Comprehensive K-Means Clustering

The k-means algorithm is a popular data clustering technique due to its speed and simplicity. However, it is susceptible to issues such as sensitivity to the chosen seeds, and inaccurate clusters due to poor initial seeds, particularly in complex datasets or datasets with non-spherical clusters. In this paper, a Comprehensive K-Means Clustering algorithm is presented, in which multiple trials of k-means are performed on a given dataset. The clustering results from each trial are transformed into a five-dimensional data point, containing the scope values of the x and y coordinates of the clusters along with the number of points within that cluster. A graph is then generated displaying the configuration of these points using Principal Component Analysis (PCA), from which we can observe and determine the common clustering patterns in the dataset. The robustness and strength of these patterns are then examined by observing the variance of the results of each trial, wherein a different subset of the data keeping a certain percentage of original data points is clustered. By aggregating information from multiple trials, we can distinguish clusters that consistently emerge across different runs from those that are more sensitive or unlikely, hence deriving more reliable conclusions about the underlying structure of complex datasets. Our experiments show that our algorithm is able to find the most common associations between different dimensions of data over multiple trials, often more accurately than other algorithms, as well as measure stability of these clusters, an ability that other k-means algorithms lack.

Quantitative Method of Classification and Discrimination of a Porous Carbonate Reservoir Integrating K-means Clustering and Bayesian Theory

Reservoir classification is a key link in reservoir evaluation.However,traditional manual means are inefficient,subjective,and classification standards are not uniform.Therefore,taking the Mishrif Formation of the Western Iraq as an example,a new reservoir classification and discrimination method is established by using the K-means clustering method and the Bayesian discrimination method.These methods are applied to non-cored wells to calculate the discrimination accuracy of the reservoir type,and thus the main reasons for low accuracy of reservoir discrimination are clarified.The results show that the discrimination accuracy of reservoir type based on K-means clustering and Bayesian stepwise discrimination is strongly related to the accuracy of the core data.The discrimination accuracy rate of TypeⅠ,TypeⅡ,and TypeⅤreservoirs is found to be significantly higher than that of TypeⅢand TypeⅣreservoirs using the method of combining K-means clustering and Bayesian theory based on logging data.Although the recognition accuracy of the new methodology for the TypeⅣreservoir is low,with average accuracy the new method has reached more than 82%in the entire study area,which lays a good foundation for rapid and accurate discrimination of reservoir types and the fine evaluation of a reservoir.

Investigation of the J-TEXT plasma events by k-means clustering algorithm

Various types of plasma events emerge in specific parameter ranges and exhibit similar characteristics in diagnostic signals,which can be applied to identify these events.A semisupervised machine learning algorithm,the k-means clustering algorithm,is utilized to investigate and identify plasma events in the J-TEXT plasma.This method can cluster diverse plasma events with homogeneous features,and then these events can be identified if given few manually labeled examples based on physical understanding.A survey of clustered events reveals that the k-means algorithm can make plasma events(rotating tearing mode,sawtooth oscillations,and locked mode)gathering in Euclidean space composed of multi-dimensional diagnostic data,like soft x-ray emission intensity,edge toroidal rotation velocity,the Mirnov signal amplitude and so on.Based on the cluster analysis results,an approximate analytical model is proposed to rapidly identify plasma events in the J-TEXT plasma.The cluster analysis method is conducive to data markers of massive diagnostic data.

Plant Leaf Diseases Classification Using Improved K-Means Clustering and SVM Algorithm for Segmentation

Several pests feed on leaves,stems,bases,and the entire plant,causing plant illnesses.As a result,it is vital to identify and eliminate the disease before causing any damage to plants.Manually detecting plant disease and treating it is pretty challenging in this period.Image processing is employed to detect plant disease since it requires much effort and an extended processing period.The main goal of this study is to discover the disease that affects the plants by creating an image processing system that can recognize and classify four different forms of plant diseases,including Phytophthora infestans,Fusarium graminearum,Puccinia graminis,tomato yellow leaf curl.Therefore,this work uses the Support vector machine(SVM)classifier to detect and classify the plant disease using various steps like image acquisition,Pre-processing,Segmentation,feature extraction,and classification.The gray level co-occurrence matrix(GLCM)and the local binary pattern features(LBP)are used to identify the disease-affected portion of the plant leaf.According to experimental data,the proposed technology can correctly detect and diagnose plant sickness with a 97.2 percent accuracy.

Evaluating Partitioning Based Clustering Methods for Extended Non-negative Matrix Factorization (NMF)

Data is humongous today because of the extensive use of World WideWeb, Social Media and Intelligent Systems. This data can be very important anduseful if it is harnessed carefully and correctly. Useful information can beextracted from this massive data using the Data Mining process. The informationextracted can be used to make vital decisions in various industries. Clustering is avery popular Data Mining method which divides the data points into differentgroups such that all similar data points form a part of the same group. Clusteringmethods are of various types. Many parameters and indexes exist for the evaluationand comparison of these methods. In this paper, we have compared partitioningbased methods K-Means, Fuzzy C-Means (FCM), Partitioning AroundMedoids (PAM) and Clustering Large Application (CLARA) on secure perturbeddata. Comparison and identification has been done for the method which performsbetter for analyzing the data perturbed using Extended NMF on the basis of thevalues of various indexes like Dunn Index, Silhouette Index, Xie-Beni Indexand Davies-Bouldin Index.

Clustering Countries on COVID-19 Data among Different Waves Using K-Means Clustering

The COVID-19 pandemic has caused an unprecedented spike in confirmed cases in 230 countries globally. In this work, a set of data from the COVID-19 coronavirus outbreak has been subjected to two well-known unsupervised learning techniques: K-means clustering and correlation. The COVID-19 virus has infected several nations, and K-means automatically looks for undiscovered clusters of those infections. To examine the spread of COVID-19 before a vaccine becomes widely available, this work has used unsupervised approaches to identify the crucial county-level confirmed cases, death cases, recover cases, total_cases_per_million, and total_deaths_per_million aspects of county-level variables. We combined countries into significant clusters using this feature subspace to assist more in-depth disease analysis efforts. As a result, we used a clustering technique to examine various trends in COVID-19 incidence and mortality across nations. This technique took the key components of a trajectory and incorporates them into a K-means clustering process. We separated the trend lines into measures that characterize various features of a trend. The measurements were first reduced in dimension, then clustered using a K-means algorithm. This method was used to individually calculate the incidence and death rates and then compare them.

A Review on Clustering Methods for Climatology Analysis and Its Application over South America

South America’s climatic diversity is a product of its vast geographical expanse, encompassing tropical to subtropical latitudes. The variations in precipitation and temperature across the region stem from the influence of distinct atmospheric systems. While some studies have characterized the prevailing systems over South America, they often lacked the utilization of statistical techniques for homogenization. On the other hand, other research has employed multivariate statistical methods to identify homogeneous regions regarding temperature and precipitation, but their focus has been limited to specific areas, such as the south, southeast, and northeast. Surprisingly, there is a lack of work that compares various multivariate statistical techniques to determine homogeneous regions across the entirety of South America concerning temperature and precipitation. This paper aims to address this gap by comparing three such techniques: Cluster Analysis (K-means and Ward) and Self Organizing Maps, using data from different sources for temperature (ERA5, ERA5-Land, and CRU) and precipitation (ERA5, ERA5-Land, and CPC). Spatial patterns and time series were generated for each region over the period 1981-2010. The results from this analysis of spatially homogeneous regions concerning temperature and precipitation have the potential to significantly benefit climate analysis and forecasts. Moreover, they can offer valuable insights for various climatological studies, guiding decision-making processes in diverse fields that rely on climate information, such as agriculture, disaster management, and water resources planning.

Study on the Development and Implementation of Different Big Data Clustering Methods

Clustering is an unsupervised learning method used to organize raw data in such a way that those with the same (similar) characteristics are found in the same class and those that are dissimilar are found in different classes. In this day and age, the very rapid increase in the amount of data being produced brings new challenges in the analysis and storage of this data. Recently, there is a growing interest in key areas such as real-time data mining, which reveal an urgent need to process very large data under strict performance constraints. The objective of this paper is to survey four algorithms including K-Means algorithm, FCM algorithm, EM algorithm and BIRCH, used for data clustering and then show their strengths and weaknesses. Another task is to compare the results obtained by applying each of these algorithms to the same data and to give a conclusion based on these results.

Geochemical and Geostatistical Studies for Estimating Gold Grade in Tarq Prospect Area by K-Means Clustering Method

Tarq geochemical 1:100,000 Sheet is located in Isfahan province which is investigated by Iran’s Geological and Explorations Organization using stream sediment analyzes. This area has stratigraphy of Precambrian to Quaternary rocks and is located in the Central Iran zone. According to the presence of signs of gold mineralization in this area, it is necessary to identify important mineral areas in this area. Therefore, finding information is necessary about the relationship and monitoring the elements of gold, arsenic, and antimony relative to each other in this area to determine the extent of geochemical halos and to estimate the grade. Therefore, a well-known and useful K-means method is used for monitoring the elements in the present study, this is a clustering method based on minimizing the total Euclidean distances of each sample from the center of the classes which are assigned to them. In this research, the clustering quality function and the utility rate of the sample have been used in the desired cluster (S(i)) to determine the optimum number of clusters. Finally, with regard to the cluster centers and the results, the equations were used to predict the amount of the gold element based on four parameters of arsenic and antimony grade, length and width of sampling points.

Oversampling Method Based on Gaussian Distribution and K-Means Clustering

Learning from imbalanced data is one of the greatest challenging problems in binary classification,and this problem has gained more importance in recent years.When the class distribution is imbalanced,classical machine learning algorithms tend to move strongly towards the majority class and disregard the minority.Therefore,the accuracy may be high,but the model cannot recognize data instances in the minority class to classify them,leading to many misclassifications.Different methods have been proposed in the literature to handle the imbalance problem,but most are complicated and tend to simulate unnecessary noise.In this paper,we propose a simple oversampling method based on Multivariate Gaussian distribution and K-means clustering,called GK-Means.The new method aims to avoid generating noise and control imbalances between and within classes.Various experiments have been carried out with six classifiers and four oversampling methods.Experimental results on different imbalanced datasets show that the proposed GK-Means outperforms other oversampling methods and improves classification performance as measured by F1-score and Accuracy.

Improved k-means clustering algorithm

In allusion to the disadvantage of having to obtain the number of clusters of data sets in advance and the sensitivity to selecting initial clustering centers in the k-means algorithm, an improved k-means clustering algorithm is proposed. First, the concept of a silhouette coefficient is introduced, and the optimal clustering number Kopt of a data set with unknown class information is confirmed by calculating the silhouette coefficient of objects in clusters under different K values. Then the distribution of the data set is obtained through hierarchical clustering and the initial clustering-centers are confirmed. Finally, the clustering is completed by the traditional k-means clustering. By the theoretical analysis, it is proved that the improved k-means clustering algorithm has proper computational complexity. The experimental results of IRIS testing data set show that the algorithm can distinguish different clusters reasonably and recognize the outliers efficiently, and the entropy generated by the algorithm is lower.

基于改进K-means算法的物流配送中心选址研究

针对传统K-means算法需要主观设定K值及无法处理类别型数据问题,文章运用肘部法及轮廓系数法确定合理K值,对类别型数据采取独热编码(One-Hot Encoding)转换为可以处理的连续型数据,并将其运用到在物流配送中心选址中;并综合考虑多种类别的影响因素,构建了相应的影响因素指标体系,提出的模型能够识别输入数据的数值型及类别型数据,实现样本的有效聚类。相关的案例分析结果表明,相比传统K-means聚类,文章的改进K-means算法选址结果可使物流总成本降低8.76%,运营成本降低14.85%,固定成本降低8.09%,效果显著。

An efficient enhanced k-means clustering algorithm

In k-means clustering, we are given a set of n data points in d-dimensional space R^d and an integer k and the problem is to determine a set of k points in R^d, called centers, so as to minimize the mean squared distance from each data point to its nearest center. In this paper, we present a simple and efficient clustering algorithm based on the k-means algorithm, which we call enhanced k-means algorithm. This algorithm is easy to implement, requiring a simple data structure to keep some information in each iteration to be used in the next iteration. Our experimental results demonstrated that our scheme can improve the computational speed of the k-means algorithm by the magnitude in the total number of distance calculations and the overall time of computation.

一种基于K-means聚类算法的沙尘天气客观识别方法

鉴于以往基于污染物浓度时间序列进行分析的沙尘天气识别方法在判断标准上存在一定的主观性,本文提出一种基于K-means聚类算法的沙尘天气客观识别方法。本方法利用环境监测总站的PM2.5和PM10小时浓度资料进行聚类,首先选取最优的分类数目K进行聚类,其次对聚类结果中离散程度较高的类别进行再次聚类,直到无需分类。将本方法应用于西安市2018年2~4月沙尘天气的识别中,结果表明,本方法可有效识别主要沙尘天气。此外,利用本方法可得到沙尘天气典型特征:PM2.5占PM10浓度的比例小于43.5%、PM10浓度高于228μg/m^(3,)符合沙尘天气期间PM10浓度较高且以粗颗粒物为主的物理特征。总体上看,本方法物理基础清晰,可操行性强,适用于大规模数据处理,具有较好的实用价值和应用前景。

Classification of Northeast China Cold Vortex Activity Paths in Early Summer Based on K-means Clustering and Their Climate Impact

The classification of the Northeast China Cold Vortex(NCCV)activity paths is an important way to analyze its characteristics in detail.Based on the daily precipitation data of the northeastern China(NEC)region,and the atmospheric circulation field and temperature field data of ERA-Interim for every six hours,the NCCV processes during the early summer(June)seasons from 1979 to 2018 were objectively identified.Then,the NCCV processes were classified using a machine learning method(k-means)according to the characteristic parameters of the activity path information.The rationality of the classification results was verified from two aspects,as follows:(1)the atmospheric circulation configuration of the NCCV on various paths;and(2)its influences on the climate conditions in the NEC.The obtained results showed that the activity paths of the NCCV could be divided into four types according to such characteristics as the generation origin,movement direction,and movement velocity of the NCCV.These included the generation-eastward movement type in the east of the Mongolia Plateau(eastward movement type or type A);generation-southeast longdistance movement type in the upstream of the Lena River(southeast long-distance movement type or type B);generationeastward less-movement type near Lake Baikal(eastward less-movement type or type C);and the generation-southward less-movement type in eastern Siberia(southward less-movement type or type D).There were obvious differences observed in the atmospheric circulation configuration and the climate impact of the NCCV on the four above-mentioned types of paths,which indicated that the classification results were reasonable.

Hierarchical hesitant fuzzy K-means clustering algorithm

Due to the limitation and hesitation in one＇s knowledge, the membership degree of an element to a given set usually has a few different values, in which the conventional fuzzy sets are invalid. Hesitant fuzzy sets are a powerful tool to treat this case. The present paper focuses on investigating the clustering technique for hesitant fuzzy sets based on the K-means clustering algorithm which takes the results of hierarchical clustering as the initial clusters. Finally, two examples demonstrate the validity of our algorithm.

Global Optimization Method Using SLE and Adaptive RBF Based on Fuzzy Clustering

High fidelity analysis models,which are beneficial to improving the design quality,have been more and more widely utilized in the modern engineering design optimization problems.However,the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable.In order to improve the efficiency of optimization involving high fidelity analysis models,the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models,which can greately reduce the computation time.An efficient heuristic global optimization method using adaptive radial basis function（RBF） based on fuzzy clustering（ARFC） is proposed.In this method,a novel algorithm of maximin Latin hypercube design using successive local enumeration（SLE） is employed to obtain sample points with good performance in both space-filling and projective uniformity properties,which does a great deal of good to metamodels accuracy.RBF method is adopted for constructing the metamodels,and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced.The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space.The numerical benchmark examples are used for validating the performance of ARFC.The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method（ARSM） proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum.This method improves the efficiency and global convergence of the optimization problems,and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.

Landslide susceptibility zonation method based on C5.0 decision tree and K-means cluster algorithms to improve the efficiency of risk management

Machine learning algorithms are an important measure with which to perform landslide susceptibility assessments, but most studies use GIS-based classification methods to conduct susceptibility zonation.This study presents a machine learning approach based on the C5.0 decision tree(DT) model and the K-means cluster algorithm to produce a regional landslide susceptibility map. Yanchang County, a typical landslide-prone area located in northwestern China, was taken as the area of interest to introduce the proposed application procedure. A landslide inventory containing 82 landslides was prepared and subsequently randomly partitioned into two subsets: training data(70% landslide pixels) and validation data(30% landslide pixels). Fourteen landslide influencing factors were considered in the input dataset and were used to calculate the landslide occurrence probability based on the C5.0 decision tree model.Susceptibility zonation was implemented according to the cut-off values calculated by the K-means cluster algorithm. The validation results of the model performance analysis showed that the AUC(area under the receiver operating characteristic(ROC) curve) of the proposed model was the highest, reaching 0.88,compared with traditional models(support vector machine(SVM) = 0.85, Bayesian network(BN) = 0.81,frequency ratio(FR) = 0.75, weight of evidence(WOE) = 0.76). The landslide frequency ratio and frequency density of the high susceptibility zones were 6.76/km^(2) and 0.88/km^(2), respectively, which were much higher than those of the low susceptibility zones. The top 20% interval of landslide occurrence probability contained 89% of the historical landslides but only accounted for 10.3% of the total area.Our results indicate that the distribution of high susceptibility zones was more focused without containing more " stable" pixels. Therefore, the obtained susceptibility map is suitable for application to landslide risk management practices.

K-MEANS CLUSTERING FOR CLASSIFICATION OF THE NORTHWESTERN PACIFIC TROPICAL CYCLONE TRACKS

Based on the Joint Typhoon Warning Center(JTWC) best-track dataset between 1965 and 2009 and the characteristic parameters including tropical cyclone(TC) position,intensity,path length and direction,a method for objective classification of the Northwestern Pacific tropical cyclone tracks is established by using k-means Clustering.The TC lifespan,energy,active season and landfall probability of seven clusters of tropical cyclone tracks are comparatively analyzed.The characteristics of these parameters are quite different among different tropical cyclone track clusters.From the trend of the past two decades,the frequency of the western recurving cluster(accounting for 21.3% of the total) increased,and the lifespan elongated slightly,which differs from the other clusters.The annual variation of the Power Dissipation Index(PDI) of most clusters mainly depended on the TC intensity and frequency.However,the annual variation of the PDI in the northwestern moving then recurving cluster and the pelagic west-northwest moving cluster mainly depended on the frequency.

Blind source separation by weighted K-means clustering

Blind separation of sparse sources （BSSS） is discussed. The BSSS method based on the conventional K-means clustering is very fast and is also easy to implement. However, the accuracy of this method is generally not satisfactory. The contribution of the vector x（t） with different modules is theoretically proved to be unequal, and a weighted K-means clustering method is proposed on this grounds. The proposed algorithm is not only as fast as the conventional K-means clustering method, but can also achieve considerably accurate results, which is demonstrated by numerical experiments.