An LS-Decomposition Approach for Robust Data Recovery in Wireless Sensor Networks

TL;DR

This paper introduces an LS-Decomposition method for robustly recovering sensor data matrices in wireless sensor networks, effectively handling missing data, noise, and anomalies with proven theoretical guarantees and superior empirical performance.

Contribution

The paper proposes an LS-Decomposition approach that decomposes corrupted data into low-rank and sparse components, with a new accelerated algorithm and theoretical error bounds.

Findings

Achieves recovery error ≤ 5% at 50% sampling rate

Almost exact recovery at 60% sampling rate

Outperforms state-of-the-art methods in real data experiments

Abstract

Wireless sensor networks are widely adopted in military, civilian and commercial applications, which fuels an exponential explosion of sensory data. However, a major challenge to deploy effective sensing systems is the presence of {\em massive missing entries, measurement noise, and anomaly readings}. Existing works assume that sensory data matrices have low-rank structures. This does not hold in reality due to anomaly readings, causing serious performance degradation. In this paper, we introduce an {\em LS-Decomposition} approach for robust sensory data recovery, which decomposes a corrupted data matrix as the superposition of a low-rank matrix and a sparse anomaly matrix. First, we prove that LS-Decomposition solves a convex program with bounded approximation error. Second, using data sets from the IntelLab, GreenOrbs, and NBDC-CTD projects, we find that sensory data matrices contain anomaly readings. Third, we propose an accelerated proximal gradient algorithm and prove that it approximates the optimal solution with convergence rate $O(1/k^2)$ ($k$ is the number of iterations). Evaluations on real data sets show that our scheme achieves recovery error $\leq 5\%$ for sampling rate $\geq 50\%$ and almost exact recovery for sampling rate $\geq 60\%$, while state-of-the-art methods have error $10\% \sim 15\%$ at sampling rate $90\%$.