自注意力超图池化网络

近年来,将卷积神经网络推广到图数据上的图卷积神经网络引起了广泛关注,主要包括重新定义图的卷积和池化操作.由于图数据只能表达二元关系的局限性,使其在实际应用中表现欠佳.相比之下,超图能够捕获数据的高阶相关性,利用其灵活的超边易于处理复杂的数据表示.然而,现有的超图卷积神经网络还不够成熟,目前尚无有效的超图池化操作.因此,提出了带有自注意机制的超图池化网络,使用超图结构建模,通过引入自注意力的超图卷积操作学习带有高阶数据信息的节点隐藏层特征,再经过超图池化操作选择并保留在结构和内容上的重要节点,进而得到更准确的超图表示.在文本分类、菜肴分类和蛋白质分类任务上的实验结果表明:与目前多种主流方法相比,该方法均取得了更好的效果.     

关系数据库中MVD超图的讨论

本文提出了ＭＶＤ超图的概念，给出了正向ＭＶＤ超图、逆向ＭＶＤ超图的定义。深入讨论了逆向ＭＶＤ超图、逆向准路（结点）、可人发准路结点、不可分准路结点及最小不可分准路结点等。在此基础上，给出了求解最小不可分结点的闭包算法。     

关于混合FD,MVD超图的理论研究

本文分别详细讨论了正向混合超图和逆向混合超图中准路的分类定义及理论。给出了正向混合超图中怀蕴池有关的理论，同时，还部分地给出了逆向混合超图中的与消除冗余有关的几个定理     

面向超图数据的最大独立集算法

超图是普通图的泛化表示, 在许多应用领域都很常见, 包括互联网、生物信息学和社交网络等. 独立集问题是图分析领域的一个基础性研究问题, 传统的独立集算法大多都是针对普通图数据, 如何在超图数据上实现高效的最大独立集挖掘是一个亟待解决的问题. 针对这一问题, 提出一种超图独立集的定义. 首先分析超图独立集搜索的两个特性, 然后提出一种基于贪心策略的基础算法. 接着提出一种超图近似最大独立集搜索的剪枝框架即精确剪枝与近似剪枝相结合, 以精确剪枝策略缩小图的规模, 以近似剪枝策略加快搜索速度. 此外, 还提出4种高效的剪枝策略, 并对每种剪枝策略进行理论证明. 最后, 通过在10个真实超图数据集上进行实验, 结果表明剪枝算法可以高效地搜索到更接近于真实结果的超图最大独立集.     

超图神经网络综述

近年来,图神经网络借助大量数据和超强计算能力在推荐系统和自然语言处理等应用领域取得显著成效,它主要处理具有成对关系的图数据.但许多现实网络中的对象之间的关系是复杂的非成对关系,如科研合作网络、蛋白质网络等.若直接用图结构将这种复杂的关系表示为成对关系,会导致信息丢失.超图是一种灵活的建模工具,可以展现出图无法完整刻画的高阶关系,弥补了图的不足.鉴于此,研究者开始关心如何在超图上设计神经网络,并相继提出应用于下游任务的超图神经网络模型（hypergraph neural network,HGNNs）.故对现有的超图神经网络模型进行综述,首先全面回顾超图神经网络在过去3年的研究历程;其次根据设计超图神经网络采用的方法不同对其进行分类,并详细地阐述代表性的模型;然后介绍了超图神经网络的应用领域;最后总结和探讨了超图神经网络未来的研究方向.     

容错多总线结构与超图

本文研究每个处理机挂在三条总线上的总线结构的容错设计问题。推广对偶图后，定义了多总线结构的对偶超图，用以设计一类具有很好的容错性和可扩充性的多总线结构。     

软件体系结构动态演化的条件超图文法及分析

针对目前.软件体系结构动态演化描述方法的不足,提出用约束超图表示软件体系结构,用左右应用条件刻画软件体系结构动态演化的前断言和后断言,用条件超图文法建模软件体系结构动态演化过程.通过案例分析,讨论了如何构建条件超图文法并应用于软件体系结构动态演化.在此基础上,建立软件体系结构动态演化的一致性条件定义,给出动态演化的一致性判定方法.最后,设计实验进行分析,验证了方法的有效性.     

网格优化有向超图任务调度算法

任务调度是网格计算的一个重要部分.分析网格环境下任务调度的特点以及传统DAG图的优缺点,吸取有向超图的优点,将有向超图理论融合网格环境特征,建立了网格环境下的优化有向超图模型,并在此基础上通过网格优化有向超图的水平构形、标号及带宽计算实现任务对网格资源的映射与调度,提出网格优化有向超图任务调度算法GODHTS.模拟实验结果证明了该模型及其算法的有效性和优越性.     

基于超图模型的复杂视频事件检测

近年来,语义事件分析越来越受到重视,典型语义事件的检测与识别是一个具有挑战性的研究领域。提出了基于超图模型的复杂视频事件检测方法,通过分析对象的运动轨迹,检测出视频中的所有子事件并构建时序关系图及依赖关系图,从而生成子事件超图,并通过谱超图聚类分析来检测相应的复杂事件。采用图变换工具AGG进行模拟实验,其实验结果表明,该方法具有较高的准确率与召回率。     

基于逆向超图的从模式到“改进的第三范式”的分解

本文以逆向超图为工具,讨论了非必要和非基本属性在超图中的性质,给出了基中超图的泛关系模式到改进的３ＮＦ的分解算法。     

Clustering ensemble via structured hypergraph learning

Clustering ensemble integrates multiple base clustering results to obtain a consensus result and thus improves the stability and robustness of the single clustering method. Since it is natural to use a hypergraph to represent the multiple base clustering results, where instances are represented by nodes and base clusters are represented by hyperedges, some hypergraph based clustering ensemble methods are proposed. Conventional hypergraph based methods obtain the final consensus result by partitioning a pre-defined static hypergraph. However, since base clusters may be imperfect due to the unreliability of base clustering methods, the pre-defined hypergraph constructed from the base clusters is also unreliable. Therefore, directly obtaining the final clustering result by partitioning the unreliable hypergraph is inappropriate. To tackle this problem, in this paper, we propose a clustering ensemble method via structured hypergraph learning, i.e., instead of being constructed directly, the hypergraph is dynamically learned from base results, which will be more reliable. Moreover, when dynamically learning the hypergraph, we enforce it to have a clear clustering structure, which will be more appropriate for clustering tasks, and thus we do not need to perform any uncertain postprocessing, such as hypergraph partitioning. Extensive experiments show that, our method not only performs better than the conventional hypergraph based ensemble methods, but also outperforms the state-of-the-art clustering ensemble methods.     

Hypergraph products for structural mechanics

In this paper Cartesian, direct and strong Cartesian product of hypergraphs are investigated. A new concept named the adjacency function is defined on hypergraphs. This definition leads to distinct adjacency and Laplacian matrices for a hypergraph and makes it possible to express it in an algebraic form. Variable adjacency functions on hypergraphs result in generation of dynamic graph products which are applied to dynamic systems. For further clarity, some examples from structural mechanics are provided. The generality of the approach is shown through some examples, indicating this fact that the hypergraph products can encompass most of the available developments on the graph products in the literature.     

一种基于超图模式的高维空间数据聚类方法

把一个救解高维空间数据聚类问题的转换为一个超图分割寻优问题，提出了一种基于超图模式的高维空间数据聚类方法，该方法不需要减少高维空间数据顶的维数，直接用超图模式描述原始数据之间的关系，并通过选择适当的支持度阈值，有效祛除噪声点，保证数据聚类的质量。     

基于超图的求解FD集最优覆盖的算法研究

本文在文献「３」、「４」、「５」所讨论的超图及 的分类的基础上，分析了最优覆盖对应的超图的结构特点，用替换化简方法解决了最优覆盖的多项式时间算法。     

Adaptive hypergraph superpixels

Superpixel segmentation, which amounts to partitioning an image into a number of superpixels each of which is a set of pixels sharing common visual meanings, requires specific needs for different computer vision tasks. Graph based methods, as a kind of popular superpixel segmentation method, regard an image as a weighted graph whose nodes correspond to pixels of the image, and partition all pixels into superpixels according to the similarity between pixels over various feature spaces. Despite their improvement of the performance of segmentation, these methods ignore high-order relationship between them incurred from either locally neighboring pixels or structured layout of the image. Moreover, they measure the similarity of pairwise pixels using Gaussian kernel where a robust radius parameter is difficult to find for pixels which exhibit multiple features (e.g., texture, color, brightness). In this paper, we propose an adaptive hypergraph superpixel segmentation (AHS) of intensity images for solving both issues. AHS constructs a hypergraph by building the hyperedges with an adaptive neighborhood scheme, which explores an intrinsic relationship of pixels. Afterwards, AHS encodes the relationship between pairwise pixels using characteristics of current two pixels as well as their neighboring pixels defined by hyperedges. Essentially, AHS models the relationship of pairwise pixels in a high-order group fashion while graph based methods evaluate it in a one-vs-one fashion. Experiments on four datasets demonstrate that AHS achieves higher or comparable performance compared with state-of-the-art methods.     

Root Mean Square filter for noisy images based on hyper graph model

In this paper, we propose a noise removal algorithm for digital images. This algorithm is based on hypergraph model of image, which enables us to distinguish noisy pixels in the image from the noise-free ones. Hence, our algorithm obviates the need for denoising all the pixels, thereby preserving as much image details as possible. The identified noisy pixels are denoised through Root Mean Square (RMS) approximation. The performance of our algorithm, based on peak-signal-to-noise-ratio (PSNR) and mean-absolute-error (MAE), was studied on various benchmark images, and found to be superior to that of other traditional filters and other hypergraph based denoising algorithms.     

A polynomial characterization of hypergraphs using the Ihara zeta function

The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs for the purposes of clustering. To this end, we develop a polynomial characterization for hypergraphs based on the Ihara zeta function. We investigate the flexibility of the polynomial coefficients for learning relational structures with different relational orders. Furthermore, we develop an efficient method for computing the coefficient set. Our representation for hypergraphs takes into account not only the vertex connections but also the hyperedge cardinalities, and thus can distinguish different relational orders, which is prone to ambiguity if the hypergraph Laplacian is used. In our experimental evaluation, we demonstrate the effectiveness of the proposed characterization for clustering irregular unweighted hypergraphs and its advantages over the spectral characterization of the hypergraph Laplacian.     

基于超图切割的半监督学习和聚类算法

本文针对超图切割上的半监督学习和聚类算法进行了研究;首先,通过对超图切割和超边展开法及其切割函数的讨论,引入了超图上的总变异作为超图切割的洛瓦兹扩展,并在此基础上提出了一组正则化函数,它对应于图上的拉普拉斯型正则化;然后,基于正则化函数族提出了半监督学习方法,并基于平衡超图切割提出了谱聚类方法;为了求解这两个学习问题,将它们转化为求解凸优化问题,并为此提出了一种主要组成部分为近端映射的可扩展算法,从而实现半监督学习和聚类;仿真实验结果表明,本文提出的基于超图切割实现的半监督学习和聚类方法相比于经典的超边展开法和其他图切割方法有更好的标准偏差和聚类误差性能。     

Probabilistic hypergraph based hash codes for social image search

With the rapid development of the Internet, recent years have seen the explosive growth of social media. This brings great challenges in performing efficient and accurate image retrieval on a large scale. Recent work shows that using hashing methods to embed high-dimensional image features and tag information into Hamming space provides a powerful way to index large collections of social images. By learning hash codes through a spectral graph partitioning algorithm, spectral hashing（SH） has shown promising performance among various hashing approaches. However, it is incomplete to model the relations among images only by pairwise simple graphs which ignore the relationship in a higher order. In this paper, we utilize a probabilistic hypergraph model to learn hash codes for social image retrieval. A probabilistic hypergraph model offers a higher order repre-sentation among social images by connecting more than two images in one hyperedge. Unlike a normal hypergraph model, a probabilistic hypergraph model considers not only the grouping information, but also the similarities between vertices in hy-peredges. Experiments on Flickr image datasets verify the performance of our proposed approach.