Method¶

AnomalyMatch combines the semi-supervised FixMatch algorithm with active learning to detect anomalies starting from as few as 5-10 labeled examples.

For full details, see the paper: AnomalyMatch: Discovering Rare Objects of Interest with Semi-supervised and Active Learning (Gomez et al., 2025).

Semi-supervised Learning with FixMatch¶

AnomalyMatch treats anomaly detection as binary classification ("normal" vs "anomaly") under severe class imbalance. The key insight is leveraging large amounts of unlabeled data alongside a small labeled set through FixMatch's consistency regularization.

Augmentation Strategy¶

FixMatch applies two levels of augmentation to unlabeled images:

• Weak augmentations: Minor transformations (horizontal flips, slight random crops) that preserve image content — used to generate reliable pseudo-labels
• Strong augmentations: Aggressive transformations including rotations, colour distortions, sharpness variations, shearing, and posterisation — used to train the model to be invariant

Pseudo-labels and Consistency Regularization¶

1. An unlabeled image receives a weak augmentation and is passed through the model
2. If the predicted probability exceeds a confidence threshold (default: 0.95), a pseudo-label is assigned
3. The same image receives a strong augmentation and is passed through the model again
4. The model is trained to match its prediction on the strongly-augmented image to the pseudo-label

This enforces prediction consistency across transformations, enabling the model to learn from unlabeled data.

Loss Function¶

The total loss combines supervised and unsupervised components:

L = L_sup + L_unsup

• L_sup: Binary cross-entropy on the labeled data
• L_unsup: Consistency loss between pseudo-labels (from weak augmentation) and predictions (from strong augmentation)

Dual-model Architecture¶

AnomalyMatch maintains two copies of the network:

• Train model: Updated via backpropagation
• Eval model: Updated via exponential moving average (EMA) of the train model's weights (momentum = 0.99)

The EMA model produces more stable predictions and is used for inference and pseudo-label generation.

Active Learning Loop¶

The active learning cycle allows iterative refinement with minimal human effort:

1. Train the model on the current labeled set + unlabeled data (semi-supervised)
2. Predict anomaly scores on all unlabeled data
3. Review the top-ranked predictions in the interactive UI — verify discoveries and correct false positives
4. Retrain with the expanded labeled set
5. Repeat for 2-3 cycles

The number of labels added per cycle is entirely up to the user — the model improves with each additional label.

Results¶

Benchmark Performance¶

Starting from just 5-10 labeled anomalies and after 3 active learning cycles:

Anomaly Discovery on Galaxy Zoo¶

The figures below show AnomalyMatch scores vs Galaxy Zoo citizen science scores after 3 active learning iterations on the Galaxy Zoo dataset. Gold borders indicate true anomalies, and the rank difference (delta) shows how much AnomalyMatch's ranking differs from the crowd-sourced ranking.

High anomaly scores (top predictions) — the model identifies visually distinctive galaxies:

Low anomaly scores (bottom predictions) — the model correctly assigns low scores to common galaxy morphologies:

Key Findings¶

• 100 iterations per cycle is optimal — more iterations lead to overfitting on the small labeled set
• Performance is robust across 100-1000 initial labels with diminishing returns beyond 500
• A weighted random sampler addresses class imbalance by oversampling the minority (anomaly) class
• ImageNet-pretrained EfficientNet backbone provides strong transfer learning for both natural and astronomical images

Citing AnomalyMatch¶

If you find AnomalyMatch useful in your research, please cite:

@article{gomez2025anomalymatch,
  title={AnomalyMatch: Discovering Rare Objects of Interest with Semi-supervised and Active Learning},
  author={G{\'o}mez, Pablo and Ruhberg, Laslo E. and Nardone, Maria Teresa and O'Ryan, David},
  journal={arXiv e-prints},
  year={2025},
  month={5},
  doi={10.48550/arXiv.2505.03509},
  url={https://arxiv.org/abs/2505.03509}
}