Session-based multimedia recommendation in edge computing remains an important issue for boosting the utilization of services since service composition has increasingly attracted attention. Existing session-based recommendations (SBRs) model the session sequence with multilevel feature extraction in graph neural networks (GNNs). However, multilevel feature extraction in disentangled graph neural networks causes over-smoothing and privacy leakage. To address the aforementioned problems, Secure and Efficient Session-based Multimedia Recommendation (SeSMR) model is proposed. In the proposed SeSMR model, based on BGV homomorphic encryption, a ciphertext training submodel is proposed to address the privacy leakage, ensuring the security in SBR. Furthermore, based on the reinforcement of feature activation, a residual attention mechanism is proposed to mitigate over-smoothing while maintaining the independence of multiple features. Finally, based on location coding, a soft attention mechanism is proposed to improve the recommendation accuracy, by introducing the position difference information between items into intra-session and inter-session scenarios. Experiments demonstrate that both Recall and MRR metrics exhibit nearly 2% to 5% improvement.

Detection of sparse signals arises in many modern applications such as signal processing, bioinformatics, finance, and disease surveillance. However, in many of these applications, the data may contain sensitive personal information, which is desirable to be protected during the data analysis. In this article, we consider the problem of ϵ-differentially private detection of the sparse Gaussian mixtures with the focus on how privacy affects the detection power. We first study the private likelihood ratio test and show it achieves vanishing error probabilities in the detectable region proposed by Ingster [1] and Donoho and Jin [2] when ϵ > n--β. Moreover, we propose an adaptive ϵ-differentially private test, which achieves vanishing error probabilities in the same detectable region when $\sqrt {\log (\log n)} \varepsilon \to \infty $. Several numerical experiments are conducted to verify our theoretical results and illustrate the performance of our proposed test.

In image detection, one problem is to test whether the set, though mainly consisting of uniformly scattered points, also contains a small fraction of points sampled from some (a priori unknown) curve, for example, a curve with Cα-norm bounded by β. One approach is to analyze the data by counting membership in multiscale multianisotropic strips, which involves an algorithm that delves into the length of the path connecting many consecutive “significant” nodes. In this paper, we develop the mathematical formalism of this algorithm and analyze the statistical property of the length of the longest significant run. The rate of convergence is derived. Using percolation theory and random graph theory, we present a novel probabilistic model named, pseudo-tree model. Based on the asymptotic results for the pseudo-tree model, we further study the length of the longest significant run in an “inflating” Bernoulli net. We find that the probability parameter p of significant node plays an important role: there is a threshold pc, such that in the cases of pcand p > pc, very different asymptotic behaviors of the length of the significant runs are observed. We apply our results to the detection of an underlying curvilinear feature and prove that the test based on our proposed longest run theory is asymptotically powerful.