global sensitivity
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Multi-label image recognition has been an indispensable fundamental component for many real computer vision applications. However, a severe threat of privacy leakage in multi-label image recognition has been overlooked by existing studies. To fill this gap, two privacy-preserving models, Privacy-Preserving Multi-label Graph Convolutional Networks (P2-ML-GCN) and Robust P2-ML-GCN (RP2-ML-GCN), are developed in this article, where differential privacy mechanism is implemented on the model’s outputs so as to defend black-box attack and avoid large aggregated noise simultaneously. In particular, a regularization term is exploited in the loss function of RP2-ML-GCN to increase the model prediction accuracy and robustness. After that, a proper differential privacy mechanism is designed with the intention of decreasing the bias of loss function in P2-ML-GCN and increasing prediction accuracy. Besides, we analyze that a bounded global sensitivity can mitigate excessive noise’s side effect and obtain a performance improvement for multi-label image recognition in our models. Theoretical proof shows that our two models can guarantee differential privacy for model’s outputs, weights and input features while preserving model robustness. Finally, comprehensive experiments are conducted to validate the advantages of our proposed models, including the implementation of differential privacy on model’s outputs, the incorporation of regularization term into loss function, and the adoption of bounded global sensitivity for multi-label image recognition.

Abstract In this paper we present a more realistic mathematical model for the transmission dynamics of malaria by extending the classical SEIRS scheme and the model of Hai-Feng Huo and Guang-Ming Qiu [21] by adding the ignorant infected humans compartment. We analyze the global asymptotically stabilities of the model by the use of the basic reproduction number R_0 and we prove that when R_0≦1, the disease-free equilibrium is globally asymptotically stable. That is malaria dies out in the population. When R_0>1, there exists a co-existing unique endemic equilibrium which is globally asymptotically stable. The global sensitivity analysis have been done through the partial rank correlation coefficient using the samples generated by the use of latin hypercube sampling method and shows that the most influence parameters in the spread of malaria are the proportion θ of infectious humans who recover and the recovery rate γ of infectious humans. In order to eradicate malaria, we have to decrease the number of ignorant infected humans by testing peoples and treat them. Numerical simulations show that malaria can be also controlled or eradicated by increasing the recovery rate γ of infectious humans, decreasing the number of ignorant infected humans and decreasing the average number n of mosquito bites.