CoMadOut -- A Robust Outlier Detection Algorithm based on CoMAD

TL;DR

CoMadOut introduces a robust, unsupervised outlier detection framework based on coMAD-PCA (comedian PCA), enabling robust subspace orientations via the comedian matrix $COM(X)$ and robust inlier margins. It presents a baseline CMO and extended CMO* variants (e.g., CMO+, CMO+k, CMO+e, CMO+ke) that score outliers by per-axis distances, optionally weighting by distribution tail features like kurtosis, and an ensemble (CMOEns) to combine multiple scores. The approach yields competitive AP, AUROC, AUPRC, and Precision@N across 21 real-world datasets against 26 baselines, highlighting robustness benefits especially in high-dimensional or noisy contexts; but it incurs higher runtimes and memory usage, motivating future work on scalability and adaptive component selection. Overall, CoMadOut offers a principled, distribution-aware alternative to existing PCA-based and deep anomaly detectors, with practical potential for robust outlier detection in diverse domains.

Abstract

Unsupervised learning methods are well established in the area of anomaly detection and achieve state of the art performances on outlier datasets. Outliers play a significant role, since they bear the potential to distort the predictions of a machine learning algorithm on a given dataset. Especially among PCA-based methods, outliers have an additional destructive potential regarding the result: they may not only distort the orientation and translation of the principal components, they also make it more complicated to detect outliers. To address this problem, we propose the robust outlier detection algorithm CoMadOut, which satisfies two required properties: (1) being robust towards outliers and (2) detecting them. Our CoMadOut outlier detection variants using comedian PCA define, dependent on its variant, an inlier region with a robust noise margin by measures of in-distribution (variant CMO) and optimized scores by measures of out-of-distribution (variants CMO*), e.g. kurtosis-weighting by CMO+k. These measures allow distribution based outlier scoring for each principal component, and thus, an appropriate alignment of the degree of outlierness between normal and abnormal instances. Experiments comparing CoMadOut with traditional, deep and other comparable robust outlier detection methods showed that the performance of the introduced CoMadOut approach is competitive to well established methods related to average precision (AP), area under the precision recall curve (AUPRC) and area under the receiver operating characteristic (AUROC) curve. In summary our approach can be seen as a robust alternative for outlier detection tasks.

Figures (22)

• Figure 1: Overview of CoMadOut (CMO*) variants in bold and their steps.
• Figure 2: Illustration of orientation and scale of principal components after applying coMAD-PCA (a) and standard PCA (b) to a synthetic dataset. It can be observed that the outlier (colored in red) has less influence to eigenvectors and eigenvalues of coMAD-PCA on the left than to those of standard PCA on the right.
• Figure 3: CoMadOut scoring and labeling of CMO baseline on synthetic data.
• Figure 4: Outlier score boundaries of competitor PCA-MADHuang2021ARA.
• Figure 5: Outlier score boundaries of CoMadOut variants CMO+, CMO+k, CMO+e, CMO+ke on a synthetic dataset (from left to right).