A Federated Filtering Framework for Internet of Medical Things

Based on the dominant paradigm, all the wearable IoT devices used in the healthcare sector also known as the internet of medical things (IoMT) are resource constrained in power and computational capabilities. The IoMT devices are continuously pushing their readings to the remote cloud servers for real-time data analytics, that causes faster drainage of the device battery. Moreover, other demerits of continuous centralizing of data include exposed privacy and high latency. This paper presents a novel Federated Filtering Framework for IoMT devices which is based on the prediction of data at the central fog server using shared models provided by the local IoMT devices. The fog server performs model averaging to predict the aggregated data matrix and also computes filter parameters for local IoMT devices. Two significant theoretical contributions of this paper are the global tolerable perturbation error (${To{l_F}}$) and the local filtering parameter ($\delta$); where the former controls the decision-making accuracy due to eigenvalue perturbation and the later balances the tradeoff between the communication overhead and perturbation error of the aggregated data matrix (predicted matrix) at the fog server. Experimental evaluation based on real healthcare data demonstrates that the proposed scheme saves upto 95\% of the communication cost while maintaining reasonable data privacy and low latency.Comment: 6 pages, 6 Figures, accepted for oral presentation in IEEE ICC 2019, Internet of Things, Federated Learning and Perturbation theor

On Blow-up criterion for the Nonlinear Schr\"{o}dinger Equation

The blowup is studied for the nonlinear Schr\"{o}dinger equation $iu_{t}+\Delta u+ |u|^{p-1}u=0$ with $p$ is odd and $p\ge 1+\frac 4{N-2}$ (the energy-critical or energy-supercritical case). It is shown that the solution with negative energy $E(u_0)<0$ blows up in finite or infinite time. A new proof is also presented for the previous result in \cite{HoRo2}, in which a similar result but more general in a case of energy-subcritical was shown.Comment: In this version, we add a reference, and change some expressions in Englis

Robust Orthogonal Complement Principal Component Analysis

Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal subspace estimation. Based on a mathematical formulation of such transformed outliers, a novel robust orthogonal complement principal component analysis (ROC-PCA) is proposed. The framework combines the popular sparsity-enforcing and low rank regularization techniques to deal with row-wise outliers as well as element-wise outliers. A non-asymptotic oracle inequality guarantees the accuracy and high breakdown performance of ROC-PCA in finite samples. To tackle the computational challenges, an efficient algorithm is developed on the basis of Stiefel manifold optimization and iterative thresholding. Furthermore, a batch variant is proposed to significantly reduce the cost in ultra high dimensions. The paper also points out a pitfall of a common practice of SVD reduction in robust PCA. Experiments show the effectiveness and efficiency of ROC-PCA in both synthetic and real data

Group Iterative Spectrum Thresholding for Super-Resolution Sparse Spectral Selection

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods break down in presence of high coherence and large noise. We propose a new regularization approach to handle model collinearity and obtain parsimonious frequency selection simultaneously. It takes advantage of the pairing structure of sine and cosine atoms in the frequency dictionary. A probabilistic spectrum screening is also developed for fast computation in high dimensions. A data-resampling version of high-dimensional Bayesian Information Criterion is used to determine the regularization parameters. Experiments show the efficacy and efficiency of the proposed algorithms in challenging situations with small sample size, high frequency resolution, and low signal-to-noise ratio