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
A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken ove...A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken over all minimal k-connected dominating sets of G.In this paper,we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.展开更多
I show how many connections of Γ?are presently existing from R?to β?as they are being inputted simultaneously through tensor products. I plan to address the Quantum state of this tensor connection st...I show how many connections of Γ?are presently existing from R?to β?as they are being inputted simultaneously through tensor products. I plan to address the Quantum state of this tensor connection step by step throughout the application presented. Also, I will show you how to prove that the connection is true for this tensor connection through its output method using a small bit of tensor calculus and mostly number theory.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
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
Utilizing granular computing to enhance artificial neural network architecture, a newtype of network emerges—thegranular neural network (GNN). GNNs offer distinct advantages over their traditional counterparts: The a...Utilizing granular computing to enhance artificial neural network architecture, a newtype of network emerges—thegranular neural network (GNN). GNNs offer distinct advantages over their traditional counterparts: The ability toprocess both numerical and granular data, leading to improved interpretability. This paper proposes a novel designmethod for constructing GNNs, drawing inspiration from existing interval-valued neural networks built uponNNNs. However, unlike the proposed algorithm in this work, which employs interval values or triangular fuzzynumbers for connections, existing methods rely on a pre-defined numerical network. This new method utilizesa uniform distribution of information granularity to granulate connections with unknown parameters, resultingin independent GNN structures. To quantify the granularity output of the network, the product of two commonperformance indices is adopted: The coverage of numerical data and the specificity of information granules.Optimizing this combined performance index helps determine the optimal parameters for the network. Finally,the paper presents the complete model construction and validates its feasibility through experiments on datasetsfrom the UCIMachine Learning Repository. The results demonstrate the proposed algorithm’s effectiveness andpromising performance.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.
文摘A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken over all minimal k-connected dominating sets of G.In this paper,we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.
文摘I show how many connections of Γ?are presently existing from R?to β?as they are being inputted simultaneously through tensor products. I plan to address the Quantum state of this tensor connection step by step throughout the application presented. Also, I will show you how to prove that the connection is true for this tensor connection through its output method using a small bit of tensor calculus and mostly number theory.
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。
基金the National Key R&D Program of China under Grant 2018YFB1700104.
文摘Utilizing granular computing to enhance artificial neural network architecture, a newtype of network emerges—thegranular neural network (GNN). GNNs offer distinct advantages over their traditional counterparts: The ability toprocess both numerical and granular data, leading to improved interpretability. This paper proposes a novel designmethod for constructing GNNs, drawing inspiration from existing interval-valued neural networks built uponNNNs. However, unlike the proposed algorithm in this work, which employs interval values or triangular fuzzynumbers for connections, existing methods rely on a pre-defined numerical network. This new method utilizesa uniform distribution of information granularity to granulate connections with unknown parameters, resultingin independent GNN structures. To quantify the granularity output of the network, the product of two commonperformance indices is adopted: The coverage of numerical data and the specificity of information granules.Optimizing this combined performance index helps determine the optimal parameters for the network. Finally,the paper presents the complete model construction and validates its feasibility through experiments on datasetsfrom the UCIMachine Learning Repository. The results demonstrate the proposed algorithm’s effectiveness andpromising performance.
