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  1. Graph sparsification has been used to improve the computational cost of learning over graphs, e.g., Laplacian-regularized estimation and graph semi-supervised learning (SSL). However, when graphs vary over time, repeated sparsification requires polynomial order computational cost per update. We propose a new type of graph sparsification namely fault-tolerant (FT) sparsification to significantly reduce the cost to only a constant. Then the computational cost of subsequent graph learning tasks can be significantly improved with limited loss in their accuracy. In particular, we give theoretical analyze to upper bound the loss in the accuracy of the subsequent Laplacian-regularized estimation and graph SSL, due to the FT sparsification. In addition, FT spectral sparsification can be generalized to FT cut sparsification, for cut-based graph learning. Extensive experiments have confirmed the computational efficiencies and accuracies of the proposed methods for learning on dynamic graphs. 
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  2. In most process control systems nowadays, process measurements are periodically collected and archived in historians. Analytics applications process the data, and provide results offline or in a time period that is considerably slow in comparison to the performance of many manufacturing processes. Along with the proliferation of Internet-of-Things (IoT) and the introduction of "pervasive sensors" technology in process industries, increasing number of sensors and actuators are installed in process plants for pervasive sensing and control, and the volume of produced process data is growing exponentially. To digest these data and meet the ever-growing requirements to increase production efficiency and improve product quality, there needs a way to both improve the performance of the analytic system and scale the system to closely monitor a much larger set of plant resources. In this paper, we present a real-time data analytics platform, referred to as RT-DAP, to support large-scale continuous data analytics in process industries. RT-DAP is designed to be able to stream, store, process and visualize a large volume of real-time data flows collected from heterogeneous plant resources, and feedback to the control system and operators in a real-time manner. A prototype of the platform is implemented on Microsoft Azure. Our extensive experiments validate the design methodologies of RT-DAP and demonstrate its efficiency in both component and system levels. 
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