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.

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.

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.

Factor and Cluster Analysis as a Tool for Patient Segmentation Applied to Hospital Marketing in Jordan

Hospital marketing is becoming important for the survival and the prosperity of the health service. In addition, it indirectly acts as a formal feedback channel for the customer requirements, preferences, suggestions and complaints. In this work we have undertaken a survey based marketing study for two main objectives: The first being to better understand the patient clusters through k-means clustering and the second to understand customer perception of the different known quality perspectives through factor rotated and unrotated analysis. All of the questionnaires were designed according to international studies. Based on general descriptive statistics, items classified with higher variance but important, are: clean environment, doctors and nurses capabilities, and specialized doctors. Items that are less important with low variance are: food type, lighting and insurance. Also, items classified as more important with low variance are: recommended, no mistakes, and the cost. Using factor analysis rotated and unrotated reduced the variables into five main variables described as: medical aspects, psychological aspects, cost aspects, hospital image and ease of access and procedures. Using k-means clustering, the customers can be clustered into four main clusters with two of them described as general patient with wide variety of interest, serious cases interested in specialized doctors and food, and very serious case with high stress on equipment, no mistakes.

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.

Group decision-making method based on entropy and experts cluster analysis

According to the aggregation method of experts＇ evaluation information in group decision-making,the existing methods of determining experts＇ weights based on cluster analysis take into account the expert＇s preferences and the consistency of expert＇s collating vectors,but they lack of the measure of information similarity.So it may occur that although the collating vector is similar to the group consensus,information uncertainty is great of a certain expert.However,it is clustered to a larger group and given a high weight.For this,a new aggregation method based on entropy and cluster analysis in group decision-making process is provided,in which the collating vectors are classified with information similarity coefficient,and the experts＇ weights are determined according to the result of classification,the entropy of collating vectors and the judgment matrix consistency.Finally,a numerical example shows that the method is feasible and effective.

Cluster analysis on summer precipitation field over Qinghai-Tibet Plateau from 1961 to 2004

The summer day-by-day precipitation data of 97 meteorological stations on the Qinghai-Tibet Plateau from 1961 to 2004 were selected to analyze the temporal-spatial distribution through accumulated variance,correlation analysis,regression analysis,empirical orthogonal function,power spectrum function and spatial analysis tools of GIS.The result showed that summer precipitation occupied a relatively high proportion in the area with less annual precipitation on the Plateau and the correlation between summer precipitation and annual precipitation was strong.The altitude of these stations and summer precipitation tendency presented stronger positive correlation below 2000 m,with correlation value up to 0.604（α=0.01）.The subtracting tendency values between 1961-1983 and 1984-2004 at five altitude ranges（2000-2500 m,2500-3000 m,3500-4000 m,4000-4500 m and above 4500 m）were above zero and accounted for 71.4%of the total.Using empirical orthogonal function, summer precipitation could be roughly divided into three precipitation pattern fields：the Southeast Plateau Pattern Field,the Northeast Plateau Pattern field and the Three Rivers＇ Headstream Regions Pattern Field.The former two ones had a reverse value from the north to the south and opposite line was along 35°N.The potential cycles of the three pattern fields were 5.33a,21.33a and 2.17a respectively,tested by the confidence probability of 90%.The station altitudes and summer precipitation potential cycles presented strong negative correlation in the stations above 4500 m,with correlation value of-0.626（α=0.01）.In Three Rivers Headstream Regions summer precipitation cycle decreased as the altitude rose in the stations above 3500 m and increased as the altitude rose in those below 3500 m.The empirical orthogonal function analysis in June precipitation,July precipitation and August precipitation showed that the June precipitation pattern field was similar to the July＇s,in which southern Plateau was positive and northern Plateau negative.But positive value area in July precipitation pattern field was obviously less than June＇s.The August pattern field was totally opposite to June＇s and July＇s.The positive area in August pattern field jumped from the southern Plateau to the northern Plateau.

Cluster Analysis on Japonica Rice(Oryza sativa L.) with Good Eating Quality Based on SSR Markers and Phenotypic Traits

Diversity of 60 conventional japonica rice accessions with good eating quality at home and abroad was analyzed using SSR molecular markers, agronomic traits and taste characteristics. A total of 290 alleles were detected in the 60 accessions at 72 SSR loci with the high similarity coefficients varying between 0.600 and 0.924. The loci on chromosome 5 showed the greatest value in average allele number. Additionally, most of the SSR loci could detect 3 to 4 alleles. An UPGMA dendrogram based on the cluster analysis of the genetic similarity coefficients showed that the grouping trend of part of the rice accessions was geographic-related and most of the rice accessions in Jiangsu Province, China were clustered together. Furthermore, many domestic accessions from south and north origins in China were close to the foreign japonica rice varieties, as proved by their pedigree origin from the foreign high-quality sources. For taste characteristics, part of the accessions with excellent taste were clearly clustered into one category though they came from different geographical regions, which indicates that taste characteristics of some varieties were mainly genetically determined. In addition, the agronomic traits of japonica rice with good taste might be closely related with their geographical origins, but the relationship between superior taste characteristics and agronomic traits should be further clarified.

Bohai crude oil identification by gas chromatogram fingerprinting quantitative analysis coupled with cluster analysis

By gas chromatogram, six crude oils fingerprinting distributed in four oilfields and four oil platforms were analyzed and the corre- sponding normal paraffin hydrocarbon （ including pristane and phytane） concentration was obtained by the internal standard methed. The normal paraffin hydrocarbon distribution patterns of six crude oils were built and compared. The cluster analysis on the normal paraffin hydrocarbon concentration was conducted for classification and some ratios of oils were used for oils comparison. The results indicated： there was a clear difference within different crude oils in different oil fields and a small difference between the crude oils in the same oil platform. The normal paraffin hydrocarbon distribution pattern and ratios, as well as the cluster analysis on the nomad paraffin hydrocarbon concentration can have a better differentiation result for the crude oils with small difference than the original gas chromatogram.