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This paper studies the distributed least-squares optimization problem with differential privacy requirement of local cost functions, for which two differentially private distributed solvers are proposed. The first is established on the distributed gradient tracking algorithm, by appropriately perturbing the initial values and parameters that contain the privacy-sensitive data with Gaussian and truncated Laplacian noises, respectively. Rigorous proofs are established to show the achievable trade-off between the ({\epsilon}, {\delta})-differential privacy and the computation accuracy. The second solver is established on the combination of the distributed shuffling mechanism and the average consensus algorithm, which enables each agent to obtain a noisy version of parameters characterizing the global gradient. As a result, the least-squares optimization problem can be eventually solved by each agent locally in such a way that any given ({\epsilon}, {\delta})-differential privacy requirement can be preserved while the solution may be computed with the accuracy independent of the network size, which makes the latter more suitable for large-scale distributed least-squares problems. Numerical simulations are presented to show the effectiveness of both solvers.

This paper studies the average consensus problem with differential privacy of initial states, for which it is widely recognized that there is a trade-off between the mean-square computation accuracy and privacy level. Considering the trade-off gap between the average consensus algorithm and the centralized averaging approach with differential privacy, we propose a distributed shuffling mechanism based on the Paillier cryptosystem to generate correlated zero-sum randomness. By randomizing each local privacy-sensitive initial state with an i.i.d. Gaussian noise and the output of the mechanism using Gaussian noises, it is shown that the resulting average consensus algorithm can eliminate the gap in the sense that the accuracy-privacy trade-off of the centralized averaging approach with differential privacy can be almost recovered by appropriately designing the variances of the added noises. We also extend such a design framework with Gaussian noises to the one using Laplace noises, and show that the improved privacy-accuracy trade-off is preserved.

Alternating Direction Method of Multipliers (ADMM) algorithm has been widely adopted for solving the distributed optimization problem (DOP). In this paper, a new distributed parallel ADMM algorithm is proposed, which allows the agents to update their local states and dual variables in a completely distributed and parallel manner by modifying the existing distributed sequential ADMM. Moreover, the updating rules and storage method for variables are illustrated. It is shown that all the agents can reach a consensus by asymptotically converging to the optimal solution. Besides, the global cost function will converge to the optimal value at a rate of O(1/k). Simulation results on a numerical example are given to show the effectiveness of the proposed algorithm.

Keypoints matching is a pivotal component for many image-relevant applications such as image stitching, visual simultaneous localization and mapping (SLAM), and so on. Both handcrafted-based and recently emerged deep learning-based keypoints matching methods merely rely on keypoints and local features, while losing sight of other available sensors such as inertial measurement unit (IMU) in the above applications. In this paper, we demonstrate that the motion estimation from IMU integration can be used to exploit the spatial distribution prior of keypoints between images. To this end, a probabilistic perspective of attention formulation is proposed to integrate the spatial distribution prior into the attentional graph neural network naturally. With the assistance of spatial distribution prior, the effort of the network for modeling the hidden features can be reduced. Furthermore, we present a projection loss for the proposed keypoints matching network, which gives a smooth edge between matching and un-matching keypoints. Image matching experiments on visual SLAM datasets indicate the effectiveness and efficiency of the presented method.

Localizing pre-visited places during long-term simultaneous localization and mapping, i.e. loop closure detection (LCD), is a crucial technique to correct accumulated inconsistencies. As one of the most effective and efficient solutions, Bag-of-Words (BoW) builds a visual vocabulary to associate features and then detect loops. Most existing approaches that build vocabularies off-line determine scales of the vocabulary by trial-and-error, which often results in unreasonable feature association. Moreover, the accuracy of the algorithm usually declines due to perceptual aliasing, as the BoW-based method ignores the positions of visual features. To overcome these disadvantages, we propose a natural convergence criterion based on the comparison between the radii of nodes and the drifts of feature descriptors, which is then utilized to build the optimal vocabulary automatically. Furthermore, we present a novel topological graph verification method for validating candidate loops so that geometrical positions of the words can be involved with a negligible increase in complexity, which can significantly improve the accuracy of LCD. Experiments on various public datasets and comparisons against several state-of-the-art algorithms verify the performance of our proposed approach., Comment: 11 pages, 9 figures

Most traditional false data injection attack (FDIA) detection approaches rely on a key assumption, i.e., the power system can be accurately modeled. However, the transmission line parameters are dynamic and cannot be accurately known during operation and thus the involved modeling errors should not be neglected. In this paper, an illustrative case has revealed that modeling errors in transmission lines significantly weaken the detection effectiveness of conventional FDIA approaches. To tackle this issue, we propose an FDIA detection mechanism from the perspective of transfer learning. Specifically, the simulated power system is treated as a source domain, which provides abundant simulated normal and attack data. The real world's running system whose transmission line parameters are unknown is taken as a target domain where sufficient real normal data are collected for tracking the latest system states online. The designed transfer strategy that aims at making full use of data in hand is divided into two optimization stages. In the first stage, a deep neural network (DNN) is built by simultaneously optimizing several well-designed objective terms with both simulated data and real data, and then it is fine-tuned via real data in the second stage. Several case studies on the IEEE 14-bus and 118-bus systems verify the effectiveness of the proposed mechanism., Comment: 9 pages, 4 figures