Comparison of supervised and unsupervised anomaly detection in Belle II pixel detector data

Machine learning has become a popular instrument for the search of undiscovered particles and mechanisms at particle collider experiments. It enables the investigation of large datasets and is therefore suitable to operate directly on minimally-processed data coming from the detector instead of reconstructed objects. Here, we study patterns of raw pixel hits recorded by the Belle II pixel detector, that is operational since 2019 and presently features 4 M pixels and trigger rates up to 5 kHz. In particular, we focus on unsupervised techniques that operate without the need for a theoretical model. These model-agnostic approaches allow for an unbiased exploration of data while filtering out anomalous detector signatures that could hint at new physics scenarios. We present the identification of hypothetical magnetic monopoles against Belle II beam background using self-organizing kohonen maps and autoencoders. These two unsupervised algorithms are compared to a Multilayer Perceptron and a superior signal efficiency of the Autoencoder is found at high background-rejection levels. Our results strengthen the case for using unsupervised machine learning techniques to complement traditional search strategies at particle colliders and pave the way to potential online applications of the algorithms in the near future.

💡 Research Summary

The paper investigates the use of machine‑learning‑based anomaly detection directly on raw pixel‑hit data from the Belle II pixel detector (PXD), comparing unsupervised methods with a conventional supervised classifier. The PXD, equipped with DEPFET sensors, contains roughly four million pixels and operates at trigger rates up to 5 kHz, generating data streams of order 20 GB s⁻¹. Because the existing online reduction system (ONSEN) relies on reconstructed tracks to define regions of interest, particles that do not leave reconstructable tracks—such as low‑pₜ particles or highly ionising exotic objects—are discarded. The authors therefore explore whether a data‑driven veto, based on anomaly detection, can rescue such events.

Two unsupervised algorithms are studied: a Self‑Organizing Map (SOM) and an Autoencoder (AE). Both are trained on beam‑background data recorded during single‑beam runs in 2020, which represent the dominant noise source in the inner detector. As a benchmark signal, the authors simulate long‑lived magnetic monopoles (mass 3 GeV, Dirac charge 68.5 e) produced in e⁺e⁻ collisions. Monopoles are expected to stop in the inner layers, producing large charge deposits in a compact 9 × 9 pixel cluster while leaving no hits in outer sub‑detectors, thus mimicking the situation where ONSEN would drop the data.

For each event, the charge values of a 9 × 9 pixel window centred on the highest‑charge pixel (the seed) are extracted, together with the seed’s global coordinates, yielding 84 normalized features per matrix. The supervised baseline is a multilayer perceptron (MLP) with two hidden layers (≈15 k trainable parameters) trained on an equal mixture of 350 k background and 350 k signal events. The SOM uses a one‑dimensional lattice of 100 nodes with a Gaussian neighbourhood and a learning rate of 0.03, resulting in ≈8 k trainable parameters. The AE consists of an encoder‑decoder architecture with ReLU activations, mean‑squared‑error loss, and ≈13 k trainable parameters; it is trained exclusively on background, minimizing reconstruction error.

Performance is evaluated via receiver‑operating‑characteristic (ROC) curves, area‑under‑curve (AUC), and signal efficiencies at fixed background‑rejection levels of 10⁻², 10⁻³, and 10⁻⁴. The MLP achieves the highest overall AUC (99.69 % ± 0.01 %) but its signal efficiency drops to 39.5 % ± 3.6 % at the stringent 10⁻⁴ background‑rejection point. The SOM’s AUC is about 3 % lower than the MLP, with a comparable signal efficiency (~30 %) at the same rejection. The AE’s AUC is only ~1 % below the MLP, yet it retains a signal efficiency of 60.1 % ± 3.3 % at 10⁻⁴ background rejection, clearly outperforming the other two methods when a high purity is required. The authors attribute this advantage to the AE’s ability to learn a compact latent representation of the background, causing anomalous monopole clusters to yield large reconstruction errors.

Robustness checks—varying hyper‑parameters, swapping signal or background samples, and repeating training with different random seeds—show that the AE’s performance is stable. This stability, together with the modest computational footprint, suggests that the AE could be implemented on FPGA‑based online hardware for real‑time vetoing of anomalous clusters. Beyond physics searches, the authors propose that such anomaly detection could serve detector‑health monitoring, flagging beam instabilities or malfunctioning sensor regions.

In summary, the study demonstrates that unsupervised learning, particularly autoencoding, can match or surpass supervised classifiers in the context of rare‑signal, high‑background environments typical of modern collider experiments. The results provide a concrete pathway toward integrating model‑agnostic anomaly detection into the Belle II data‑acquisition chain, enhancing sensitivity to exotic phenomena while also offering ancillary benefits for detector operation and data quality assurance.