R-Factor Analysis of Data Based on Population Models Comprising R- and Q-Factors Leads to Biased Loading Estimates

Effects of performing an R-factor analysis of observed variables based on population models comprising R- and Q-factors were investigated. Although R-factor analysis of data based on a population model comprising R- and Q-factors is possible, this may lead to model error. Accordingly, loading estimates resulting from R-factor analysis of sample data drawn from a population based on a combination of R- and Q-factors will be biased. It was shown in a simulation study that a large amount of Q-factor variance induces an increase in the variation of R-factor loading estimates beyond the chance level. Tests of the multivariate kurtosis of observed variables are proposed as an indicator of possible Q-factor variance in observed variables as a prerequisite for R-factor analysis.

Research on Competitiveness of County Economy Based on Factor Analysis and Cluster Analysis——Taking 88 Counties in Guizhou as Samples

17 indices are selected,such as the growth rate of total regional output value,the proportion of tertiary industry in GDP,per capita financial expenditure,and soil erosion rate of Guizhou Province in 2009.According to the relevant indices data of statistical yearbook and governmental website,by using the method of factor analysis and the method of cluster analysis,we assess the competitiveness of county economy in 88 counties of Guizhou Province.The results show that the competitiveness of county economy in Guizhou Province is impacted by factors of location and economic foundation.In addition,the resources environment,economic structure,economic developmental speed and other factors also impact the competitiveness of county economy in Guizhou Province.Based on these,in the light of the developmental characteristics of different counties in conjunction with different developmental advantages in different regions,we should adopt different developmental strategies according to local conditions,which is significant to rapid,healthy and sustainable development of county economy in Guizhou Province.

ARHCS (Automatic Rainfall Half-Life Cluster System): A Landslides Early Warning System (LEWS) Using Cluster Analysis and Automatic Threshold Definition

A significant portion of Landslide Early Warning Systems (LEWS) relies on the definition of operational thresholds and the monitoring of cumulative rainfall for alert issuance. These thresholds can be obtained in various ways, but most often they are based on previous landslide data. This approach introduces several limitations. For instance, there is a requirement for the location to have been previously monitored in some way to have this type of information recorded. Another significant limitation is the need for information regarding the location and timing of incidents. Despite the current ease of obtaining location information (GPS, drone images, etc.), the timing of the event remains challenging to ascertain for a considerable portion of landslide data. Concerning rainfall monitoring, there are multiple ways to consider it, for instance, examining accumulations over various intervals (1 h, 6 h, 24 h, 72 h), as well as in the calculation of effective rainfall, which represents the precipitation that actually infiltrates the soil. However, in the vast majority of cases, both the thresholds and the rain monitoring approach are defined manually and subjectively, relying on the operators’ experience. This makes the process labor-intensive and time-consuming, hindering the establishment of a truly standardized and rapidly scalable methodology on a large scale. In this work, we propose a Landslides Early Warning System (LEWS) based on the concept of rainfall half-life and the determination of thresholds using Cluster Analysis and data inversion. The system is designed to be applied in extensive monitoring networks, such as the one utilized by Cemaden, Brazil’s National Center for Monitoring and Early Warning of Natural Disasters.

Research on Tourism Competitiveness of Chinese Island Counties:Based on Factor and Cluster Analysis

From the perspective of tourism competitiveness,the paper takes 12 island counties of China as the research object,and applies the method of factor analysis to study their competitiveness.The result shows that Putuo and Dinghai are more competitive while Pingtan and Nan'ao are less competitive.Finally,the 12 island counties are divided into four styles:first-class competitive county (Putuo),seond-class competitive counties (Dinghai,Yuhuan),third-class competitive counties (Chongming,Daishan,Changdao,Changhai and Shengsi),fourth-class competitive counties (Dongshan,Dongtou,Pingtan and Nan'ao) by cluster analysis.The classification of island counties is to clear their relative position,then to promote their development.

Factor and Cluster Analysis on the Competitiveness of Agri-food Processing Industry in China

This paper establishes 13 evaluation indicators for the competitiveness of agri-food processing industry,uses factor analysis to evaluate the competitiveness of agri-food processing industry in 31 provinces(cities,autonomous regions)of China,and does cluster analysis to divide these regions into several categories according to the difference in competitiveness,in order to understand the level of competitiveness of agri-food processing industry in China.

Fuzzy cluster analysis of water mass in the western Taiwan Strait in spring 2019

The classification of the springtime water mass has an important influence on the hydrography,regional climate change and fishery in the Taiwan Strait.Based on 58 stations of CTD profiling data collected in the western and southwestern Taiwan Strait during the spring cruise of 2019,we analyze the spatial distributions of temperature(T)and salinity(S)in the investigation area.Then by using the fuzzy cluster method combined with the T-S similarity number,we classify the investigation area into 5 water masses:the Minzhe Coastal Water(MZCW),the Taiwan Strait Mixed Water(TSMW),the South China Sea Surface Water(SCSSW),the South China Sea Subsurface Water(SCSUW)and the Kuroshio Branch Water(KBW).The MZCW appears in the near surface layer along the western coast of Taiwan Strait,showing low-salinity(<32.0)tongues near the Minjiang River Estuary and the Xiamen Bay mouth.The TSMW covers most upper layer of the investigation area.The SCSSW is mainly distributed in the upper layer of the southwestern Taiwan Strait,beneath which is the SCSUW.The KBW is a high temperature(core value of 26.36℃)and high salinity(core value of 34.62)water mass located southeast of the Taiwan Bank and partially in the central Taiwan Strait.

Analysis of inhomogeneity of solidified microstructure of continuous casting copper tubular billet based on factor analysis

The horizontal continuous casting process,the initial step in TP2 copper tubular processing,directly determines the microstructure and properties of copper tubular.However,the process parameters of the continuous casting characterize time variation,multiple disturbances and strong coupling.As a consequence,their influence on a casting billet is difficult to be determined.Due to the above issues,the common factor and special factor analysis of the factor analysis model were used in this study,and the casting experiment and billet metallographic experiment were carried out to diagnose and analyze the reason of the microstructure inhomogeneity.The multiple process parameters were studied and classified using common factor analysis,2 the cast billets with abnormal microstructures were identified by GT^(2) statistics,and the most important factors affecting the microstructural homogeneity were found by special factor analysis.The calculated and experimental results show that the principal parameters influencing the inhomogeneity of solidified microstructure are the primary inlet water pressure and the primary outlet water temperature.According to the consequence of the above investigation,the inhomogeneity of the copper billet microstructure can be effectively improved when the process parameters are controlled and adjusted.

Dealing with Multicollinearity in Factor Analysis: The Problem, Detections, and Solutions

Multicollinearity in factor analysis has negative effects, including unreliable factor structure, inconsistent loadings, inflated standard errors, reduced discriminant validity, and difficulties in interpreting factors. It also leads to reduced stability, hindered factor replication, misinterpretation of factor importance, increased parameter estimation instability, reduced power to detect the true factor structure, compromised model fit indices, and biased factor loadings. Multicollinearity introduces uncertainty, complexity, and limited generalizability, hampering factor analysis. To address multicollinearity, researchers can examine the correlation matrix to identify variables with high correlation coefficients. The Variance Inflation Factor (VIF) measures the inflation of regression coefficients due to multicollinearity. Tolerance, the reciprocal of VIF, indicates the proportion of variance in a predictor variable not shared with others. Eigenvalues help assess multicollinearity, with values greater than 1 suggesting the retention of factors. Principal Component Analysis (PCA) reduces dimensionality and identifies highly correlated variables. Other diagnostic measures include the condition number and Cook’s distance. Researchers can center or standardize data, perform variable filtering, use PCA instead of factor analysis, employ factor scores, merge correlated variables, or apply clustering techniques for the solution of the multicollinearity problem. Further research is needed to explore different types of multicollinearity, assess method effectiveness, and investigate the relationship with other factor analysis issues.

Using Factor Analysis to Determine the Factors Impacting Learning Python for Non-Technical Business Analytics Graduate Students

This pioneering research represents a unique and singular study conducted within the United States, with a specific focus on non-technical graduate students pursuing degrees in business analytics. The primary impetus behind this study stems from the escalating demand for data-driven professionals, the diverse academic backgrounds of students, the imperative for adaptable pedagogical methods, the ever-evolving landscape of curriculum designs, and the overarching commitment to fostering educational equity. To investigate these multifaceted dynamics, we employed a data collection method that included the distribution of an online survey on platforms such as LinkedIn. Our survey reached and engaged 74 graduate students actively pursuing degrees in Business Analytics within the United States. This comprehensive research is the first and only one of its kind conducted in this context, and it serves as a vanguard exploration into the challenges and influences that shape the learning journey of Python among non-technical graduate Business Analytics students. The analytical insights derived from this research underscore the pivotal role of hands-on learning strategies, exemplified by practice exercises and assignments. Moreover, the study highlights the positive and constructive influence of collaboration and peer support in the process of learning Python. These invaluable findings significantly augment the existing body of knowledge in the field of business analytics. Furthermore, they offer an essential resource for educators and institutions seeking to optimize the educational experiences of non-technical students as they acquire essential Python skills.

CPSO: Chaotic Particle Swarm Optimization for Cluster Analysis

Background:To solve the cluster analysis better,we propose a new method based on the chaotic particle swarm optimization(CPSO)algorithm.Methods:In order to enhance the performance in clustering,we propose a novel method based on CPSO.We first evaluate the clustering performance of this model using the variance ratio criterion(VRC)as the evaluation metric.The effectiveness of the CPSO algorithm is compared with that of the traditional particle swarm optimization(PSO)algorithm.The CPSO aims to improve the VRC value while avoiding local optimal solutions.The simulated dataset is set at three levels of overlapping:non-overlapping,partial overlapping,and severe overlapping.Finally,we compare CPSO with two other methods.Results:By observing the comparative results,our proposed CPSO method performs outstandingly.In the conditions of non-overlapping,partial overlapping,and severe overlapping,our method has the best VRC values of 1683.2,620.5,and 275.6,respectively.The mean VRC values in these three cases are 1683.2,617.8,and 222.6.Conclusion:The CPSO performed better than other methods for cluster analysis problems.CPSO is effective for cluster analysis.

Evaluation and classification of residential greenbelt quality based on factor analysis & clustering analysis:An example of Xinxiang City,China

Five factors expressing greenbelt quality and one factor expressing quantity were adopted for evaluation of the residential greenbelt, and the AHP （Analytical Hierarchy Process） method was used to determine the value of factors. Thirty residential areas were selected as the samples. Two principal components were extracted and their expression was constructed by method of factor anlysis, therefore, quality evaluation of residential greenbelt was obtained. The accuracy of the function and implement quality classification toward the residential greenbelts in Xinxiang City were validated by clustering analysis method. The results showed that the greenbelt quality of fourteen residential areas was higher than the average level, of which eleven were newly-built residential areas. The 30 residential areas were classified into three types according to their greenbelt features and their formation by clustering analysis method. Finally rational proposal basing on aforesaid evaluating results was proposed for construction and renewal of residential greenbelt, upon which directive basis was provided for construction and renewal of residential greenbelt.

Mathematical Tools of Cluster Analysis

The paper deals with cluster analysis and comparison of clustering methods. Cluster analysis belongs to multivariate statistical methods. Cluster analysis is defined as general logical technique, procedure, which allows clustering variable objects into groups-clusters on the basis of similarity or dissimilarity. Cluster analysis involves computational procedures, of which purpose is to reduce a set of data on several relatively homogenous groups-clusters, while the condition of reduction is maximal and simultaneously minimal similarity of clusters. Similarity of objects is studied by the degree of similarity (correlation coefficient and association coefficient) or the degree of dissimilarity-degree of distance (distance coefficient). Methods of cluster analysis are on the basis of clustering classified as hierarchical or non-hierarchical methods.

Slope deformation partitioning and monitoring points optimization based on cluster analysis

The scientific and fair positioning of monitoring locations for surface displacement on slopes is a prerequisite for early warning and forecasting.However,there is no specific provision on how to effectively determine the number and location of monitoring points according to the actual deformation characteristics of the slope.There are still some defects in the layout of monitoring points.To this end,based on displacement data series and spatial location information of surface displacement monitoring points,by combining displacement series correlation and spatial distance influence factors,a spatial deformation correlation calculation model of slope based on clustering analysis was proposed to calculate the correlation between different monitoring points,based on which the deformation area of the slope was divided.The redundant monitoring points in each partition were eliminated based on the partition's outcome,and the overall optimal arrangement of slope monitoring points was then achieved.This method scientifically addresses the issues of slope deformation zoning and data gathering overlap.It not only eliminates human subjectivity from slope deformation zoning but also increases the efficiency and accuracy of slope monitoring.In order to verify the effectiveness of the method,a sand-mudstone interbedded CounterTilt excavation slope in the Chongqing city of China was used as the research object.Twenty-four monitoring points deployed on this slope were monitored for surface displacement for 13 months.The spatial location of the monitoring points was discussed.The results show that the proposed method of slope deformation zoning and the optimized placement of monitoring points are feasible.

Influencing factor analysis of interception probability and classification-regression neural network based estimation

The interception probability of a single missile is the basis for combat plan design and weapon performance evaluation,while its influencing factors are complex and mutually coupled.Existing calculation methods have very limited analysis of the influence mechanism of influencing factors,and none of them has analyzed the influence of the guidance law.This paper considers the influencing factors of both the interceptor and the target more comprehensively.Interceptor parameters include speed,guidance law,guidance error,fuze error,and fragment killing ability,while target performance includes speed,maneuverability,and vulnerability.In this paper,an interception model is established,Monte Carlo simulation is carried out,and the influence mechanism of each factor is analyzed based on the model and simulation results.Finally,this paper proposes a classification-regression neural network to quickly estimate the interception probability based on the value of influencing factors.The proposed method reduces the interference of invalid interception data to valid data,so its prediction accuracy is significantly better than that of pure regression neural networks.

Factor-Cluster Analysis and Effect of Particle Size on Total Recoverable Metal Concentration in Sediments of the Lower Tennessee River Basin

Total recoverable concentration of five elements of concern: Aluminum, Iron, Manganese, Arsenic and Lead (Al, Fe, Mn, As, Pb) were measured by inductively coupled plasma atomic emission spectrometry, and mass spectrometry. The results show that sediment texture plays a controlling role in the concentrations and their spatial distribution. Principal Component Analysis and Cluster Analysis were used to analyze the grain sizes of the sediments. Result of texture analysis classified the samples into three main components in percentages: sand, silt, and clay. Significant differences among the element concentrations in the three groups were observed, and the concentrations of the elements in each group are reported in this study. Most of the elements have their highest concentrations in the fine-grained samples with clay playing an important role, in comparison with the sand component of the soil/sediment samples. There appears to be a strong correlation between samples with high silt, and clay content with the areas of elevated concentrations for Al, Fe, and Mn. There was a strong correlation between aluminum and lead with clay;lead with silt;and sand with manganese, aluminum, and lead. However, there was no strong relationship between the soil textures and iron or arsenic. All elements measured were statistically significant (at P ≤ 0.05) by watershed. The upland areas, and depositional areas’ spatial variation of element concentrations in the sediments were also observed, which was in line with the spatial distribution of the grain size and was thought to be related to the watersheds hydrological dynamics.

Variation and Cluster Analysis on Leaf Characters from Different Provenance Sources of Polygonum multiflorum Thunb

[Objective] The aim was to study the variation of leaf characters from different provenance sources of Polygonum multiflorum Thunb,as well as to carry out cluster analysis on P.multiflorum from different provenance sources to provide basis for the classification,identification,breeding and improved variety selection of P.multiflorum.[Method] Leaf shape characters of 31 copies of germplasm resources in the major distribution region of the whole country were determined,and the genetic variation of P.multiflorum leaves from different producing areas was analyzed.[Result] The leaf characters of single plant of the same experimental provenance source of P.multiflorum were relatively stable,the variation was mainly found on the single leaf area,1/2 leaf width,leaf width and other indicators;the variation of each leaf character among different provenance sources was obvious,and the variation was mainly found on the single leaf weight,leaf area,1/2 leaf width,leaf length and other indicators.The correlation analysis of each leaf character in P.multiflorum suggested that the single leaf area and single leaf weight showed extremely significant positive correlation with leaf length,1/2 leaf width,leaf width,leaf thickness and leaf stem length,while the single leaf area and single leaf weight showed significant negative correlation with WWR（leaf width/1/2 leaf width）and LWR（leaf length/1/2 leaf length）,in addition,several macroscopic leaf characters such as leaf length,1/2 leaf width,leaf width,leaf stem length showed extremely positive correlation.The main component analysis result suggested that the contribution rate of accumulation variance of the front three main components was up to 97.4%,which could better reflect the comprehensive performance of leaf characters of different provenance sources of P.multiflorum.The cluster analysis showed that the experimental 31 copies of P.multiflorum provenance sources should be divided into three classes,the first class was distributed in the Middle,Western of Guizhou,northwestern of Guangxi and western areas with higher altitude;the second class was distributed in Hunan,Hubei,Sichuan,Guangdong and the most area of Guangxi;the third class was distributed in Anhui,Jiangsu and Henan and Shandong.[Conclusion] Cluster analysis of leaf characters indicated that the kinds of provenance sources which the geographical position was closer could be got together.The study had provided a certain basis for the classification of P.multiflorum.

Application of cluster analysis and stepwise regression in predicting the traffic volume of lanes

Because of the difficulty to obtain the traffic flow information of lanes at non-detector intersections in most metropolises of the world,based on the relationships between the lanes of signal-controlled intersections,cluster analysis and stepwise regression are integrated to predict the traffic volume of lanes at non-detector isolated controlled intersections.First cluster analysis is used to cluster the lanes of non-detector isolated signal-controlled intersections and the lanes of all signal-controlled intersections with detectors.Then, by the results of cluster analysis,the traffic volume samples are selected randomly and stepwise regression is used to predict the traffic volume of lanes at non-detector isolated signal-controlled intersections.The method is tested by the traffic volume data of lanes of the road network of Nanjing city.The problem of predicting the traffic volume of lanes at non-detector isolated signal-controlled intersections was resolved and can be widely used in urban traffic flow guidance and urban traffic control in cities without enough intersections equipped with detectors.

Characterizing heterogeneity in vehicular traffic speed using two-step cluster analysis

In order to analyze the heterogeneity in vehicular traffic speed, a new method that integrates cluster analysis and probability distribution function fitting is presented. First, for identifying the optimal number of clusters, the two-step cluster method is applied to analyze actual speed data, which suggests that dividing speed data into two clusters can best reflect the intrinsic patterns of traffic flows. Such information is then taken as guidance in probability distribution function fitting. The normal, skew-normal and skew-t distribution functions are used to fit the probability distribution of each cluster respectively, which suggests that the skew-t distribution has the highest fitting accuracy; the second is skew-normal distribution; the worst is normal distribution. Model analysis results demonstrate that the proposed mixture model has a better fitting and generalization capability than the conventional single model. In addition, the new method is more flexible in terms of data fitting and can provide a more accurate model of speed distribution.

Cluster Analysis of Morphologic Characteristic of Eight Geographical Populations of Rana Dybowskii

[ObJective] The research aimed to determine the geographic distribution map of system of Rana dybowskii. [Method] Four morphologic indices （body length, body weight, forelimb length, hindlimb length） of eight geographical populations of R.dybowskii which naturally distribute in Changhai Mountain and Xiaoxing＇an Mountain were measured. Measure results were variance analyzed and cluster analyzed. [Result] Variance analysis showed： the genetic branching among the Dongfanghong male population（ belongs to Wandashan） and Xiaoxing＇an Mountain male population and Changbai Mountain male population were significantly different （P〈0.05） ; the genetic branching between the Hebei female population （belongs to Xiaoxing＇an Mountain） and Changbai Mountain female population was significantly different （P〈0.05 ）. Cluster analysis showed ： male R.dybowskii can be divided into three groups ： the first group included Quanyang, Tianbei, Chaoyang and Ddkouqin, the second group included Tieli and Anshan, the third group included Dongfanghong; and the female R. dybowskii can be divided into three groups ： the first group included Quanyang and Chaoyang, the second group included Tianbei and Dakouqin, the third group included Hebei. [Condusion] The paper deduced that the Sanjiang Plain was the geographical origin center ofR. dybowskii which radiated to Changbai Mountain and Xiaoxing＇an Mountain along the adverse current of Songhua River basin, therefore, the current distribution pattern of R. dybowskii was formed.

Principal Component Analysis and Cluster Analysis of Fagopyrum tataricum Varieties(Lines)

In order to reveal the genetic differences and agronomic traits of Fagopy-rum tataricum_ varieties （lines） intuitively, explore good resources and avoid the blindness of parent selection during the breeding process, six primary agronomic traits of 45 F. tataricum_ varieties （lines） that came from the eleven buckwheat breeding departments across the country were analyzed with principal component analysis and cluster analysis. The results of principal component analysis showed that the six agronomic traits could be simplified into three principal components, and the cumulative contribution rate reached 83%. The results of cluster analysis showed that the 45 F. tataricum varieties （lines） were classified into four groups：high stalk, medium yield and smal grain type, medium stalk, high yield and large grain type, medium stalk, low yield and smal grain type and high stalk, medium yield and medium grain type. Among them, performance of comprehensive trait of the second type was better than that of the other types. Thus, the F. tataricum_va-rieties （lines） that were classified into the second type could be considered as good varieties （lines） or breeding materials. The genetic differences among F. tataricum_varieties （lines） had no necessary correlations with origin and geographical distance. ln addition to complementary traits and geographical distance, genetic distances （dif-ferent populations） should be taken into consideration during parent selection in cross breeding.