互补产品推荐旨在为用户提供经常一起购买的产品,以满足共同的需求。现有的互补产品推荐方法大多考虑对产品的内容特性(视觉和文本内容)建模,而没有考虑用户购买产品的偏好。为此设计了一种融合用户偏好的互补产品推荐模型(complementar...互补产品推荐旨在为用户提供经常一起购买的产品,以满足共同的需求。现有的互补产品推荐方法大多考虑对产品的内容特性(视觉和文本内容)建模,而没有考虑用户购买产品的偏好。为此设计了一种融合用户偏好的互补产品推荐模型(complementary product recommendation models that integrate user preferences, CPRUP)。该模型首先计算产品之间图像和文本特征的互补关系;然后将知识图谱与注意力机制相结合,基于n-hop邻居挖掘用户历史购买产品之间的相关性,提出一种基于知识图谱的用户表征来提取用户对互补产品的偏好;最后基于神经网络实现互补关系与用户偏好的共同学习。使用Amazon数据集进行实验,提出的CPRUP模型与次优基线模型相比,ACC提升了5%,precision提升了4%,表明CPRUP模型可以更准确地为用户推荐互补产品。展开更多
In this paper, the relationship between network synchronizability and the edge-addition of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network sync...In this paper, the relationship between network synchronizability and the edge-addition of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network synchronizability. Then, since sometimes the synchronizability can be enhanced by changing the network structure, the question of whether the networks with more edges are easier to synchronize is addressed. Based on a subgraph and complementary graph method, it is shown by examples that the answer is negative even if the network structure is arbitrarily optimized. This reveals that generally there are redundant edges in a network, which not only make no contributions to synchronization but actually may reduce the synchronizability. Moreover, a simple example shows that the node betweenness centrality is not always a good indicator for the network synchronizability. Finally, some more examples are presented to illustrate how the network synchronizability varies following the addition of edges, where all the examples show that the network synchronizability globally increases but locally fluctuates as the number of added edges increases.展开更多
Let the chromatic number of G, the edge chromatic number of G and thetotal chromatic number of G be denoted by x（G）, x<sub>1</sub>（G） and x<sub>2</sub>（G）, respectively. Forany simple gra...Let the chromatic number of G, the edge chromatic number of G and thetotal chromatic number of G be denoted by x（G）, x<sub>1</sub>（G） and x<sub>2</sub>（G）, respectively. Forany simple graph G of order p and its complement G, the following inequalities of theNordhaus-Gaddum class are obtained:（i）|2p<sup>1/2</sup>|-ε<sub>1</sub>≤x（G）+x<sub>1</sub>（G）≤2p-2 and 0≤x（G）·x<sub>1</sub>（G）≤（p-1）<sup>2</sup> for p≥2,（ii）|2p<sup>1/2</sup>|+ε<sub>1</sub>≤x（G）+x<sub>2</sub>（G）≤2p-1 and 0≤x（G）·x<sub>2</sub>（G）≤p（p-1） for p≥3,（iii）p≤x<sub>1</sub>（G）+x<sub>2</sub>（G）≤2p-1 and 0≤x<sub>1</sub>（G）·x<sub>2</sub>（G）≤p（p-1） for p≥3,where ε<sub>1</sub>=0, if p<sup>1/2</sup> is an odd integer, 1, otherwise,ε<sub>2</sub>=1, if p<sup>1/2</sup> is an even integer, 0, otherwise,and [x] denotes the ceiling of x. We also show that these bounds are sharp for everypositive integer p.展开更多
The Wiener index W（G） of a graph G is defined as the sum of distances between all pairs of vertices of the graph, Let G＊c, is the set of the complements of bipartite graphs with order n. In this paper, we character...The Wiener index W（G） of a graph G is defined as the sum of distances between all pairs of vertices of the graph, Let G＊c, is the set of the complements of bipartite graphs with order n. In this paper, we characterize the graphs with the maximum and second-maximum Wiener indices among all the graphs in G＊c, respectively.展开更多
文摘互补产品推荐旨在为用户提供经常一起购买的产品,以满足共同的需求。现有的互补产品推荐方法大多考虑对产品的内容特性(视觉和文本内容)建模,而没有考虑用户购买产品的偏好。为此设计了一种融合用户偏好的互补产品推荐模型(complementary product recommendation models that integrate user preferences, CPRUP)。该模型首先计算产品之间图像和文本特征的互补关系;然后将知识图谱与注意力机制相结合,基于n-hop邻居挖掘用户历史购买产品之间的相关性,提出一种基于知识图谱的用户表征来提取用户对互补产品的偏好;最后基于神经网络实现互补关系与用户偏好的共同学习。使用Amazon数据集进行实验,提出的CPRUP模型与次优基线模型相比,ACC提升了5%,precision提升了4%,表明CPRUP模型可以更准确地为用户推荐互补产品。
基金supported by the National Natural Science Foundation of China (Grant Nos 10832006 and 60674093)the Foundation for Key Program of Educational Ministry,China (Grant No 107110)the City University of Hong Kong under the Research Enhancement Scheme and SRG (Grant No 9041335)
文摘In this paper, the relationship between network synchronizability and the edge-addition of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network synchronizability. Then, since sometimes the synchronizability can be enhanced by changing the network structure, the question of whether the networks with more edges are easier to synchronize is addressed. Based on a subgraph and complementary graph method, it is shown by examples that the answer is negative even if the network structure is arbitrarily optimized. This reveals that generally there are redundant edges in a network, which not only make no contributions to synchronization but actually may reduce the synchronizability. Moreover, a simple example shows that the node betweenness centrality is not always a good indicator for the network synchronizability. Finally, some more examples are presented to illustrate how the network synchronizability varies following the addition of edges, where all the examples show that the network synchronizability globally increases but locally fluctuates as the number of added edges increases.
文摘Let the chromatic number of G, the edge chromatic number of G and thetotal chromatic number of G be denoted by x（G）, x<sub>1</sub>（G） and x<sub>2</sub>（G）, respectively. Forany simple graph G of order p and its complement G, the following inequalities of theNordhaus-Gaddum class are obtained:（i）|2p<sup>1/2</sup>|-ε<sub>1</sub>≤x（G）+x<sub>1</sub>（G）≤2p-2 and 0≤x（G）·x<sub>1</sub>（G）≤（p-1）<sup>2</sup> for p≥2,（ii）|2p<sup>1/2</sup>|+ε<sub>1</sub>≤x（G）+x<sub>2</sub>（G）≤2p-1 and 0≤x（G）·x<sub>2</sub>（G）≤p（p-1） for p≥3,（iii）p≤x<sub>1</sub>（G）+x<sub>2</sub>（G）≤2p-1 and 0≤x<sub>1</sub>（G）·x<sub>2</sub>（G）≤p（p-1） for p≥3,where ε<sub>1</sub>=0, if p<sup>1/2</sup> is an odd integer, 1, otherwise,ε<sub>2</sub>=1, if p<sup>1/2</sup> is an even integer, 0, otherwise,and [x] denotes the ceiling of x. We also show that these bounds are sharp for everypositive integer p.
文摘The Wiener index W（G） of a graph G is defined as the sum of distances between all pairs of vertices of the graph, Let G＊c, is the set of the complements of bipartite graphs with order n. In this paper, we characterize the graphs with the maximum and second-maximum Wiener indices among all the graphs in G＊c, respectively.
