Matrix completion has emerged very recently and provides a new venue for low cost data gathering in Wireless sensor networks (W SNs). Existing schemes often assume that the data matrix has a known and fixed low-rank, which is unlikely to hold in a practical system for environment monitoring. Environmental data vary in temporal and spatial domain. By analyzing a large set of weather data collected from 196 sensors in ZhuZhou, China, we reveal that weather data has the features of low-rank, temporal stability, and relative rank stability. Taking advantage of these features, we propose an on-line data gathering scheme based on matrix completion theory, named MC-Weather, to adaptively sample different locations according to environmental and weather conditions. To better schedule sampling process while satisfying the required reconstruction accuracy, we propose several novel techniques, including three sample learning principles, an adaptive sampling algorithm based on matrix completion, and a uniform time slot and cross sample model. With these techniques, our MC-Weather scheme can collect the sensory data at required accuracy while largely reduce the cost for sensing, communication and computation. We perform extensive simulations based on the data traces from weather monitoring and the simulation results validate the efficiency and efficacy of the proposed scheme.

Tensor completion is a higher way analog of matrix completion, which has proven to be a powerful tool for data analysis. In this paper, we formulate the missing data recovery problem of a three-way tensor as a tensor completion problem. We propose a novel tensor completion method based on tensor-CUR decomposition to estimate the missing data from limited samples. Computational experiments demonstrate that the proposed method yields a superior performance over other existing approaches.