基于局部有限搜索的无向图近似最大团快速求解算法

无向图最大团求解是一个著名的NP-完全问题,解决该问题的经典算法基本上都采用完全精确搜索策略。鉴于NP-完全问题本身所固有的复杂性,这些算法或许仅适用于某些特殊的小规模图,对于具有大规模顶点和边的复杂图还是显得无力,难以适用。针对完全精确搜索策略下的无向图最大团求解算法的大部分时间都用于对图进行额外而无效的查找的问题,采用分划递归技术将图划分为邻接子图和悬挂子图,然后对邻接子图进行递归求解,而对悬挂子图则通过设置搜索范围控制函数进行局部有限搜索。在DIMACS数据集上将所提算法与当前主要的最大团求解算法进行对比实验,结果表明,文中提出的局部有限搜索求解策略能在75%的基准数据上获得最大团,剩下不能得到最大团的数据实际上也可以获得接近于最大团的近似最大团,但算法的平均求解时间仅为目前最大团精确求解算法的20%左右。因此,在很多最大团非精确要求的场景中,所提算法具有极高的应用价值。     

基于双向搜索的最大频繁项目集挖掘算法

结合自底向上与自顶向下的搜索策略,提出一种快速发现最大频繁项目集的算法.该算法利用非频繁项目集对候选最大频繁项目集进行剪枝和降维,减少了候选最大频繁项目集的数量,缩小了搜索空间,提高了算法的效率.算法分析和实验表明,该算法是一种有效、快速的算法.     

基于不确定性PPI网络的最大稠密子图挖掘*

研究表明使用PPI数据进行蛋白质功能预测是很有意义的。然而,从生物学实验得到的PPI数据一般是含有噪声的、不完全的和不精确的,这使得将PPI网络作为不确定图来处理变得更加合理。提出了一种基于深度优先搜索策略和点扩展的挖掘算法,它可以有效地从不确定的PPI网络中挖掘最大稠密子图。该算法使用了几种高效的剪枝技术来提高挖掘的时间效率。在酵母菌PPI数据上的实验结果表明该算法在精度和效率上都有很好的表现。     

基于父子等价剪枝策略的最大频繁项集挖掘

在传统剪枝策略中,具有相同事务集的父子结点搜索空间没有充分剪枝,效率较低.为此,提出父子等价的剪枝策略.采用深度优先搜索集合枚举树,对于父子结点中具有相同事务集的搜索空间进行剪枝,有效地缩小搜索空间,减少频繁项计算的次数,给出基于该剪枝策略的最大频繁项集挖掘算法.实验结果表明,该算法可缩短同一支持度下的最大频繁项集挖掘时间.     

量子近似优化算法在最大独立集中的应用

最大独立集问题是著名的NP问题,并且在许多场景中都有应用。传统的精确算法解决最大独立集问题需要指数级的时间复杂度。为更高效地解决最大独立集问题,提出了一种基于量子近似优化算法的量子线路解决方案。该方案由最大独立集的数学模型,推导出最大独立集问题的哈密顿量表达式;设计了基于量子近似优化算法的量子线路,采用COBYLA经典优化算法对参数量子门中的参数进行优化,并使用IBM提供的量子开发框架Qiskit进行仿真实验。仿真结果表明,使用量子近似优化算法可以在多项式时间内以高概率获得最大独立集问题的解,实现了指数加速。量子近似优化算法对解决最大独立集问题有一定的可行性和有效性。     

基于粗糙集的无向图最小支配集启发式算法

图的最小支配集在许多领域有广泛应用,但其求解是一个NP问题.针对现有近似求解算法的复杂度和精度有待改进的问题,基于粗糙集理论提出一种低复杂度、高精度的最小支配集启发式求解算法.首先,利用图的邻接矩阵构造诱导决策表,证明了图的最小支配集与其诱导决策表的最小属性约简等价.然后,提出一种启发式的最小支配集近似算法.该方法采用前向和后向搜索机制,有效提高了最小支配集求解的近似精度;采用累积策略计算诱导决策表的正域,有效降低了计算复杂度.最后,在公用数据集上与典型算法进行了实验对比分析,结果表明该算法在运行效率方面具有明显优势,能得到更高精度的近似最小支配集,且输出结果具有较好的稳定性.     

异质信息网络的复杂条件社区搜索

社区是信息网络的重要属性, 社区搜索旨在寻找满足用户给定条件的节点集合, 是信息网络分析的重要研究内容. 异质信息网络由于包含更加全面、丰富的结构和语义信息, 所以异质信息网络的社区搜索近年来受到人们的广泛关注. 针对现有异质信息网络的社区搜索方法难以满足复杂条件社区搜索要求的不足, 定义了复杂条件社区搜索问题, 提出了考虑非对称元路径、受限元路径和禁止节点约束的搜索算法. 3种算法分别通过元路径补全策略、调整带标签的批量搜索策略和拆分复杂搜索条件的方式搜索社区, 同时针对禁止节点约束的搜索算法设计了基于剪枝策略和近似策略的优化算法以提高搜索效率. 在真实数据集上进行了大量实验, 实验结果证明了所提算法的有效性和高效性.     

一种基于ESEquivPS的封闭频繁项集挖掘算法

本文提出一种基于ESEquivPS(扩展支持度相等性剪枝策略)的封闭频繁项集挖掘算法ECFIMA。该算法采用深度优先和广度优先相结合的策略访问搜索空间,使用垂直位图向量格式存储表示项集和事务数据库,同时利用基本剪枝策略、相等性剪枝策略、扩展支持度相等性剪枝策略1和扩展支持度相等性剪枝策略2进行候选空间剪枝,并采用多种不同特性的测试数据集进行实验。实验结果表明,ECFIMA算法是一种高效的封闭频繁项集挖掘算法,在多种测试数据集上性能都优于CHARM算法,尤其是在拥有大量长的封闭频繁项集的测试数据集上,效率比CHARM算法提高约2~3倍。     

基于B-list的最大频繁项集挖掘算法

针对现有的最大频繁项集挖掘算法挖掘时间过长、内存消耗较大的问题,提出了一种基于构造链表B-list的最大频繁项集挖掘算法BMFI,该算法利用B-list数据结构来挖掘频繁项集并采用全序搜索树作为搜索空间,然后采用父等价剪枝技术来缩小搜索空间,最后再结合基于MFI-tree的投影策略实现超集检测来提高算法的效率。实验结果表明,BMFI算法在时间效率与空间效率方面均优于FPMAX算法与MFIN算法。该算法在稠密数据集与稀疏数据集中进行最大频繁项集挖掘时均有良好的效果。     

一种约束最大频繁模式快速挖掘算法

为了避免用户通过"二次挖掘"才能得到有用的结果集,本文提出了一种新的约束最大频繁模式挖掘算法CSMFPMax.CSMFP-Max算法基于CFP树和对称矩阵,在挖掘过程中采用了多种剪枝策略并结合了自顶向下和自底向上的双向搜索策略,大大缩小了候选集规模,避免了不必要的条件CFP树的产生.理论分析和实验结果表明CSMFP-Max算法是一种高效的约束最大频繁模式挖掘算法,具有良好的时空效率.     

从图数据库中挖掘频繁跳跃模式

很多频繁子图挖掘算法已被提出.然而,这些算法产生的频繁子图数量太多而不能被用户有效地利用.为此,提出了一个新的研究问题:挖掘图数据库中的频繁跳跃模式.挖掘频繁跳跃模式既可以大幅度地减少输出模式的数量,又能使有意义的图模式保留在挖掘结果中.此外,跳跃模式还具有抗噪声干扰能力强等优点.然而,由于跳跃模式不具有反单调性质,挖掘它们非常具有挑战性.通过研究跳跃模式自身的特性,提出了两种新的裁剪技术:基于内扩展的裁剪和基于外扩展的裁剪.在此基础上又给出了一种高效的挖掘算法GraphJP(an algorithm for mining jump patterns from graph databases).另外,还严格证明了裁剪技术和算法GraphJP的正确性.实验结果表明,所提出的裁剪技术能够有效地裁剪图模式搜索空间,算法GraphJP是高效、可扩展的.     

Hypergraph-based image retrieval for graph-based representation

In this paper, we introduce a novel method for graph indexing. We propose a hypergraph-based model for graph data sets by allowing cluster overlapping. More precisely, in this representation one graph can be assigned to more than one cluster. Using the concept of the graph median and a given threshold, the proposed algorithm detects automatically the number of classes in the graph database. We consider clusters as hyperedges in our hypergraph model and we index the graph set by the hyperedge centroids. This model is interesting to traverse the data set and efficient to retrieve graphs.     

gMLC: a multi-label feature selection framework for graph classification

Graph classification has been showing critical importance in a wide variety of applications, e.g. drug activity predictions and toxicology analysis. Current research on graph classification focuses on single-label settings. However, in many applications, each graph data can be assigned with a set of multiple labels simultaneously. Extracting good features using multiple labels of the graphs becomes an important step before graph classification. In this paper, we study the problem of multi-label feature selection for graph classification and propose a novel solution, called gMLC, to efficiently search for optimal subgraph features for graph objects with multiple labels. Different from existing feature selection methods in vector spaces that assume the feature set is given, we perform multi-label feature selection for graph data in a progressive way together with the subgraph feature mining process. We derive an evaluation criterion to estimate the dependence between subgraph features and multiple labels of graphs. Then, a branch-and-bound algorithm is proposed to efficiently search for optimal subgraph features by judiciously pruning the subgraph search space using multiple labels. Empirical studies demonstrate that our feature selection approach can effectively boost multi-label graph classification performances and is more efficient by pruning the subgraph search space using multiple labels.     

Fast exact feature based data correspondence search with an efficient bit-parallel MCP solver

The problem of finding the optimal correspondence between two sets of geometric entities or features is known to be NP-hard in the worst case. This problem appears in many real scenarios such as fingerprint comparisons, image matching and global localization of mobile robots. The inherent complexity of the problem can be avoided by suboptimal solutions, but these could fail with high noise or corrupted data. The correspondence problem has an interesting equivalent formulation in finding a maximum clique in an association graph. We have developed a novel algorithm to solve the correspondence problem between two sets of features based on an efficient solution to the Maximum Clique Problem using bit parallelism. It outperforms an equivalent non bit parallel algorithm in a number of experiments with simulated and real data from two different correspondence problems. This article validates for the first time, to the best of our knowledge, that bit parallel optimization techniques can greatly reduce computational cost, thus making feasible the use of an exact solution in real correspondence search problems despite their inherent NP computational complexity.     

一种新颖的对比子图索引算法

针对当前图索引算法存在的问题,提出一种基于对比子图索引框架,开发冗余感知机制,选择一个小型的具有明显区分力的索引特征集,改善索引性能。实验结果表明,该算法对不同的包容搜索载荷能达到近优化的修剪力,与传统图搜索方法相比,具有明显的索引性能优势。     

SNS:一种快速无偏的分层图抽样算法

抽样作为一种有效的统计分析方法,常被用于大规模图数据分析领域以提升性能。现有的图抽样算法大多存在高度节点或低度节点过度入样的问题,较大程度地影响了算法的性能。复杂网络具有无标度特性,即节点的度服从幂律分布,节点个体之间存在较大差异。在基于点选择策略的抽样方法的基础上,通过结合节点的近似度分布策略,设计并实现了高效无偏的分层图抽样算法SNS。在3个真实的图数据集上的实验结果表明,SNS算法比其他图抽样算法保留了更多的拓扑属性,且执行效率比FFS更高。SNS算法在度的无偏性、抽样结果拓扑属性近似性方面的表现均优于现有算法。     

Top-<Emphasis Type="Italic">k</Emphasis> probabilistic prevalent co-location mining in spatially uncertain data sets

A co-location pattern is a set of spatial features whose instances frequently appear in a spatial neighborhood. This paper efficiently mines the top-k probabilistic prevalent co-locations over spatially uncertain data sets and makes the following contributions: 1) the concept of the top-k probabilistic prevalent co-locations based on a possible world model is defined; 2) a framework for discovering the top-k probabilistic prevalent co-locations is set up; 3) a matrix method is proposed to improve the computation of the prevalence probability of a top-k candidate, and two pruning rules of the matrix block are given to accelerate the search for exact solutions; 4) a polynomial matrix is developed to further speed up the top-k candidate refinement process; 5) an approximate algorithm with compensation factor is introduced so that relatively large quantity of data can be processed quickly. The efficiency of our proposed algorithms as well as the accuracy of the approximation algorithms is evaluated with an extensive set of experiments using both synthetic and real uncertain data sets.     

Attributed hypergraph matching on a Riemannian manifold

If we consider a matching that preserves high-order relationships among points in the same set, we can int-roduce a hypergraph-matching technique to search for correspondence according to high-order feature values. While graph matching has been widely studied, there is limited research available regarding hypergraph matching. In this paper, we formulate hypergraph matching in terms of tensors. Then, we reduce the hypergraph matching to a bipartite matching problem that can be solved in polynomial time. We then extend this hypergraph matching to attributed hypergraph matching using a combination of different attributes with different orders. We perform analyses that demonstrate that this method is robust when handling noisy or missing data and can achieve inexact graph matching. To the best of our knowledge, while attributed graph-matching and hypergraph-matching have been heavily researched, methods for attributed hypergraph matching have not been proposed before.     

Effective optimizations of cluster-based nearest neighbor search in high-dimensional space

Nearest neighbor (NN) search in high-dimensional space plays a fundamental role in large-scale image retrieval. It seeks efficient indexing and search techniques, both of which are simultaneously essential for similarity search and semantic analysis. However, in recent years, there has been a rare breakthrough. Achievement of current techniques for NN search is far from satisfactory, especially for exact NN search. A recently proposed method, HB, addresses the exact NN search efficiently in high-dimensional space. It benefits from cluster-based techniques which can generate more compact representation of the data set than other techniques by exploiting interdimensional correlations. However, HB suffers from huge cost for lower bound computations and provides no further pruning scheme for points in candidate clusters. In this paper, we extend the HB method to address exact NN search in correlated, high-dimensional vector data sets extracted from large-scale image database by introducing two new pruning/selection techniques and we call it HB+. The first approach aims at selecting more quickly the subset of hyperplanes/clusters that must be considered. The second technique prunes irrelevant points in the selected subset of clusters. Performed experiments show the improvement of HB+ with respect to HB in terms of efficiency (I/O cost and CPU response time) and also demonstrate the superiority over other exact NN indexes.