Noise-Resilient Point-wise Anomaly Detection in Time Series Using Weak Segment Labels

TL;DR

NRdetector tackles point-level anomaly detection in time series when training data contain noisy segment-level labels and no point-level labels. It introduces a two-stage framework: Stage-1 performs coarse-grained PU learning with temporal embeddings, a confidence-based sample selector, and a PU criterion that couples a non-negative PU risk $R_{pu}$ with a time-constraint loss $L_c$, yielding the objective $L=R_{pu}+\,\lambda L_c$; Stage-2 then detects point-level anomalies by ranking points within predicted positive segments and auto-thresholding via a training-free anomaly-rate estimator. The method relies on temporal embeddings from a DiCNN backbone, a six-layer MLP classifier, and a data-centric point detector, with loss terms designed to enforce smoothness of point scores and separability across segments. Experiments on five real-world, multivariate TSAD benchmarks show NRdetector consistently outperforms baselines under noisy segment labels, validating its robustness and practical impact for real-world monitoring systems.

Abstract

Detecting anomalies in temporal data has gained significant attention across various real-world applications, aiming to identify unusual events and mitigate potential hazards. In practice, situations often involve a mix of segment-level labels (detected abnormal events with segments of time points) and unlabeled data (undetected events), while the ideal algorithmic outcome should be point-level predictions. Therefore, the huge label information gap between training data and targets makes the task challenging. In this study, we formulate the above imperfect information as noisy labels and propose NRdetector, a noise-resilient framework that incorporates confidence-based sample selection, robust segment-level learning, and data-centric point-level detection for multivariate time series anomaly detection. Particularly, to bridge the information gap between noisy segment-level labels and missing point-level labels, we develop a novel loss function that can effectively mitigate the label noise and consider the temporal features. It encourages the smoothness of consecutive points and the separability of points from segments with different labels. Extensive experiments on real-world multivariate time series datasets with 11 different evaluation metrics demonstrate that NRdetector consistently achieves robust results across multiple real-world datasets, outperforming various baselines adapted to operate in our setting.

Figures (3)

• Figure 1: Illustration of the insights. The x-axis in (a) and (b) represents the time step, and the y-axis represents the feature vector. When true point labels are accessible, we observe: a) Continuity: The point-level anomaly scores vary smoothly between points within either abnormal (red) or normal (green) segments; b) Discriminability: The range of scores (as in the color bar) of anomalous segments ($\pm$20) is sufficiently different from the normal segments ($\pm$6). When point labels are missing, the learned embeddings should also preserve both properties.
• Figure 2: The workflow of the NRdetector framework. NRdetector consists of two main stages: coarse-grained PU learning and fine-grained abnormal point detection. In the Sample Selector module, $\mathcal{X}_L$ denotes the set of labeled positive segments, $\mathcal{X}_U$ denotes the set of unlabeled segments, $\mathcal{X}_{RN}$ denotes the set of extracted reliable negatives based on the confidence scores, and $\mathcal{X}_{LP}$ denotes the set of likely negatives after the label propagation process. $f(X)$ represents the output from the last linear layer of our classifier, processed through a Sigmoid function. TC Loss is the time constraint loss and PU Loss is the non-negative PU risk estimator in Section \ref{['sec:criterion']}.
• Figure 3: Parameter sensitivity studies of hyper-parameters, Class Prior and Batch Size in NRdetector. Both studies are conducted on the MSL dataset.

Theorems & Definitions (3)

• theorem 1
• lemma 1
• theorem 2: Generalization Error