Reconstruction model geometry affects success of anomaly detection
When Does Unsupervised Learning Succeed or Fail? A PoS Perspective on Reconstruction-Based Anomaly Detection
Machine Learning
Summary
Detecting unusual patterns without labels can be tricky because models might either copy unusual things too well or miss normal variations. The authors explain this problem using geometric ideas about how data parts combine. They propose new ways to train models to better separate normal from unusual data without needing examples of anomalies. Their methods improve how models identify defects in images and heart signals, confirming their theoretical ideas through experiments.
What this means in practice
- •For image processing teams: Improve quality control by detecting defective images more reliably using better unsupervised anomaly detection.
- •For medical device developers: Enhance electrocardiogram data analysis with improved unsupervised feature learning to support downstream heart condition classification.$Commercial implications: Enables more accurate and robust ECG diagnostic tools through better anomaly-aware data representations.
Authors
Mehmet Yamaç, Yagmur Mustu, Muhammad Numan Yousaf, Lei Xu, Marcel van Gerven
Abstract
Reconstruction-based unsupervised learning can fail in two opposing ways: a model may reconstruct anomalies too accurately or discard valid nominal variation. Using the Pursuit of Subspaces hypothesis, we characterize these failures through the meet, union, and join geometries induced by the nominal components. Excess learned range produces join blindness, while insufficient capacity produces meet preference and loss of nominal fidelity. We show that the compact nominal union is optimal among nominal faithful ranges and generally requires a nonlinear reconstruction map. Based on this geometry, we introduce Dynamic Push and Pull, which learns from controlled perturbations without anomaly labels, and nested manifold carving, which applies the same principle recursively in latent space. Experiments confirm the predicted changes in latent geometry across every tested Push and Pull configuration. The proposed methods improve reconstruction-based anomaly detection across standard benchmarks and unseen image degradations, while also improving pretrained ECG representations for downstream classification. These results connect reconstruction failures to identifiable geometric conditions and provide practical mechanisms for learning compact representations.