A unified L^q(L^p) theory establishes weak differentiability of SDE flows, a Bismut-Elworthy-Li derivative formula, and endpoint weak well-posedness for singular locally integrable coefficients.
Reconstruction of Missing Big Sensor Data
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abstract
With ubiquitous sensors continuously monitoring and collecting large amounts of information, there is no doubt that this is an era of big data. One of the important sources for scientific big data is the datasets collected by Internet of things (IoT). It's considered that these datesets contain highly useful and valuable information. For an IoT application to analyze big sensor data, it is necessary that the data are clean and lossless. However, due to unreliable wireless link or hardware failure in the nodes, data loss in IoT is very common. To reconstruct the missing big sensor data, firstly, we propose an algorithm based on matrix rank-minimization method. Then, we consider IoT with multiple types of sensor in each node. Accounting for possible correlations among multiple-attribute sensor data, we propose tensor-based methods to estimate missing values. Moreover, effective solutions are proposed using the alternating direction method of multipliers. Finally, we evaluate the approaches using two real sensor datasets with two missing data-patterns, i.e., random missing pattern and consecutive missing pattern. The experiments with real-world sensor data show the effectiveness of the proposed methods.
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math.PR 1years
2019 1verdicts
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$L^q(L^p)$-theory of stochastic differential equations
A unified L^q(L^p) theory establishes weak differentiability of SDE flows, a Bismut-Elworthy-Li derivative formula, and endpoint weak well-posedness for singular locally integrable coefficients.