Locally varying distance transform for unsupervised visual anomaly detection

Unsupervised anomaly detection on image data is notoriously unstable. We believe this is because many classical anomaly detectors implicitly assume data is low dimensional. However, image data is always high dimensional. Images can be projected to a low dimensional embedding but such projections rely on global transformations that truncate minor variations. As anomalies are rare, the final embedding often lacks the key variations needed to distinguish anomalies from normal instances. This paper proposes a new embedding using a set of locally varying data projections, with each projection responsible for persevering the variations that distinguish a local cluster of instances from all other instances. The locally varying embedding ensures the variations that distinguish anomalies are preserved, while simultaneously allowing the probability that an instance belongs to a cluster, to be statistically inferred from the one-dimensional, local projection associated with the cluster. Statistical agglomeration of an instance’s cluster membership probabilities, creates a global measure of its affinity to the dataset and causes anomalies to emerge, as instances whose affinity scores are surprisingly low.