Graph Laplacian Eigenvalues Empowered VAEs: A Novel Approach to Adaptive Latent Dimension Choice

Abstract

Anomaly detection in multivariate time series (MTS) data is crucial for identifying unusual behaviors or events that may indicate system failures, fraud, or other issues. In many real-world scenarios, labeled anomalies are scarce or non-existent, making unsupervised learning methods essential. Neural network architectures, such as Autoencoders and Variational Autoencoders (VAEs), are popular and effective for MTS anomaly detection. These models learn to compress and reconstruct data by capturing underlying patterns and identifying anomalies through reconstruction errors. However, VAEs require careful tuning of latent space dimensionality, architecture, and loss functions to achieve optimal results. We propose an unsupervised anomaly detection model for MTS data based on a Variational Autoencoder enhanced with Graph Laplacian Eigenvalues (GLE) for latent dimension selection, termed VAE-GLE. The GLE method dynamically adapts the latent dimension, which is traditionally a crucial hyperparameter in VAEs, thereby improving the model’s performance. Our methodology involves integrating GLE into the VAE framework to capture the intrinsic structure of the data better. Extensive experiments demonstrate that the proposed VAE-GLE model outperforms traditional autoencoders and GAN-based anomaly detection methods, significantly improving detection accuracy and robustness. The results indicate that VAE-GLE can effectively identify anomalies in MTS data without the need for labeled data, making it a valuable tool for real-world applications such as predictive maintenance, cybersecurity, and fraud detection.

Keywords

• MTS Analysis
• Deep Learning
• MTS anomaly detection
• Variational Autoencoders (VAE)
• Latent Dimension
• Graph Laplacian Eigenvalues (GLE)