Grey wolf optimization (GWO) is one of the recently proposed heuristic algorithms imitating the leadership hierarchy and hunting mechanism of grey wolves in nature. The aim of these algorithms is to perform global optimization. This paper presents a modified GWO algorithm based on complex-valued encoding; namely the complex-valued encoding grey wolf optimization (CGWO). We use CGWO to test 16 unconstrained benchmark functions with seven different scales and infinite impulse response (IIR) model identification. Compared to the real-valued GWO algorithm and other optimization algorithms; the CGWO performs significantly better in terms of accuracy; robustness; and convergence speed.

Graph embedding maps a graph into low-dimensional vectors, i.e., embedding matrix, while preserving the graph structure, solving the high computation and space cost for graph analysis. Matrix factorization (MF) is an effective means to achieve graph embedding since maintaining the utility of the graph structure. The personalized graph structure features implied in embedding matrix can identify the individual, which potentially breaches individual sensitive information in the original graph. Currently, protecting individual privacy without compromising the utility is the key to sharing embedding matrix. Differential privacy is a gold standard for publishing sensitive information while protecting privacy. Existing methods on differentially private MF, however, cannot be directly incorporated onto MF-based graph embedding as they undergo either high global sensitivity or iterative noise error accumulation, potentially rendering poor utility of MF-based graph embedding. To address the deficiency, this study proposes PPGD, a differentially private perturbed gradient descent method for MF-based graph embedding matrix sharing. Specifically, a Lipschitz condition on the objective function of MF and a gradient clipping strategy are devised for bounding global sensitivity. Along the way, a scalable solution to global sensitivity that is independent on original dataset is proposed. Further, a composite noise added means in the gradient descent is designed to guarantee privacy while enhance the utility. Theoretical analysis shows that PPGD can generate processed embedding matrix with the utility maximization while achieving (ε,δ)-differential privacy. Experimental evaluations confirm the effectiveness and efficiency of PPGD.

Recent studies show that privacy leakages may occur in vertical federated learning (VFL), where parties hold split features of the same samples. While various attacks, including label and feature inference, focus on record-level privacy risks in VFL, few studies delve into the distribution-level privacy threat. In this paper, we explore property inference attacks (PIAs) in VFL, where an adversarial party seeks to deduce global distribution information about a target property in the victim party’s training set. Our key observation is that the L_p-norm distribution of intermediate results in VFL could reflect the fraction of the target property in a training set. Inspired by this, we present ProVFL, a novel PIA framework involving distribution comparison and correlation augmentation modules. To achieve property inference, we design a distribution comparison module by creating various intermediate-result populations with different proportions, aiming to learn the relationship between L_p-norm distributions and their fractions. Then, we theoretically analyze the factors that contribute to the attack effectiveness and develop a correlation augmentation module based on label replacement and model refinement to amplify property information leakage. Extensive experimental results demonstrate that our attacks can achieve inferences with low estimation errors as low as 1%. This poses the immediate threat of property information leakage from private training data in the VFL setting.

The goal of privacy-preserving social graph publishing is to protect individual privacy while preserving graph utility. Node nearest neighbor structure is a crucial social graph utility as it is the basis for many graph analysis tasks. Most existing methods with differential privacy focus on preserving degree distribution yet neglect the maintenance of connections between nodes’ neighbors. Moreover, they require massive noise added to mask the change of a single edge, thereby rendering poor utility on the neighbor structure. As a result, it is tough to preserve high utility on the neighbor structure under differential privacy. To tackle these problems, we propose Priv-NNS, a private graph publishing algorithm to preserve the neighbor structure while guaranteeing individual privacy. This algorithm first decomposes a graph into subgraphs via extracting a nearest neighbor structure around each node. Then to yield node vectors satisfying differential privacy while preserving the neighbor structure, we design a private graph encoding approach with structure-awareness, which learns topological features of the subgraph by maximizing the co-occurrence probability among nodes. During this process, a novel objective perturbation approach with a random term, only requiring a scalar noise rather than a vector noise, is devised to balance the neighbor structure retained against the noise injected. Through formal privacy analysis, we prove that the yielded synthetic graph obeys ε-edge differential privacy. Experimental results demonstrate that Priv-NNS preserves high utility on the neighbor structure.

Many real-world networks can be modeled as decentralized heterogeneous graphs with different types of nodes, each holds a piece of whole network and has its own privacy preference. Local differential privacy (LDP) has been widely used in decentralized graph synthesis to provide privacy guarantees. This paper shows that existing LDP-based graph synthesis approaches are insufficient for preserving topological properties and satisfying the different privacy requirements of heterogeneous nodes when generating synthetic decentralized graphs. To address these problems due to the clueless perturbation and ignorance of the topological properties of existing approaches, we introduce HeG-LDP, a novel privacy-preserving decentralized heterogeneous graph synthesis approach that achieves a considerable utility boost compared to other methods while satisfying the privacy requirements of different types of nodes. Concretely, we propose a heterogeneous graph information extraction approach that exploits the inherent topological nature of graphs to construct background knowledge from the partial nodes in a diffusion manner, which is then used to guide individuals in topological information extraction and perturbation. In addition, to further improve the quality of the generated graph, we propose a dK-series-based graph generation approach, which can optimize the connection probability of node pairs via a delicate combination of degree values and dK-series information, resulting in better maintenance of the topological utility. Comprehensive experiments and theoretical analysis show that our proposed HeG-LDP can yield high-quality synthetic heterogeneous graphs while satisfying edge-LDP. To promote research in this field, we make our source code and data publicly available at https://github.com/HeG-LDP/Paper-codes.