Graph Cuts算法实现过程中的关键问题研究

Graph Cuts（GC）算法是一个基于图论的交互式目标提取算法,该方法将图像建模为一个区域和边缘的约束模型,通过求解该模型的最小割获得一个优化的目标分割边界。在使用程序实现该算法时会遇到种种问题,详细叙述了GC算法的实现过程,为进一步研究GC相关方法奠定基础。     

关于几类图的Fractional全控制数

设G=（V,E）是一个无孤立点的图,一个实值函数f：V→[0,1]满足∑v∈N（u）f（v）≥1对一切u∈V（G）都成立,则称f为图G的一个Fractional全控制函数。图的Fractional全控制数定义为γ0f（）G=min{f（V）｜f为图G的Fractional全控制函数},文章中研究了图的Fractional全控制问题,主要给出了关于联图的Fractional全控制数的一个上界,由此确定了几类特殊图的Fractional全控制数,并推广了部分已知结果。     

最佳旅行问题的一种求解方法

本文建立最佳旅行线路的图论模型,在此模型中将求解走遍全中国的最佳旅行线路转化为最佳哈密尔顿回路的问题,通过Floyd算法和二边逐次修正法找到最佳H圈的近似解,即为最短路旅行线路。     

Personalized recommendation via user preference matching

Graph-based recommendation approaches use a graph model to represent the relationships between users and items, and exploit the graph structure to make recommendations. Recent graph-based recommendation approaches focused on capturing users’ pairwise preferences and utilized a graph model to exploit the relationships between different entities in the graph. In this paper, we focus on the impact of pairwise preferences on the diversity of recommendations. We propose a novel graph-based ranking oriented recommendation algorithm that exploits both explicit and implicit feedback of users. The algorithm utilizes a user-preference-item tripartite graph model and modified resource allocation process to match the target user with users who share similar preferences, and make personalized recommendations. The principle of the additional preference layer is to capture users’ pairwise preferences, provide detailed information of users for further recommendations. Empirical analysis of four benchmark datasets demonstrated that our proposed algorithm performs better in most situations than other graph-based and ranking-oriented benchmark algorithms.     

如何运用存在图逻辑建构说理文的框架

存在图逻辑理论能够在形式逻辑和科学实践中架起一座理论应用于实践的桥梁。在创作分析性、说理性文章的实践过程中,提出问题、梳理理论与证实假设,并且这三者的逻辑关系是理论演绎假设、假设回答问题、问题融入理论。采用理论论述与案例分析相结合的研究方法,先阐述相关的存在图逻辑理论,再结合具体的文章案例用存在图直观地展示这种逻辑关系背后的理论依据和推演过程。存在图逻辑作为一种严格的分析性工具,能够帮助构思,检验文章的逻辑框架。学习和使用存在图逻辑不但有利于提高使用者的科学读写能力,而且有利于提高使用者的学术论文的写作水平。     

粗糙集理论与图形匹配相结合的规则提取方法

文章提出了在粗糙集理论中规则提取的新方法——利用图形的匹配来提取规则.粗糙集理论在数据分类应用中的主要思想是保持分类能力不变的情况下,利用等价类,通过属性约简和决策规则约简,达到挖掘知识并简化知识的目的.     

基于Internet的统计图表功能实现技术

研究了基于Internet 的管理信息系统中统计图表功能的解决方案, 并在此基础上, 设计并实施了基于Internet 的百分家政管理信息系统, 同时利用M icrosoft 的Office Web 组件将统计图表功能嵌入其中, 极大地丰富了该系统功能, 使各类统计信息的表示更为直观。     

Drawing Subway Maps: A?Survey

This paper deals with automating the drawing of subway maps. There are two features of schematic subway maps that make them different from drawings of other networks such as flow charts or organigrams. First, most schematic subway maps use not only horizontal and vertical lines, but also diagonals. This gives more flexibility in the layout process, but it also makes the problem provably hard. Second, a subway map represents a network whose components have geographic locations that are roughly known to the users of such a map. This knowledge must be respected during the search for a clear layout of the network. For the sake of visual clarity the underlying geography may be distorted, but it must not be given up, otherwise map users will be hopelessly confused. In this paper we first give a rather generally accepted list of rules that should be adhered to by a good subway map. Next we survey three recent methods for drawing subway maps, analyze their performance with respect to the above rules, and compare the resulting maps among each other and to official subway maps drawn by graphic designers. We then focus on one of the methods, which is based on mixed-integer linear programming, a widely-used global optimization technique. This method guarantees to find a drawing that fulfills a subset of the above-mentioned rules (if such a drawing exists) and optimizes a weighted sum of costs that correspond to the remaining rules. The method can draw even large subway networks such as the London Underground in an aesthetically pleasing manner, similar to maps made by professional graphic designers. If station labels are included in the optimization process, so far only medium-size networks can be drawn. Finally we give evidence why drawing good subway maps is difficult (even without labels).     

Some further development on the eigensystem approach for graph isomorphism detection

Many science and engineering problems can be represented by a network, a generalization of which is a graph. Examples of the problems that can be represented by a graph include: cyclic sequential circuit, organic molecule structures, mechanical structures, etc. The most fundamental issue with these problems (e.g., designing a molecule structure) is the identification of structure, which further reduces to be the identification of graph. The problem of the identification of graph is called graph isomorphism. The graph isomorphism problem is an NP problem according to the computational complexity theory. Numerous methods and algorithms have been proposed to solve this problem. Elsewhere we presented an approach called the eigensystem approach. This approach is based on a combination of eigenvalue and eigenvector which are further associated with the adjacency matrix. The eigensystem approach has been shown to be very effective but requires that a graph must contain at least one distinct eigenvalue. The adjacency matrix is not shown sufficiently to meet this requirement. In this paper, we propose a new matrix called adjusted adjacency matrix that meets this requirement. We show that the eigensystem approach based on the adjusted adjacency matrix is not only effective but also more efficient than that based on the adjacency matrix.     

支配数为2的图的最小特征值

主要考虑简单图,其特征值定义为它的邻接矩阵的特征值.在所有给定阶数且支配数为2的连通图中,完全刻画了最小特征值达到极小的图.