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.

Optimized air-ground data fusion method for mine slope modeling

Refined 3D modeling of mine slopes is pivotal for precise prediction of geological hazards.Aiming at the inadequacy of existing single modeling methods in comprehensively representing the overall and localized characteristics of mining slopes,this study introduces a new method that fuses model data from Unmanned aerial vehicles(UAV)tilt photogrammetry and 3D laser scanning through a data alignment algorithm based on control points.First,the mini batch K-Medoids algorithm is utilized to cluster the point cloud data from ground 3D laser scanning.Then,the elbow rule is applied to determine the optimal cluster number(K0),and the feature points are extracted.Next,the nearest neighbor point algorithm is employed to match the feature points obtained from UAV tilt photogrammetry,and the internal point coordinates are adjusted through the distanceweighted average to construct a 3D model.Finally,by integrating an engineering case study,the K0 value is determined to be 8,with a matching accuracy between the two model datasets ranging from 0.0669 to 1.0373 mm.Therefore,compared with the modeling method utilizing K-medoids clustering algorithm,the new modeling method significantly enhances the computational efficiency,the accuracy of selecting the optimal number of feature points in 3D laser scanning,and the precision of the 3D model derived from UAV tilt photogrammetry.This method provides a research foundation for constructing mine slope model.

Optimal operation of Internet Data Center with PV and energy storage type of UPS clusters

With the development of green data centers,a large number of Uninterruptible Power Supply(UPS)resources in Internet Data Center(IDC)are becoming idle assets owing to their low utilization rate.The revitalization of these idle UPS resources is an urgent problem that must be addressed.Based on the energy storage type of the UPS(EUPS)and using renewable sources,a solution for IDCs is proposed in this study.Subsequently,an EUPS cluster classification method based on the concept of shared mechanism niche(CSMN)was proposed to effectively solve the EUPS control problem.Accordingly,the classified EUPS aggregation unit was used to determine the optimal operation of the IDC.An IDC cost minimization optimization model was established,and the Quantum Particle Swarm Optimization(QPSO)algorithm was adopted.Finally,the economy and effectiveness of the three-tier optimization framework and model were verified through three case studies.

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.

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.

Kernel method-based fuzzy clustering algorithm

The fuzzy C-means clustering algorithm(FCM) to the fuzzy kernel C-means clustering algorithm(FKCM) to effectively perform cluster analysis on the diversiform structures are extended, such as non-hyperspherical data, data with noise, data with mixture of heterogeneous cluster prototypes, asymmetric data, etc. Based on the Mercer kernel, FKCM clustering algorithm is derived from FCM algorithm united with kernel method. The results of experiments with the synthetic and real data show that the FKCM clustering algorithm is universality and can effectively unsupervised analyze datasets with variform structures in contrast to FCM algorithm. It is can be imagined that kernel-based clustering algorithm is one of important research direction of fuzzy clustering analysis.

Cluster structure prediction via CALYPSO method

Cluster science as a bridge linking atomic molecular physics and condensed matter inspired the nanomaterials development in the past decades, ranging from the single-atom catalysis to ligand-protected noble metal clusters. The corresponding studies not only have been restricted to the search for the geometrical structures of clusters, but also have promoted the development of cluster-assembled materials as the building blocks. The CALYPSO cluster prediction method combined with other computational techniques have significantly stimulated the development of the cluster-based nanomaterials. In this review, we will summarize some good cases of cluster structure by CALYPSO method, which have also been successfully identified by the photoelectron spectra experiments. Beginning with the alkali-metal clusters, which serve as benchmarks, a series of studies are performed on the size-dependent elemental clusters which possess relatively high stability and interesting chemical physical properties. Special attentions are paid to the boron-based clusters because of their promising applications. The NbSi12 and BeB16 clusters, for example, are two classic representatives of the silicon-and boron-based clusters, which can be viewed as building blocks of nanotubes and borophene. This review offers a detailed description of the structural evolutions and electronic properties of medium-sized pure and doped clusters, which will advance fundamental knowledge of cluster-based nanomaterials and provide valuable information for further theoretical and experimental studies.

3D Model Retrieval Method Based on Affinity Propagation Clustering

In order to improve the accuracy and efficiency of 3D model retrieval,the method based on affinity propagation clustering algorithm is proposed. Firstly,projection ray-based method is proposed to improve the feature extraction efficiency of 3D models. Based on the relationship between model and its projection,the intersection in 3D space is transformed into intersection in 2D space,which reduces the number of intersection and improves the efficiency of the extraction algorithm. In feature extraction,multi-layer spheres method is analyzed. The two-layer spheres method makes the feature vector more accurate and improves retrieval precision. Secondly,Semi-supervised Affinity Propagation ( S-AP) clustering is utilized because it can be applied to different cluster structures. The S-AP algorithm is adopted to find the center models and then the center model collection is built. During retrieval process,the collection is utilized to classify the query model into corresponding model base and then the most similar model is retrieved in the model base. Finally,75 sample models from Princeton library are selected to do the experiment and then 36 models are used for retrieval test. The results validate that the proposed method outperforms the original method and the retrieval precision and recall ratios are improved effectively.

An unsupervised clustering method for nuclear magnetic resonance transverse relaxation spectrums based on the Gaussian mixture model and its application

To make the quantitative results of nuclear magnetic resonance(NMR) transverse relaxation(T;) spectrums reflect the type and pore structure of reservoir more directly, an unsupervised clustering method was developed to obtain the quantitative pore structure information from the NMR T;spectrums based on the Gaussian mixture model(GMM). Firstly, We conducted the principal component analysis on T;spectrums in order to reduce the dimension data and the dependence of the original variables. Secondly, the dimension-reduced data was fitted using the GMM probability density function, and the model parameters and optimal clustering numbers were obtained according to the expectation-maximization algorithm and the change of the Akaike information criterion. Finally, the T;spectrum features and pore structure types of different clustering groups were analyzed and compared with T;geometric mean and T;arithmetic mean. The effectiveness of the algorithm has been verified by numerical simulation and field NMR logging data. The research shows that the clustering results based on GMM method have good correlations with the shape and distribution of the T;spectrum, pore structure, and petroleum productivity, providing a new means for quantitative identification of pore structure, reservoir grading, and oil and gas productivity evaluation.

APPLICATION OF THE CLUSTERING METHOD IN ANALYSING SHALLOW WATER MASSES AND MODIFIED WATER MASSES IN THE HUANGHAI SEA AND EAST CHINA SEA

The idea of modified water masses is introduced and a cluster analysis is used for determining the boundary of modified water masses and its variety in the shallow water area of the Huanghai Sea (Yellow Sea) and the East China Sea. According to the specified standards to make the cluster, we have determined the number and boundary of the water masses and the mixed zones.The results obtained by the cluster method show that there are eight modified water masses in this area. According to the relative index of temperature and salinity,the modified water masses are divided into nine different characteristic parts. The water, masses may also be divided into three salinity types. On the TS-Diagram, the points concerning temperature and safinity of different modified mater masses are distributed around a curve, from which the characteristics of gradual modification may be embodied. The variation ranges of different modified water masses are all large, explaining the intensive modification of water masses in

The tidal tails of globular cluster Palomar 5 based on the neural networks method

The sixth Data Release （DR6） of the Sloan Digital Sky Survey （SDSS） provides more photometric regions, new features and more accurate data around globular cluster Palomar 5. A new method, Back Propagation Neural Network （BPNN）, is used to estimate the cluster membership probability in order to detect its tidal tails. Cluster and field stars, used for training the networks, are extracted over a 40 × 20 deg^2 field by color-magnitude diagrams （CMDs）. The best BPNNs with two hidden layers and a Levenberg-Marquardt （LM） training algorithm are determined by the chosen cluster and field samples. The membership probabilities of stars in the whole field are obtained with the BPNNs, and contour maps of the probability distribution show that a tail extends .5.42° to the north of the cluster and another tail extends 3.77° to the south. The tails are similar to those detected by Odenkirchen et al., but no more debris from the cluster is found to the northeast in the sky. The radial density profiles are investigated both along the tails and near the cluster center. Quite a few substructures are discovered in the tails. The number density profile of the cluster is fitted with the King model and the tidal radius is determined as 14.28＇. However, the King model cannot fit the observed profile at the outer regions （R 〉 8＇） because of the tidal tails generated by the tidal force. Luminosity functions of the cluster and the tidal tails are calculated, which confirm that the tails originate from Palomar 5.

SELECTING CLUSTER MODEL IN Sn - BASED SOLDER ALLOY DESIGN WITH DV - X_α CALCULATION METHOD

Applying calculation method in alloy design should be an important tendency due to its characters of inexpensive cost, high efficiency and prediction. DOS calculations of AuSn, AsSn and SbSn Sn- based alloys have been investigated by employing DV - Xa method, in which different cluster models were adopted to calculate electron structure.It is proved that some regulations must be taken into ac- count in order to carry out alloy design calculation successfully,which are described in this paper in detail.

A Research on Competitiveness of Guangxi City——Based on System Clustering Method and Principal Component Analysis Method

A total of 10 indices of regional economic development in Guangxi are selected.According to the relevant economic data,regional economic development in Guangxi is analyzed by using System Clustering Method and Principal Component Analysis Method.Result shows that System Clustering Method and Principal Component Analysis Method have revealed similar results analysis of economic development level.Overall economic strength of Guangxi is weak and Nanning has relatively high scores of factors due to its advantage of the political,economic and cultural center.Comprehensive scores of other regions are all lower than 1,which has big gap with the development of Nanning.Overall development strategy points out that Guangxi should accelerate the construction of the Ring Northern Bay Economic Zone,create a strong logistics system having strategic significance to national development,use the unique location advantage and rely on the modern transportation system to establish a logistics center and business center connecting the hinterland and the Asean Market.Based on the problems of unbalanced regional economic development in Guangxi,we should speed up the development of service industry in Nanning,construct the circular economy system of industrial city,and accelerate the industrialization process of tourism city in order to realize balanced development of regional economy in Guangxi,China.

Research on the Optimization of a Drilling Rock Breaking Method Based on Fuzzy Cluster Analysis

Improving drilling efficiency is the best way to reduce drilling costs and the choice of the drilling mode is instrumental in doing so.At present,however,a standard approach for the optimization of these processes does not exists yet.Through a comparative statistical analysis of the rock-breaking mechanisms and the characteristics of different drilling methods,this research proposes a set of cues to achieve this objective.Available statistical data are classified by means of a fuzzy cluster analysis according to the anti-drilling characteristic parameters of formation.The results show that different drilling methods rely on their own rock breaking mechanisms and have distinct characteristics.The rotary table drilling method is the most commonly used drilling mode,however,it displays some limitations with regard to deep wells,ultra-deep wells and difficult formations.The combined drilling method has the advantages of both the rotary table drilling and the down-hole power drilling modes.Polycrystalline diamond compact(PDC)drill bits can lead to good results for medium hardness and weakly abrasive formations.Underbalanced drilling for formations with high hardness and strong abrasiveness displays some limitations.

An Eigenspace Method for Detecting Space-Time Disease Clusters with Unknown Population-Data

Space-time disease cluster detection assists in conducting disease surveillance and implementing control strategies.The state-of-the-art method for this kind of problem is the Space-time Scan Statistics(SaTScan)which has limitations for non-traditional/non-clinical data sources due to its parametric model assumptions such as Poisson orGaussian counts.Addressing this problem,an Eigenspace-based method called Multi-EigenSpot has recently been proposed as a nonparametric solution.However,it is based on the population counts data which are not always available in the least developed countries.In addition,the population counts are difficult to approximate for some surveillance data such as emergency department visits and over-the-counter drug sales,where the catchment area for each hospital/pharmacy is undefined.We extend the population-based Multi-EigenSpot method to approximate the potential disease clusters from the observed/reported disease counts only with no need for the population counts.The proposed adaptation uses an estimator of expected disease count that does not depend on the population counts.The proposed method was evaluated on the real-world dataset and the results were compared with the population-based methods:Multi-EigenSpot and SaTScan.The result shows that the proposed adaptation is effective in approximating the important outputs of the population-based methods.

A New Approach to Investigate Students’ Behavior by Using Cluster Analysis as an Unsupervised Methodology in the Field of Education

The problem of taking a set of data and separating it into subgroups where the elements of each subgroup are more similar to each other than they are to elements not in the subgroup has been extensively studied through the statistical method of cluster analysis. In this paper we want to discuss the application of this method to the field of education: particularly, we want to present the use of cluster analysis to separate students into groups that can be recognized and characterized by common traits in their answers to a questionnaire, without any prior knowledge of what form those groups would take (unsupervised classification). We start from a detailed study of the data processing needed by cluster analysis. Then two methods commonly used in cluster analysis are before described only from a theoretical point a view and after in the Section 4 through an example of application to data coming from an open-ended questionnaire administered to a sample of university students. In particular we describe and criticize the variables and parameters used to show the results of the cluster analysis methods.

Coarse-Graining Method Based on Hierarchical Clustering on Complex Networks

With the rapid development of big data, the scale of realistic networks is increasing continually. In order to reduce the network scale, some coarse-graining methods are proposed to transform large-scale networks into mesoscale networks. In this paper, a new coarse-graining method based on hierarchical clustering (HCCG) on complex networks is proposed. The network nodes are grouped by using the hierarchical clustering method, then updating the weights of edges between clusters extract the coarse-grained networks. A large number of simulation experiments on several typical complex networks show that the HCCG method can effectively reduce the network scale, meanwhile maintaining the synchronizability of the original network well. Furthermore, this method is more suitable for these networks with obvious clustering structure, and we can choose freely the size of the coarse-grained networks in the proposed method.

A LOW-PRESSURE AND ONE-STEP METHOD FOR THE SYNTHESIS OF ALKYLIDYNETRICOBALT NONACARBONYL CLUSTERS:RCCo_8(CO)_9

Metal clusters RCCo_3(CO)_9(R-H,C1,Br,CH_3,Ph) were prepared in 18.8-57.3% yields from the reaction of cobalt(Ⅱ)salt and RCX_a under mild PTC conditions(latm CO,25℃).The cobalt salt was reduced to Co(CO)_4 in the presence of Na_3S_2O_4.

Identification of Strong Earthquake Sites in Hebei Region by Making Use of Cluster Method

The Cluster and Hamming methods are used in this paper for a comprehensive study on geology,geomorphology,geophysical field,crustal deformation,active faults,regional stress axes and their relation in Hebei region.Fourteen potential seismic zones in which shocks with M≥6 may happen have been identified.Shocks with M≥6 have occurred in seven of them,and the others have been considered as a future strong earthquake areas.Both the K value and testing of deleting nodes show the stability of results obtained in this paper.The potential seismic zones identified in the paper fall into the areas of marked risk areas within 10 years in North China,but the scale of the identified zones is smaller.The Datong-Yanggao earthquake with M-6.1 occurred in October 1989 precisely in the 14th potential seismic zone mentioned above.

Scanning for Clusters of Large Values in Time Series: Application of the Stein-Chen Method

The purpose of this application paper is to apply the Stein-Chen (SC) method to provide a Poisson-based approximation and corresponding total variation distance bounds in a time series context. The SC method that is used approximates the probability density function (PDF) defined on how many times a pattern such as It,It+1,It+2 = {1 0 1} occurs starting at position t in a time series of length N that has been converted to binary values using a threshold. The original time series that is converted to binary is assumed to consist of a sequence of independent random variables, and could, for example, be a series of residuals that result from fitting any type of time series model. Note that if {1 0 1} is known to not occur, for example, starting at position t = 1, then this information impacts the probability that {1 0 1} occurs starting at position t = 2 or t = 3, because the trials to obtain {1 0 1} are overlapping and thus not independent, so the Poisson distribution assumptions are not met. Nevertheless, the results shown in four examples demonstrate that Poisson-based approximation (that is strictly correct only for independent trials) can be remarkably accurate, and the SC method provides a bound on the total variation distance between the true and approximate PDF.