In this article, we study the problem of maximal biclique enumeration on large uncertain bipartite graphs. Given an uncertain bipartite graph$\mathcal {G}=(U,V,E,p)$, a probability threshold$\tau$, and two size constraints$\alpha$and$\beta$, we aim to efficiently enumerate all maximal$\tau$-bicliques in$\mathcal {G}$, where a maximal$\tau$-biclique$B(L,R)$is a complete subgraph of$\mathcal {G}$with (1) the probability of$B$is no less than$\tau$, (2)$|L| \geq \alpha$and$|R| \geq \beta$, and (3)$B$is a maximal complete subgraph satisfying (1) and (2). This problem has many applications, such as biclustering of gene expression data, fraud detection, similar group identification, etc. Despite the wide range of applications, to the best of our knowledge, we note that there are no efficient and scalable solutions to this problem in the literature. This problem is computationally challenging due to its #P-completeness. In this article, we propose a competitive branch-and-bound method, namely${\sf MBEN}$, which explores the search space in a depth-first manner with a variety of pruning techniques. To improve the performance of${\sf MBEN}$, we propose several novel and efficient search processing optimizations. First, we always select the side with fewer candidates to expand the search space. With this search strategy, we have a chance to prune the fruitless branches early. Second, we devise an advanced pruning technique by considering the size pruning and probability pruning at the same time to boost the pruning capacity. Last, we implement${\sf MBEN}$with pre-allocated arrays and pointer maintaining techniques such that the frequent work sets creating operations can be substituted by array element switching operations. In addition, we introduce useful graph reduction techniques to further accelerate the computation. Comprehensive performance studies on 10 real datasets demonstrate that our proposals can significantly outperform the baseline methods by more than two orders of magnitude.

Given a bipartite graph, the maximum edge biclique problem (MEB) aims to find a biclique with the largest number of edges. MEB is a fundamental problem with many real applications, such as community analysis, E-commerce services and bioinformatics. However, in some scenarios, the weight of an edge reflects valuable and important information on the relationship between two entities. Motivated by this, in this paper, we investigate the problem of maximum edge-weighted biclique search (MEWB), which finds a biclique with the largest total weight of edges in a weighted bipartite graph. MEWB has many real applications, including item recommendation, fraud detection, gene clustering, etc. Although we show that MEWB can be resolved by adapting the search algorithm designed for MEB, the performance of this method is yet unsatisfactory. To improve the computation efficiency, two optimizations in terms of upper bound and search order are proposed. For the upper bound, we consider the degree distribution for vertices in the candidate set, and thus have a chance to discard a few edges to tighten the upper bound. For search order, we theoretically show that a vertex order generating the most similar search depth on vertices can achieve the least time cost for MEWB. Guided by this fact, we propose the global summation vertex order. To further accelerate the computation, we extend our approach to a parallel environment, and develop a heuristic approach to deal with large-scale graphs by slightly sacrificing the answer quality. Extensive performance studies conducted on real datasets demonstrate that our proposals can significantly outperform the baseline method by up to two orders of magnitude. Besides, our heuristic approach gives the optimal result on 8 out of 10 real datasets, while achieving more than an order of magnitude of speed-up.

Data collected from nature is usually unlabeled, and it is difficult to be used directly. This issue is well addressed by crowdsourcing, which provides a reasonable way for effectively using these unlabeled data. Generally, workers in crowdsourcing tasks are not professionals, so it is hard to obtain high-quality labels. To address this issue, a robust sparse weighted classification algorithm is proposed, which try to adjust the samples that are not correctly classified in the original lables as much as possible. Specifically, we evalute the ability of different workers(indicator weight matrix) to accurately label different samples by fitting the real data matrix to its weighted reconstruction matrix. And then,$ l_{2,1}$-norm and worker labeling ability similarity matrix are added, and negative effects of some bad workers are eliminated through the row sparsity property of$ l_{2,1}$-norm. Finally, the optimal indicator weight matrix is obtained by optimizing the two matrices in the objective function simultaneously. Therefore, the obtained optimal indicator weight matrix takes the similarity of worker labeling ability into consideration, and infers all the predicted labels. The results on synthetic and real data sets demonstrate that our algorithm is superior to other state-of-the-art methods.

Cross-modal hashing is a hot issue in the multimedia community, which is to generate compact hash code from multimedia content for efficient cross-modal search. Two challenges, i.e., (1) How to efficiently enhance cross-modal semantic mining is essential for cross-modal hash code learning, and (2) How to combine multiple semantic correlations learning to improve the semantic similarity preserving, cannot be ignored. To this end, this paper proposed a novel end-to-end cross-modal hashing approach, named Multiple Semantic Structure-Preserving Quantization (MSSPQ) that is to integrate deep hashing model with multiple semantic correlation learning to boost hash learning performance. The multiple semantic correlation learning consists of inter-modal and intra-modal pairwise correlation learning and Cosine correlation learning, which can comprehensively capture cross-modal consistent semantics and realize semantic similarity preserving. Extensive experiments are conducted on three multimedia datasets, which confirms that the proposed method outperforms the baselines.

SimRank is an attractive link-based similarity measure used in fertile fields of Web search and sociometry. However, the existing deterministic method by Kusumoto et al. [ 24 ] for retrieving SimRank does not always produce high-quality similarity results, as it fails to accurately obtain diagonal correction matrix D. Moreover, SimRank has a “connectivity trait” problem: increasing the number of paths between a pair of nodes would decrease its similarity score. The best-known remedy, SimRank++ [ 1 ], cannot completely fix this problem, since its score would still be zero if there are no common in-neighbors between two nodes. In this article, we study fast high-quality link-based similarity search on billion-scale graphs. (1) We first devise a “varied-D” method to accurately compute SimRank in linear memory. We also aggregate duplicate computations, which reduces the time of [ 24 ] from quadratic to linear in the number of iterations. (2) We propose a novel “cosine-based” SimRank model to circumvent the “connectivity trait” problem. (3) To substantially speed up the partial-pairs “cosine-based” SimRank search on large graphs, we devise an efficient dimensionality reduction algorithm,PSR#, with guaranteed accuracy. (4) We give mathematical insights to the semantic difference between SimRank and its variant, and correct an argument in [ 24 ] that “ifDis replaced by a scaled identity matrix (1-Ɣ)I, their top-K rankings will not be affected much”. (5) We propose a novel method that can accurately convert from Li et al. SimRank ~{S} to Jeh and Widom’s SimRankS. (6) We proposeGSR#, a generalisation of our “cosine-based” SimRank model, to quantify pairwise similarities across two distinct graphs, unlike SimRank that would assess nodes across two graphs as completely dissimilar. Extensive experiments on various datasets demonstrate the superiority of our proposed approaches in terms of high search quality, computational efficiency, accuracy, and scalability on billion-edge graphs.

With the rapid development of online social recommendation system, substantial methods have been proposed. Unlike traditional recommendation system, social recommendation performs by integrating social relationship features, where there are two major challenges, i.e., early summarization and data sparsity. Thus far, they have not been solved effectively. In this article, we propose a novel social recommendation approach, namely Multi-Graph Heterogeneous Interaction Fusion (MG-HIF), to solve these two problems. Our basic idea is to fuse heterogeneous interaction features from multi-graphs, i.e., user–item bipartite graph and social relation network, to improve the vertex representation learning. A meta-path cross-fusion model is proposed to fuse multi-hop heterogeneous interaction features via discrete cross-correlations. Based on that, a social relation GAN is developed to explore latent friendships of each user. We further fuse representations from two graphs by a novel multi-graph information fusion strategy with attention mechanism. To the best of our knowledge, this is the first work to combine meta-path with social relation representation. To evaluate the performance of MG-HIF, we compare MG-HIF with seven states of the art over four benchmark datasets. The experimental results show that MG-HIF achieves better performance.

Cross-modal hashing is a critical but very challenging task that is to retrieve similar samples of one modality via queries of other modalities. To improve the unsupervised cross-modal hashing, domain adaptation techniques can be used to support unsupervised hashing learning by transferring semantic knowledge from labeled source domain to unlabeled target domain. However, there are two problems that cannot be ignored: (1) most of domain adaptation based researches mainly focused on unimodal hashing or cross-modal real value-based retrieval but the study for cross-modal hashing is limited; (2) most existing studies only consider one or two consistency constraints during the domain adaptation learning. To this end, this paper propose a novel end-to-end framework to realize unsupervised domain adaptation for cross-modal hashing. This method, dubbed M$^2$GUDA, including four different consistency constraints: structure consistency, domain consistency, semantic consistency and modality consistency for domain adaptation learning. Besides, to enhance the structure consistency learning, we develop a multi-metrics graph modeling method to capture structure information comprehensively. Extensive experiments are performed on three common used benchmarks to evaluate the effectivity of our method. The results show that our method outperforms several state-of-the-art cross-modal hashing methods.

Different from previous imputation methods which impute missing values in the incomplete samples by using the information in the complete samples, this paper proposes a Date-drive Incremental imputation Model, DIM for short, which uses all available information in the data set to impute missing values economically, effectively, orderly, and iteratively. To this end, we propose a scoring rule to rank the missing features by taking into account both the economical criterion and the effective imputation information. The economical criterion takes both the imputation cost and the discriminative ability of the feature into account, while the effective imputation information enables to use all observed information in the data set including the imputed missing values to impute the left missing values. During the imputation process, our DIM first detects the neednot-impute samples for reducing the imputation cost and noise, and then selects the missing features with the top rank to impute first. The imputation process orderly imputes the missing features until all missing values are imputed or the imputation cost is exhausted. Experimental results on UCI data sets demonstrated the advantages of our proposed DIM, compared to the comparison methods, in terms of prediction accuracy and classification accuracy.

Many web applications demand a measure of similarity between two entities, such as collaborative filtering, web document ranking, linkage prediction, and anomaly detection. P-Rank (Penetrating-Rank) has been accepted as a promising graph-based similarity measure, as it provides a comprehensive way of encoding both incoming and outgoing links into assessment. However, the existing method to compute P-Rank is iterative in nature and rather cost-inhibitive. Moreover, the accuracy estimate and stability issues for P-Rank computation have not been addressed. In this article, we consider the optimization techniques for P-Rank search that encompasses its accuracy, stability, and computational efficiency. (1) The accuracy estimation is provided for P-Rank iterations, with the aim to find out the number of iterations, k , required to guarantee a desired accuracy. (2) A rigorous bound on the condition number of P-Rank is obtained for stability analysis. Based on this bound, it can be shown that P-Rank is stable and well-conditioned when the damping factors are chosen to be suitably small. (3) Two matrix-based algorithms, applicable to digraphs and undirected graphs, are, respectively, devised for efficient P-Rank computation, which improves the computational time from O ( kn 3 ) to O (υ n 2 +υ 6 ) for digraphs, and to O (υ n 2 ) for undirected graphs, where n is the number of vertices in the graph, and υ (≪ n ) is the target rank of the graph. Moreover, our proposed algorithms can significantly reduce the memory space of P-Rank computations from O ( n 2 ) to O (υ n +υ 4 ) for digraphs, and to O (υ n ) for undirected graphs, respectively. Finally, extensive experiments on real-world and synthetic datasets demonstrate the usefulness and efficiency of the proposed techniques for P-Rank similarity assessment on various networks.

With advances in geo-positioning technologies and geo-location services, there are a rapidly growing amount ofspatio-textualobjects collected in many applications such as location based services and social networks, in which an object is described by its spatial location and a set of keywords (terms). Consequently, the study of spatial keyword search which explores both location and textual description of the objects has attracted great attention from the commercial organizations and research communities. In the paper, we study two fundamental problems in the spatial keyword queries: top$k$spatial keyword search (TOPK-SK), and batch top$k$spatial keyword search (BTOPK-SK). Given a set ofspatio-textualobjects, a query location and a set of query keywords, the TOPK-SK retrieves the closest$k$objects each of which contains all keywords in the query. BTOPK-SK is the batch processing of sets of TOPK-SK queries. Based on the inverted index and the linear quadtree, we propose a novel index structure, called inverted linear quadtree (IL-Quadtree), which is carefully designed to exploit both spatial and keyword based pruning techniques to effectively reduce the search space. An efficient algorithm is then developed to tackle top$k$spatial keyword search. To further enhance the filtering capability of the signature of linear quadtree, we propose a partition based method. In addition, to deal with BTOPK-SK, we design a new computing paradigm which partition the queries into groups based on both spatial proximity and the textual relevance between queries. We show that the IL-Quadtree technique can also efficiently support BTOPK-SK. Comprehensive experiments on real and synthetic data clearly demonstrate the efficiency of our methods.

With the increasing pervasiveness of the geo-positioning tech-nologies, there is an enormous amount of spatio-textual ob-jects available in many applications such as location based services and social networks. Consequently, various types of spatial keyword searches which explore both locations and textual descriptions of the objects have been intensively studied by the research communities and commercial orga-nizations. In many important applications (e.g., location based services), the closeness of two spatial objects is mea-sured by the road network distance. Moreover, the result diversification is becoming a common practice to enhance the quality of the search results. Motived by the above facts, in this paper we study the problem of diversified spa-tial keyword search on road networks which considers both the relevance and the spatial diversity of the results. An efficient signature-based inverted indexing technique is pro-posed to facilitate the spatial keyword query processing on road networks. Then we develop an efficient diversified spa-tial keyword search algorithm by taking advantage of spatial keyword pruning and diversity pruning techniques. Com-prehensive experiments on real and synthetic data clearly demonstrate the efficiency of our methods. 1.

With advances in geo-positioning technologies and geo-location services, there are a rapidly growing amount of spatio-textual objects collected in many applications such as location based services and social networks, in which an object is described by its spatial location and a set of keywords (terms). Consequently, the study of spatial keyword search which explores both location and textual description of the objects has attracted great attention from the commercial organizations and research communities. In the paper, we study the problem of top k spatial keyword search (TOPK-SK), which is fundamental in the spatial keyword queries. Given a set of spatio-textual objects, a query location and a set of query keywords, the top k spatial keyword search retrieves the closest k objects each of which contains all keywords in the query. Based on the inverted index and the linear quadtree, we propose a novel index structure, called inverted linear quadtree (IL-Quadtree), which is carefully designed to exploit both spatial and keyword based pruning techniques to effectively reduce the search space. An efficient algorithm is then developed to tackle top k spatial keyword search. In addition, we show that the IL-Quadtree technique can also be applied to improve the performance of other spatial keyword queries such as the direction-aware top k spatial keyword search and the spatio-textual ranking query. Comprehensive experiments on real and synthetic data clearly demonstrate the efficiency of our methods.