Tuning-Free One-Class Discriminant Learning for Tabular Anomaly Detection

Anomaly detection (AD) on real-world tabular data is challenged by diverse anomaly types, scarce labels, and high sensitivity to data-specific hyperparameter tuning. A central difficulty is that different anomaly types favor opposing representations: compactness - tightening the normal class to expose pointwise deviations - and structure preservation - retaining cluster and cross-feature relationships. Existing one-class detectors capture only one of these or balance them via hyperparameters, which is problematic without validation labels. We propose Discriminant Vector Machine for Anomaly Detection (DVM-AD) , a closed-form one-class method derived from discriminant analysis that captures both behaviors under a single fixed configuration. From a deterministic reference point built from the training data, DVM-AD derives a bounded ratio whose two ends correspond to compressive and structure-preserving directions. This bound enables selecting directions from both ends simultaneously without dataset-specific tuning. In addition, a Moore-Penrose pseudo-inverse keeps the method well-posed under high-dimensional or rank-deficient settings, and test samples are scored by nearest-neighbor distance in the discriminant space, normalized for thresholding-ready use. Across 47 ADBench tabular datasets and 10 NLP/CV embedding benchmarks against 28 baselines, DVM-AD achieves the best average AUROC (89.65%, average rank 2.98) on tabular datasets and remains top-ranked across four anomaly types and on embedding tasks (average rank 1.60, AUROC 72.68%).