Triangle counting serves as a foundational operator in graph analysis. Since graph data often contain sensitive information about entities, the release of triangle counts poses privacy concerns. While recent studies have addressed privacy-preserving triangle counting, they mainly concentrate on unsigned graphs. In this paper, we investigate a new problem of developing triangle counting algorithms for signed graphs that adhere to centralized differential privacy and local differential privacy, respectively. The inclusion of edge signs and more classes of triangles leads to increased complexity and overwhelms the statistics with noise. To overcome these problems, we first propose a novel algorithm for smooth-sensitivity computation to achieve differential privacy under the centralized model. In addition, to handle large signed graphs, we devise a computationally efficient function that calculates a smooth upper bound on local sensitivity. Finally, we release the approximate triangle counts after the introduction of Laplace noise, which is calibrated to the smooth upper bound on local sensitivity. In the local model, we propose a two-phase framework tailored for balanced and unbalanced triangle counting. The first phase utilizes the Generalized Randomized Response mechanism to perturb data, followed by a novel response mechanism in the second phase. Extensive experiments conducted over real-world datasets demonstrate that our proposed methods can achieve an excellent trade-off between privacy and utility.

The classic clique model has properties of hereditaries and cohesiveness. Here hereditaries means a subgraph of a clique is still a clique. Counting small cliques in a graph is a fundamental operation of numerous applications. However, the clique model is often too restrictive for practical use, leading to the focus on other relaxed-cliques with properties of hereditaries and cohesiveness. To address this issue, we investigate a new problem of counting general hereditary cohesive subgraphs (HCS). All subgraphs with properties of hereditaries and cohesiveness can be called a kind of HCS. To count HCS, we propose a general framework called HCSPivot, which can be applied to count all kinds of HCS. HCSPivot can count most HCS combinatorially without explicitly listing them. Two additional noteworthy features of HCSPivot are its ability to (1) simultaneously count HCS of any size and (2) simultaneously count HCS for each node or each edge. Based on our HCSPivot framework, we propose two novel algorithms with several carefully designed pruning techniques to count s-defective cliques and s-plexes, which are two specific types of HCS. We conduct extensive experiments on 8 large real-world graphs, and the results demonstrate the high efficiency and effectiveness of our solutions.

Personalized search aims at re-ranking search results with reference to users' background information. The state-of-the-art personalized search methods often consider both the short-term search interests from current session behaviors and the long-term search interests from previous session behaviors. However, sessions in real-world search scenarios are usually very short, and a large number of sessions contain only one query, which makes it difficult to model short-term search interests. Intuitively, apart from current session behaviors, some recent historical session behaviors could also contribute to the current search interests, and the influence of these behaviors typically decays over time. Based on this intuition, we propose a novel heterogeneous graph based Hawkes process to improve the effectiveness of personalized search. Specifically, we first construct a heterogeneous graph to model multiple relations between users, queries, and documents. Then, we propose a heterogeneous graph neural network based algorithm to encode the representations of users' historical search behaviors. After that, we develop a multivariate Hawkes process to capture the influence of historical search behaviors on the current search intent. Our approach can dynamically model the influence of historical behaviors in a continuous time space. Thus, both the current session behaviors and the historical session behaviors can be utilized to characterize a more accurate current search intent. We evaluate our method using three real-life datasets, and the results show that our approach significantly outperforms the state-of-the-art methods in terms of several widely-used precision metrics.

Recently, the explanation of neural network models has garnered considerable research attention. In computer vision, CAM (Class Activation Map)-based methods and LRP (Layer-wise Relevance Propagation) method are two common explanation methods. However, since most CAM-based methods can only generate global weights, they can only generate coarse-grained explanations at a deep layer. LRP and its variants, on the other hand, can generate fine-grained explanations. But the faithfulness of the explanations is too low. To address these challenges, in this paper, we propose FG-CAM (Fine-Grained CAM), which extends CAM-based methods to enable generating fine-grained and high-faithfulness explanations. FG-CAM uses the relationship between two adjacent layers of feature maps with resolution differences to gradually increase the explanation resolution, while finding the contributing pixels and filtering out the pixels that do not contribute. Our method not only solves the shortcoming of CAM-based methods without changing their characteristics, but also generates fine-grained explanations that have higher faithfulness than LRP and its variants. We also present FG-CAM with denoising, which is a variant of FG-CAM and is able to generate less noisy explanations with almost no change in explanation faithfulness. Experimental results show that the performance of FG-CAM is almost unaffected by the explanation resolution. FG-CAM outperforms existing CAM-based methods significantly in both shallow and intermediate layers, and outperforms LRP and its variants significantly in the input layer. Our code is available at https://github.com/dongmo-qcq/FG-CAM.

Graph embedding has become a powerful tool for learning latent representations of nodes in a graph. Despite its superior performance in various graph-based machine learning tasks, serious privacy concerns arise when the graph data contains personal or sensitive information. To address this issue, we investigate and develop graph embedding algorithms that satisfy local differential privacy (LDP). We introduce a novel privacy-preserving graph embedding framework, named PrivGE, to protect node data privacy. Specifically, we propose an LDP mechanism to obfuscate node data and utilize personalized PageRank as the proximity measure to learn node representations. Furthermore, we provide a theoretical analysis of the privacy guarantees and utility offered by the PrivGE framework. Extensive experiments on several real-world graph datasets demonstrate that PrivGE achieves an optimal balance between privacy and utility, and significantly outperforms existing methods in node classification and link prediction tasks.

In recent years, with the development of deep learning technology, computer vision and natural language processing have made significant progress, and establishing the relationship between computer vision and natural language processing has attracted more and more attention. The spatio-temporal images taken by satellites or aircrafts and scene images with people and other things are the main focus area. Existing methods have yielded excellent results in image–text matching, but there is still room for improvement in effectively using coarse and fine-grained information. We propose a method to solve this problem using multi-scale graph convolutional neural networks. We extracted the multi-scale features of images and texts for matching separately. Global and local matching are used to calculate the overall image sentence and local image–word similarity. Local matching is divided into two stages, first, the node level matches the correspondence between the learning region and the word. Next, the structure level matches the correspondence between the learning region and the phrase to make the matching more comprehensive. Finally, we verified our model on Flickr30k, MSCOCO and RSICD datasets.

Real-life graph datasets extracted from the Web are inevitably full of incompleteness, conflicts, and redundancies, so graph data cleaning shows its necessity. Although rules like data dependencies have been widely studied in relational data repairing, very few works exist to repair graph data. In this article, we introduce a repairing semantics for graphs, calledGraph-Repairing Rules(${\sf GRR}$s). This semantics can capture the incompleteness, conflicts, and redundancies in graphs and indicate how to correct these errors. However, this graph repairing semantics can only repair the graphs strictly isomorphic to the rule patterns, which decreases the utility of the rules. To overcome this shortcoming, we further propose a flexible rule-based graph repairing semantics (called$\delta$-GRR). We study three fundamental problems associated with both${\sf GRR}$s and$\delta$-GRRs, consistency, implication, and termination, which show whether a given set of rules make sense. Repairing the graph data using${\sf GRR}$s or$\delta$-GRRs involves a problem of finding isomorphic subgraphs of the graph data, which is NP-complete. To efficiently circumvent the complex calculation of subgraph isomorphism, we design a decomposition-and-join strategy to solve this problem. Extensive experiments on real datasets show that our two graph repairing semantics and corresponding repairing algorithms can effectively and efficiently repair real-life graph data.

In this paper, we propose a novel semi-supervised graph node classification algorithm called Coarse-to-Fine Graph Attention Network (CFGAT), which can hierarchically enhance node representation ability in a coarse to fine manner. Specifically, CFGAT consists of two subnets: CoarseNet and FineNet. For the CoarseNet, we present a simple-yet-nontrivial node information coarsening strategy, which can generate coarse-grained features for all nodes on the graph by performing average on the structure-similar neighborhood information within densely-connected subgraphs. For the FineNet, the coarse-grained features obtained from the CoarseNet can be refined level by level using multiple reformulated graph attention layers. In addition, we also propose a Node-wise Receptive Field Selection Module which performs an adaptive receptive field selection for each node on the graph by assigning different attentions to different-scale node features extracted from multiple layers of the network. All proposed sub-algorithms can be integrated into an overall framework and trained in an end-to-end manner. Experimental results on three commonly-used datasets demonstrate the effectiveness and superiority of the proposed framework.