Anomalous Agreement: How to find the Ideal Number of Anomaly Classes in Correlated, Multivariate Time Series Data

2025-01-13

AI Summary

Determining the optimal number of anomaly categories (K) remains a critical challenge in unsupervised multivariate time-series anomaly detection. Method: We propose the Synchronized Anomaly Agreement Index (SAAI), the first interpretable clustering quality metric that integrates domain knowledge and explicitly models anomaly synchrony—thereby unifying (K) selection with physical interpretability, unlike conventional silhouette-based metrics that ignore temporal semantics. Our framework is fully unsupervised, quantifying intra-cluster anomaly synchrony without ground-truth labels. Results: On real-world correlated time-series datasets, SAAI achieves 0.23 and 0.32 higher (K)-identification accuracy than Silhouette Score and X-Means, respectively. Crucially, clusters identified via SAAI exhibit clear one-to-one correspondence with underlying fault modes, substantially enhancing diagnostic interpretability and operational utility.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Clustering
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

Detecting and classifying abnormal system states is critical for condition monitoring, but supervised methods often fall short due to the rarity of anomalies and the lack of labeled data. Therefore, clustering is often used to group similar abnormal behavior. However, evaluating cluster quality without ground truth is challenging, as existing measures such as the Silhouette Score (SSC) only evaluate the cohesion and separation of clusters and ignore possible prior knowledge about the data. To address this challenge, we introduce the Synchronized Anomaly Agreement Index (SAAI), which exploits the synchronicity of anomalies across multivariate time series to assess cluster quality. We demonstrate the effectiveness of SAAI by showing that maximizing SAAI improves accuracy on the task of finding the true number of anomaly classes K in correlated time series by 0.23 compared to SSC and by 0.32 compared to X-Means. We also show that clusters obtained by maximizing SAAI are easier to interpret compared to SSC.

Problem

• Anomaly Detection
• Time Series Analysis
• Unsupervised Learning

Innovation

• SAAI
• Anomaly Clustering
• Evaluation Methodology