Calibrated One-class Classification for Unsupervised Time Series Anomaly Detection

TL;DR

This paper tackles unsupervised time-series anomaly detection under anomaly contamination by introducing Calibrated One-class Classification for Unsupervised Time series Anomaly detection (COUTA). It combines two calibration strategies: uncertainty modeling-based calibration (UMC), which imposes a Gaussian prior on the one-class distance and adaptively downweights contaminated samples, and native anomaly-based calibration (NAC), which generates dummy anomalies via tailored perturbations and adds a supervised branch to sharpen the normality boundary. The method maps subsequences to a compact hypersphere centered at $\mathbf{c}$ and uses combined distances $d_s$ and $\tilde{d}_s$ to score anomalies, with a final loss $\mathcal{L} = \mathcal{L}_{\text{UMC}} + \alpha \mathcal{L}_{\text{NAC}}$. Extensive experiments on ten real-world datasets show that COUTA outperforms sixteen baselines in both $F_1$ and $AUC$-PR, while exhibiting robustness to anomaly contamination and scalability to large, high-dimensional time-series. The work provides a practical framework for contamination-tolerant, anomaly-informed normality learning in real-world monitoring systems.

Abstract

Time series anomaly detection is instrumental in maintaining system availability in various domains. Current work in this research line mainly focuses on learning data normality deeply and comprehensively by devising advanced neural network structures and new reconstruction/prediction learning objectives. However, their one-class learning process can be misled by latent anomalies in training data (i.e., anomaly contamination) under the unsupervised paradigm. Their learning process also lacks knowledge about the anomalies. Consequently, they often learn a biased, inaccurate normality boundary. To tackle these problems, this paper proposes calibrated one-class classification for anomaly detection, realizing contamination-tolerant, anomaly-informed learning of data normality via uncertainty modeling-based calibration and native anomaly-based calibration. Specifically, our approach adaptively penalizes uncertain predictions to restrain irregular samples in anomaly contamination during optimization, while simultaneously encouraging confident predictions on regular samples to ensure effective normality learning. This largely alleviates the negative impact of anomaly contamination. Our approach also creates native anomaly examples via perturbation to simulate time series abnormal behaviors. Through discriminating these dummy anomalies, our one-class learning is further calibrated to form a more precise normality boundary. Extensive experiments on ten real-world datasets show that our model achieves substantial improvement over sixteen state-of-the-art contenders.

Figures (11)

• Figure 1: Demonstration of our key insights. (a) Broadly-used canonical one-class classification may learn an inaccurate, biased normality boundary due to the anomaly contamination problem and the absence of knowledge about anomalies. (b) By contrast, the two proposed calibration methods, UMC and NAC, respectively address these two issues, and our calibrated one-class classifier can produce a more accurate, clearer normality boundary. (c) UMC helps weaken contaminated data during optimization based on model uncertainty scores, while (d) NAC helps ground the normality boundary by calibrating the normality with native anomaly examples.
• Figure 2: (a) Time series data with three anomaly segments; (b) Learned feature space of canonical (non-calibrated) one-class classification and the proposed methods by using NAC/UMC separately and two calibration methods simultaneously (i.e., COUTA). Normal data is expected to be enclosed in a compact hypersphere, and anomalies can be successfully identified if they are distant from the center.
• Figure 3: The framework of COUTA.
• Figure 4: Loss values in $\mathcal{L}_{\text{UMC}}$ w.r.t. $d_{\bm{s}} + \tilde{d}_{\bm{s}}$ and $(d_{\bm{s}} - \tilde{d}_{\bm{s}})^2$. As indicated by the yellow line, the penalty of a fixed $d_{\bm{s}} + \tilde{d}_{\bm{s}}$ is first adjusted to more mild levels with the increase of the uncertainty $(d_{\bm{s}} - \tilde{d}_{\bm{s}})^2$, while the loss function further penalizes heavily when the uncertainty reaches a high value.
• Figure 5: Native anomaly examples generated from a time series sub-sequence $\bm{s}$ by six perturbation functions in $\Omega$.