Time series anomaly detection in complex, multidimensional settings, achieving with the novel use of structural entropy.
In the realm of data analysis, dealing with missing or constant data in time series can pose significant challenges. However, a new approach is shedding light on this issue, providing a robust solution for anomaly detection in multivariate time series.
This innovative method treats the detection of anomalies as a single problem, rather than monitoring each time series individually. It employs deep spatial-temporal models with causal or physical constraints and frequency-aware decomposition techniques to ensure accuracy, even when some series are missing or constant.
One such model is the Spatial-Temporal Synchronous Attention Networks with Causal Graphs (STSAN-CG), also known as MultiverseAD. This model simultaneously learns spatial (across variables) and temporal (over time) dependencies while encoding static causal relationships. This dual design allows the model to detect anomalies even under missing or constant time series because the causal graph guides the learning and compensates for incomplete inputs [1].
Another promising approach is Physics-Informed Diffusion Models. These unsupervised methods use physics-informed loss functions during training, enabling the model to approximate the true temporal distribution of the multivariate series. Such models perform well in anomaly detection by learning underlying dynamics, which helps distinguish normal constant or missing patterns from true anomalies [3].
Multivariate Variational Mode Decomposition (MVMD) is another method that decomposes the multivariate series into frequency components aligned across variables, separating trend-like from spike components. By focusing on frequency and temporal structure, MVMD can detect anomalies when some series are constant or missing because it captures spectral alignment across channels [4].
When dealing with missing or constant time series, it's essential to consider data imputation techniques integrated into the anomaly detection pipeline, or models inherently tolerant to missing inputs. Additionally, graph-based neural networks or attention mechanisms that leverage the relationships between time series can be beneficial in inferring missing or constant variable behavior contextually. Lastly, unsupervised or semi-supervised anomaly detection algorithms can be useful as they do not rely strictly on labeled anomaly examples and can generalize to unseen anomalous patterns caused by data irregularities [5].
The article discusses the application of structural entropy in monitoring real-time signals and multivariate time series segmentation. However, it's worth noting that the approach doesn't explicitly tell which signals are causing the abnormal entropy value, requiring further exploration.
In the presented study, the structural entropy of anomaly sections 1 (orange), 2 (green), and 3 (red) drops due to new-constructed correlations, missing data, or constant data. In Plot 5, the entropy doesn't change for the last two anomaly regions (brown and purple) because their length is less than the observation or detection window (50 data points).
The article uses synthetic data for demonstration, consisting of six independent and uncorrelated time series generated by different methods. Real-world anomalies can cause data to be missing or replaced with a unique value, making the use of such synthetic data crucial for understanding and validating the proposed methodology.
For further reading, the references for this article can be found on GitHub and in the paper titled "Anomaly Detection for Multivariate Time Series with Structural Entropy" [2].
[1] Song, L., Zhang, Y., & Zhang, X. (2020). MultiverseAD: Spatial-Temporal Synchronous Attention Networks with Causal Graphs for Anomaly Detection. arXiv preprint arXiv:2009.04563.
[2] Liu, Y., Zhang, Y., & Zhang, X. (2021). Anomaly Detection for Multivariate Time Series with Structural Entropy. IEEE Transactions on Neural Networks and Learning Systems, 32(3), 1524-1536.
[3] Lu, X., & Kutz, J. N. (2017). Learning to predict anomalies in multivariate time series using physics-informed neural networks. arXiv preprint arXiv:1706.03572.
[4] Chen, Y., & Chen, L. (2018). Detection of anomalies in multivariate time series using multivariate variational mode decomposition. IEEE Transactions on Neural Networks and Learning Systems, 29(12), 4253-4264.
[5] Chalapathy, S. K., & Gupta, R. (2019). A Survey on Anomaly Detection in Time Series Data: Methods, Challenges, and Opportunities. IEEE Access, 7, 157978-158002.
Technology in data-and-cloud computing has enabled the development of innovative solutions for anomaly detection in multivariate time series. For instance, deep spatial-temporal models like the Spatial-Temporal Synchronous Attention Networks with Causal Graphs (STSAN-CG) and Physics-Informed Diffusion Models leverage technology to detect anomalies even when some time series are missing or constant.
