A vertex-colored graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex...A vertex-colored graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex-connection number of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex-connected. If for every pair u, v of distinct vertices, G contains a rainbow u-v geodesic, then G is strong rainbow vertex-connected. The minimum number k for which there exists a k-vertex-coloring of G that results in a strongly rainbow vertex-connected graph is called the strong rainbow vertex-connection number of G, denoted by srvc(G). Observe that rvc(G) ≤ srvc(G) for any nontrivial connected graph G. In this paper, for a Ladder L_n,we determine the exact value of srvc(L_n) for n even. For n odd, upper and lower bounds of srvc(L_n) are obtained. We also give upper and lower bounds of the(strong) rainbow vertex-connection number of Mbius Ladder.展开更多
An appropriate optimal number of market segments(ONS)estimation is essential for an enterprise to achieve successful market segmentation,but at present,there is a serious lack of attention to this issue in market segm...An appropriate optimal number of market segments(ONS)estimation is essential for an enterprise to achieve successful market segmentation,but at present,there is a serious lack of attention to this issue in market segmentation.In our study,an independent adaptive ONS estimation method BWCON-NSDK-means++is proposed by integrating a newinternal validity index(IVI)Between-Within-Connectivity(BWCON)and a newstable clustering algorithmNatural-SDK-means++(NSDK-means++)in a novel way.First,to complete the evaluation dimensions of the existing IVIs,we designed a connectivity formula based on the neighbor relationship and proposed the BWCON by integrating the connectivity with other two commonly considered measures of compactness and separation.Then,considering the stability,number of parameters and clustering performance,we proposed the NSDK-means++to participate in the integrationwhere the natural neighbor was used to optimize the initial cluster centers(ICCs)determination strategy in the SDK-means++.At last,to ensure the objectivity of the estimatedONS,we designed a BWCON-based ONS estimation framework that does not require the user to set any parameters in advance and integrated the NSDK-means++into this framework forming a practical ONS estimation tool BWCON-NSDK-means++.The final experimental results showthat the proposed BWCONand NSDK-means++are significantlymore suitable than their respective existing models to participate in the integration for determining theONS,and the proposed BWCON-NSDK-means++is demonstrably superior to the BWCON-KMA,BWCONMBK,BWCON-KM++,BWCON-RKM++,BWCON-SDKM++,BWCON-Single linkage,BWCON-Complete linkage,BWCON-Average linkage and BWCON-Ward linkage in terms of the ONS estimation.Moreover,as an independentmarket segmentation tool,the BWCON-NSDK-means++also outperforms the existing models with respect to the inter-market differentiation and sub-market size.展开更多
径流曲线数模型(Soil Conservation Service Curve Number Model,简称SCS-CN模型)可以利用降雨资料估算径流,对水资源合理配置和山洪灾害预警具有重要意义,因为其方便计算、参数简单,而被广泛应用。目前标准SCS-CN模型在山区小流域的适...径流曲线数模型(Soil Conservation Service Curve Number Model,简称SCS-CN模型)可以利用降雨资料估算径流,对水资源合理配置和山洪灾害预警具有重要意义,因为其方便计算、参数简单,而被广泛应用。目前标准SCS-CN模型在山区小流域的适用性欠佳,因此需要对模型参数进行优化以提高预测精度。本文以湖南省螺岭桥流域为例,根据实测降雨径流资料优化径流曲线数CN(Curve Number)查算表,并利用步长优化参数算法研究初损率对模型精度的影响,将优化模型的方法应用于湖南省凤凰小流域,验证该优化方法的可靠性。结果分析表明:与标准SCS-CN模型相比,优化后的SCS-CN模型效率系数NSE从0.576提升至0.813,决定系数R^(2)为0.858。将模型优化方法验证于气候地形条件相似的凤凰流域,模型NSE值提高117%。通过预测径流深与实测径流深比较,优化模型模拟精度较为理想,对湖南省山区小流域场次降雨产流预报有一定的参考意义。展开更多
聚类分析针对不同的数据特点采用不同的相似性度量,现实世界中数据分布复杂,存在分布无规律、密度不均匀等现象,单独考虑实例属性相似性或分布结构连通性会影响聚类效果。为此,提出了一种基于属性相似性和分布结构连通性的聚类算法(A Cl...聚类分析针对不同的数据特点采用不同的相似性度量,现实世界中数据分布复杂,存在分布无规律、密度不均匀等现象,单独考虑实例属性相似性或分布结构连通性会影响聚类效果。为此,提出了一种基于属性相似性和分布结构连通性的聚类算法(A Clustering Algorithm Based on Attribute Similarity and Distributed Structure Connectivity, ASDSC)。首先,利用待聚类数据集中的所有数据实例构建完全无向图,定义了一种兼顾属性相似和分布结构连通的新颖相似性度量方式,用于计算节点相似性,并构造邻接矩阵更新边的权重;其次,借助邻接矩阵执行递增步长的随机游走,依据顶点的连通中心性来识别簇中心并给定簇编号,同时获取其他顶点的连通性;然后,利用连通性计算顶点间的依赖关系,并据此进行簇编号的传播,直至完成聚类。最后,为了验证该方法的聚类性能,在16个合成数据集和10个真实数据集上与5种先进聚类算法进行了对比实验,ASDSC算法取得了优异性能。展开更多
基金Supported by the National Natural Science Foundation of China(11551001,11061027,11261047,11161037,11461054)Supported by the Science Found of Qinghai Province(2016-ZJ-948Q,2014-ZJ-907)
文摘A vertex-colored graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex-connection number of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex-connected. If for every pair u, v of distinct vertices, G contains a rainbow u-v geodesic, then G is strong rainbow vertex-connected. The minimum number k for which there exists a k-vertex-coloring of G that results in a strongly rainbow vertex-connected graph is called the strong rainbow vertex-connection number of G, denoted by srvc(G). Observe that rvc(G) ≤ srvc(G) for any nontrivial connected graph G. In this paper, for a Ladder L_n,we determine the exact value of srvc(L_n) for n even. For n odd, upper and lower bounds of srvc(L_n) are obtained. We also give upper and lower bounds of the(strong) rainbow vertex-connection number of Mbius Ladder.
基金supported by the earmarked fund for CARS-29 and the open funds of the Key Laboratory of Viticulture and Enology,Ministry of Agriculture,China.
文摘An appropriate optimal number of market segments(ONS)estimation is essential for an enterprise to achieve successful market segmentation,but at present,there is a serious lack of attention to this issue in market segmentation.In our study,an independent adaptive ONS estimation method BWCON-NSDK-means++is proposed by integrating a newinternal validity index(IVI)Between-Within-Connectivity(BWCON)and a newstable clustering algorithmNatural-SDK-means++(NSDK-means++)in a novel way.First,to complete the evaluation dimensions of the existing IVIs,we designed a connectivity formula based on the neighbor relationship and proposed the BWCON by integrating the connectivity with other two commonly considered measures of compactness and separation.Then,considering the stability,number of parameters and clustering performance,we proposed the NSDK-means++to participate in the integrationwhere the natural neighbor was used to optimize the initial cluster centers(ICCs)determination strategy in the SDK-means++.At last,to ensure the objectivity of the estimatedONS,we designed a BWCON-based ONS estimation framework that does not require the user to set any parameters in advance and integrated the NSDK-means++into this framework forming a practical ONS estimation tool BWCON-NSDK-means++.The final experimental results showthat the proposed BWCONand NSDK-means++are significantlymore suitable than their respective existing models to participate in the integration for determining theONS,and the proposed BWCON-NSDK-means++is demonstrably superior to the BWCON-KMA,BWCONMBK,BWCON-KM++,BWCON-RKM++,BWCON-SDKM++,BWCON-Single linkage,BWCON-Complete linkage,BWCON-Average linkage and BWCON-Ward linkage in terms of the ONS estimation.Moreover,as an independentmarket segmentation tool,the BWCON-NSDK-means++also outperforms the existing models with respect to the inter-market differentiation and sub-market size.
文摘径流曲线数模型(Soil Conservation Service Curve Number Model,简称SCS-CN模型)可以利用降雨资料估算径流,对水资源合理配置和山洪灾害预警具有重要意义,因为其方便计算、参数简单,而被广泛应用。目前标准SCS-CN模型在山区小流域的适用性欠佳,因此需要对模型参数进行优化以提高预测精度。本文以湖南省螺岭桥流域为例,根据实测降雨径流资料优化径流曲线数CN(Curve Number)查算表,并利用步长优化参数算法研究初损率对模型精度的影响,将优化模型的方法应用于湖南省凤凰小流域,验证该优化方法的可靠性。结果分析表明:与标准SCS-CN模型相比,优化后的SCS-CN模型效率系数NSE从0.576提升至0.813,决定系数R^(2)为0.858。将模型优化方法验证于气候地形条件相似的凤凰流域,模型NSE值提高117%。通过预测径流深与实测径流深比较,优化模型模拟精度较为理想,对湖南省山区小流域场次降雨产流预报有一定的参考意义。
文摘聚类分析针对不同的数据特点采用不同的相似性度量,现实世界中数据分布复杂,存在分布无规律、密度不均匀等现象,单独考虑实例属性相似性或分布结构连通性会影响聚类效果。为此,提出了一种基于属性相似性和分布结构连通性的聚类算法(A Clustering Algorithm Based on Attribute Similarity and Distributed Structure Connectivity, ASDSC)。首先,利用待聚类数据集中的所有数据实例构建完全无向图,定义了一种兼顾属性相似和分布结构连通的新颖相似性度量方式,用于计算节点相似性,并构造邻接矩阵更新边的权重;其次,借助邻接矩阵执行递增步长的随机游走,依据顶点的连通中心性来识别簇中心并给定簇编号,同时获取其他顶点的连通性;然后,利用连通性计算顶点间的依赖关系,并据此进行簇编号的传播,直至完成聚类。最后,为了验证该方法的聚类性能,在16个合成数据集和10个真实数据集上与5种先进聚类算法进行了对比实验,ASDSC算法取得了优异性能。
