PDCM: Periodicity-based Division and Covariance Matrix for Time Series Anomaly Detection

Abstract

Purpose: The purpose of this study was to develop a multivariate time series anomaly detection model that distinguishes between periodic and non-periodic variables and processes them using dedicated architectures to improve anomaly detection performance.Methods: PDCM first applies the Fast Fourier Transform (FFT) to identify whether each time series variable exhibits clear periodicity. Variables with clear periodicity are processed through a Conv2D block to capture temporal 2D variations, while variables without clear periodicity are reconstructed using a GAN-based autoencoder. Furthermore, a covariance matrix loss is incorporated to preserve relationships between periodic and non-periodic variables during training. The proposed model was evaluated on five real-world multivariate time series anomaly detection datasets and compared with existing state-of-the-art methods.Results: Experimental results demonstrate that PDCM consistently outperforms existing methods across all benchmark datasets. In particular, the proposed model achieves notable improvements in F1-score on datasets such as MSL, SMD, and SMAP, where many variables do not exhibit clear periodicity. These results indicate that separately modeling periodic and non-periodic variables, while preserving inter-variable dependencies, effectively improves anomaly detection performance.Conclusion: The proposed PDCM improves multivariate time series anomaly detection by separately modeling periodic and non-periodic variables while preserving inter-variable dependencies. Future research will focus on developing more robust periodicity identification methods and handling variables with mixed temporal characteristics.