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The use of deep learning techniques in detecting anomalies in time series data has been an active area of research with a long history of development and a variety of approaches. In particular, reconstruction-based unsupervised anomaly detection methods have gained popularity due to their intuitive assumptions and low computational requirements. However, these methods are often susceptible to outliers and do not effectively model anomalies, leading to suboptimal results. This paper presents a novel approach for unsupervised anomaly detection, called the Cooperative Network Time Series (CNTS) approach. The CNTS system consists of two components: a detector and a reconstructor. The detector is responsible for directly detecting anomalies, while the reconstructor provides reconstruction information to the detector and updates its learning based on anomalous information received from the detector. The central aspect of CNTS is a multi-objective optimization problem, which is solved through a cooperative solution strategy. Experiments on three real-world datasets demonstrate the state-of-the-art performance of CNTS and confirm the effectiveness of the detector and reconstructor. The source code for this study is publicly available on GitHub (https://github.com/BomBooooo/CNTS/tree/main).

Two-dimensional principal component analysis (2DPCA) has been widely used to extract image features. As opposed to PCA, 2DPCA directly treats 2D matrices to extract image features instead of transforming 2D matrices into vectors. However, the classical 2DPCA based on F-norm square is sensitive to noise. To handle this problem, 2DPCAs based on ℓ1-norm, ℓp-norm, and other norms have been studied. In this paper, as a further development, 2DPCA based on Tℓ1 criterion is proposed, referred as 2DPCA-Tℓ1. Notice that, different from some norms used before, Tℓ1 criterion is bounded and Lipschitz-continuous. So it can be expected that our 2DPCA-Tℓ1 should be more robust. In fact, the experimental results have shown that its performance is superior to that of classical 2DPCA, 2DPCA-L1, 2DPCAL1-S, N-2-DPCA, G2DPCA, and Angle-2DPCA.