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.

Safety Risk Assessment of Overturning Construction of Towering Structure Based on Cloud Matter–Element Coupled Model

Rapid urbanization has led to a surge in the number of towering structures,and overturning is widely used because it can better accommodate the construction of shaped structures such as variable sections.The complexity of the construction process makes the construction risk have certain randomness,so this paper proposes a cloudbased coupled matter-element model to address the ambiguity and randomness in the safety risk assessment of overturning construction of towering structures.In the pretended model,the digital eigenvalues of the cloud model are used to replace the eigenvalues in the matter–element basic element,and calculate the cloud correlation of the risk assessment metrics through the correlation algorithm of the cloud model to build the computational model.Meanwhile,the improved hierarchical analysis method based on the cloud model is used to determine the weight of the index.The comprehensive evaluation scores of the evaluation event are then obtained through the weighted average method,and the safety risk level is determined accordingly.Through empirical analysis,(1)the improved hierarchical analysis method based on the cloud model can incorporate the data of multiple decisionmakers into the calculation formula to determine theweights,which makes the assessment resultsmore credible;(2)the evaluation results of the cloud-basedmatter-element coupledmodelmethod are basically consistent with those of the other two commonly used methods,and the confidence factor is less than 0.05,indicating that the cloudbased physical element coupled model method is reasonable and practical for towering structure overturning;(3)the cloud-based coupled element model method,which confirms the reliability of risk level by performing Spearman correlation on comprehensive assessment scores,can provide more comprehensive information of instances compared with other methods,and more comprehensively reflects the fuzzy uncertainty relationship between assessment indexes,which makes the assessment results more realistic,scientific and reliable.

Study on Land Use Regionalization in Henan Province

According to the natural ecology and socio-economic conditions in Henan Province, a land use regionalization index system with 6 factors and 24 factor layers was constructed by combining with the characteristics of land use in Henan Province. Expert scoring method was used to determine the weights of the indicators. Based on the similarities and differences of these factors in the index system at county （city, district） levels, hierarchical clustering method was used to make the quantitative analysis to the land use regionalization in Henan Province. And constrastive analysis and qualitative analysis were made to the regionalization scheme by combining with the acutal conditions in the counties （cities, districts）, and finally, Henan Province was classified into 6 regions.