Let D = (V, E) be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD(v), is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu,...Let D = (V, E) be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD(v), is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu, we order the vertices of D so that exPD(V1) ≤ exPD(V2) …≤ exPD(Vn). Then exPD(Vk) is called the k- point exponent of D and is denoted by exPD (k), 1≤ k ≤ n. In this paper we define e(n, k) := max{expD (k) | D ∈ PD(n, 2)} and E(n, k) := {exPD(k)| D ∈ PD(n, 2)}, where PD(n, 2) is the set of all primitive digraphs of order n with girth 2. We completely determine e(n, k) and E(n, k) for all n, k with n ≥ 3 and 1 ≤ k ≤ n.展开更多
密度峰值聚类(density peaks clustering,DPC)是一种基于密度的聚类算法,该算法可以直观地确定类簇数量,识别任意形状的类簇,并且自动检测、排除异常点.然而,DPC仍存在些许不足:一方面,DPC算法仅考虑全局分布,在类簇密度差距较大的数据...密度峰值聚类(density peaks clustering,DPC)是一种基于密度的聚类算法,该算法可以直观地确定类簇数量,识别任意形状的类簇,并且自动检测、排除异常点.然而,DPC仍存在些许不足:一方面,DPC算法仅考虑全局分布,在类簇密度差距较大的数据集聚类效果较差;另一方面,DPC中点的分配策略容易导致“多米诺效应”.为此,基于代表点(representative points)与K近邻(K-nearest neighbors,KNN)提出了RKNN-DPC算法.首先,构造了K近邻密度,再引入代表点刻画样本的全局分布,提出了新的局部密度;然后,利用样本的K近邻信息,提出一种加权的K近邻分配策略以缓解“多米诺效应”;最后,在人工数据集和真实数据集上与5种聚类算法进行了对比实验,实验结果表明,所提出的RKNN-DPC可以更准确地识别类簇中心并且获得更好的聚类结果.展开更多
基金Supported by the National Natural Science Foundation of China(No.10771061,No.10771058)SRF of Hunan Provincial Education Department(No.07C267).
文摘Let D = (V, E) be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD(v), is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu, we order the vertices of D so that exPD(V1) ≤ exPD(V2) …≤ exPD(Vn). Then exPD(Vk) is called the k- point exponent of D and is denoted by exPD (k), 1≤ k ≤ n. In this paper we define e(n, k) := max{expD (k) | D ∈ PD(n, 2)} and E(n, k) := {exPD(k)| D ∈ PD(n, 2)}, where PD(n, 2) is the set of all primitive digraphs of order n with girth 2. We completely determine e(n, k) and E(n, k) for all n, k with n ≥ 3 and 1 ≤ k ≤ n.
文摘密度峰值聚类(density peaks clustering,DPC)是一种基于密度的聚类算法,该算法可以直观地确定类簇数量,识别任意形状的类簇,并且自动检测、排除异常点.然而,DPC仍存在些许不足:一方面,DPC算法仅考虑全局分布,在类簇密度差距较大的数据集聚类效果较差;另一方面,DPC中点的分配策略容易导致“多米诺效应”.为此,基于代表点(representative points)与K近邻(K-nearest neighbors,KNN)提出了RKNN-DPC算法.首先,构造了K近邻密度,再引入代表点刻画样本的全局分布,提出了新的局部密度;然后,利用样本的K近邻信息,提出一种加权的K近邻分配策略以缓解“多米诺效应”;最后,在人工数据集和真实数据集上与5种聚类算法进行了对比实验,实验结果表明,所提出的RKNN-DPC可以更准确地识别类簇中心并且获得更好的聚类结果.