Set Features for Anomaly Detection

TL;DR

The paper tackles anomaly detection where anomalies arise from unusual combinations of normal elements rather than anomalous components alone. It introduces SINBAD, a fixed-feature, density-estimation framework that treats each sample as an unordered set of element features and describes the set with histograms of random projections, followed by Mahalanobis (or kNN) density scoring. The approach yields state-of-the-art results on logical anomaly detection and competitive results on time-series anomaly detection across diverse datasets, while remaining simple and augmentation-free. By linking set descriptors to Wasserstein-based distances and leveraging multi-granularity representations in images and time series, the work presents a robust, modality-agnostic method for detecting complex inter-element anomalies with practical impact in industrial and sequential data settings.

Abstract

This paper proposes to use set features for detecting anomalies in samples that consist of unusual combinations of normal elements. Many leading methods discover anomalies by detecting an unusual part of a sample. For example, state-of-the-art segmentation-based approaches, first classify each element of the sample (e.g., image patch) as normal or anomalous and then classify the entire sample as anomalous if it contains anomalous elements. However, such approaches do not extend well to scenarios where the anomalies are expressed by an unusual combination of normal elements. In this paper, we overcome this limitation by proposing set features that model each sample by the distribution of its elements. We compute the anomaly score of each sample using a simple density estimation method, using fixed features. Our approach outperforms the previous state-of-the-art in image-level logical anomaly detection and sequence-level time series anomaly detection.

Figures (4)

• Figure 1: In set anomalies, each image element (e.g., patch) may be normal even when their combination is anomalous. This is challenging as the variation in the normal data may be higher than between normal and anomalous elements (e.g., swapping a bolt and a washer in the screw bag class).
• Figure 2: Random projection histograms allow us to distinguish between sets where other methods could not. The two sets are similar in their averages and histograms along the original axes, but result in different histograms when projected along a random axis.
• Figure 3: For both image and time series samples, we extract set elements at different granularity. For images (left), the sets of elements are extracted from different ResNet levels. For time series (right), we take pyramids of windows at different strides around each time step.
• Figure 4: Ablation of accuracy vs. the number of projections (left) and the number of bins (right) for different time series datasets.