Monitoring data contain the important status information of the monitored object, and are the basis for following data mining and analysis. However, the monitoring data usually suffer the pollution of the outliers, leading to negative effect on the subsequent data processing. To address the problem, this paper proposed an outlier detection method based on stacked autoencoder (SAE). SAE has a powerful capability of feature extraction and greatly preserves the original information of the data. The trained SAE by normal data can learn the characteristics of normal data. When a set of data with outliers are inputted to the trained network, there are larger reconstruction errors at the outliers between the original input data and the reconstructed data obtained by using the encoding parameters and the decoding parameter mapping, which provides a basis for locating outliers. Meanwhile, this paper introduced the Grubbs criterion and the PauTa criterion to identify the reconstruction errors corresponding to the outliers based on the traditional threshold method. The method can quickly isolate the abnormal data from the normal data according to the reconstruction error and the identification criterion. The effectiveness and superiority of the proposed method have been validated by experiment on real data and comparisons with traditional outlier detection algorithms.

Under false data-injection (FDI) attacks, the data of some agents are tampered with by the FDI attackers, which causes that the distributed algorithm cannot estimate the ideal unknown parameter. Due to the concealment of the malicious data tampered with by the FDI attacks, many detection algorithms against FDI attacks often have poor detection results or low detection efficiencies. To solve these problems, a conveniently distributed diffusion least-mean-square (DLMS) algorithm with cross-verification (CV) is proposed against FDI attacks. The proposed DLMS with CV (DLMS-CV) algorithm is comprised of two subsystems: one subsystem provides a detection test of agents based on the CV mechanism, while the other provides a secure distribution estimation. In the CV mechanism, a smoothness strategy is introduced, which can improve the detection performance. The convergence performance of the proposed algorithm is analyzed, and then the design method of the adaptive threshold is also formulated. In particular, the probabilities of missing alarm and false alarm are examined, and they decay exponentially to zero under sufficiently small step size. Finally, simulation experiments are provided to illustrate the effectiveness and simplicity of the proposed DLMS-CV algorithm in comparison to other algorithms against FDI attacks.