Machine for data clustering Problems

第26届中国控制与决策会议

作者： Li Zhonghua Fang Xianshu Zhou Jieying School of Information Science and Technology Sun Yat-sen University

ISBN: (纸本)9781479937097

data clustering is one of the most popular techniques in data mining.The attributes of the objects within the same cluster should be similar to each other,while the attributes of the objects within different clusters should be different.Most of classical clustering algorithms suffer from such disadvantages as local optima,initial centroid selection and the lack of a way to automatically determine the optimal number of clusters,and thus fail to cluster datasets with complex distributions.This paper proposes a novel clustering algorithm based on artificial immune network with elitist learning（Ocopt-aiNet-EL）.Some elaborated operators are implemented for automatic data clustering and the Manifold distance is used for the dissimilarity measure of antibodies.A number of benchmark cases including artificial datasets and real-world datasets are arranged to evaluate the performance of the proposed Ocopt-aiNet-EL algorithm and the other clustering algorithms,such as K-means,EAC and Ocopt-aiNet.The experimental results demonstrate that the proposed Ocopt-aiNet-EL is an effective and efficient clustering method.

关键词： Artificial immune network data clustering elitist learning entropy measure manifold distance

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An Evolutionary Multi-Layer Extreme Learning Machine for Dat...

A novel method for road network mining from floating car data

第40届中国控制会议

作者： Xian Wu Tianfang Zhou Kaixiang Yi Minrui Fei Yayu Chen JiaLan Ding Shanghai Key Laboratory of Power Station Automation Technology School of Mechatronic Engineering and Automation Shanghai University The Faculty of Engineering Architecture and Information Technology The University of Queensland

clustering technology such as K-means is a critical method in data analysis, and it occupies an even more important place with the explosion of information. Due to the complicated distribution of data in the original feature space, it is difficult to find suitable clusters of the data. To address this problem, Existing extreme learning machines（ELM） based clustering methods construct an embedding space to reveal the clusters more easily. In ELM and K-means, some parameters are randomly assigned,so it may lead to unstable or non-optimal results. In this paper, an evolutionary extreme learning machine method（LBH-MLELM）based on a black hole algorithm is proposed, in which a more effective embedding space is constructed by a multi-layer extreme learning machine, and the final results are subsequently derived by K-means algorithm. What’s more, by optimizing not only the input weights, hidden biases of ELM, but also the initial center of K-means, the accuracy and robustness of clustering are improved. The experimental results on several public datasets demonstrated the effectiveness of the proposed method, and further analyzed the properties of the proposed method.

关键词： Extreme learning machine data clustering black hole algorithm machine learning

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Geo-Spatial Information Science 2022年第2期25卷 197-211页

作者： Yuan Guo Bijun Li Zhi Lu Jian Zhou State Key Laboratory of Information Engineering in Surveying Mappingand Remote SensingWuhan UniversityWuhanChina

Vehicles have been increasingly equipped with GPS receivers to record their trajectories,which we call floating car data.Compared with other data sources,these data are characterized by low cost,wide coverage,and rapid updating.The data have become an important source for road network extraction.In this paper,we propose a novel approach for mining road networks from floating car data.First,a Gaussian model is used to transform the data into bitmap,and the Otsu algorithm is utilized to detect road intersections.Then,a clothoid-based method is used to resample the GPS points to improve the clustering accuracy,and the data are clustered based on a distance-direction algorithm.Last,road centerlines are extracted with a weighted least squares algorithm.We report on experiments that were conducted on floating car data from Wuhan,China.To conclude,existing methods are compared with our method to prove that the proposed method is practical and effective.

关键词： GPS trajectory floating car data road intersection extraction data clustering