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\%).

Spotting unusual records - fraudulent transactions, faulty sensors, suspicious medical results - is one of the oldest problems in data science, but it remains surprisingly hard for everyday tabular data (the kind you'd find in a spreadsheet). Existing methods usually require careful, dataset-specific tuning to work well, which is awkward because the very thing we are looking for - the anomalies - is what we don't have labels for. Worse, no single method handles all the different "shapes" anomalies can take: some stick out from their neighbors, some lie in empty regions, some form their own small groups, and some only look wrong when you consider several attributes together. We developed DVM-AD, a method that learns a single data-viewpoint in which normal records cluster tightly while preserving the data's natural structure. It does this with a closed-form mathematical recipe - no trial-and-error tuning and no neural-network training. Across 47 standard benchmarks, DVM-AD outperforms dozens of competing methods on average, while being fast to train and easier to deploy. This makes reliable anomaly detection more accessible in settings where practitioners cannot afford to hand-tune a model for every new dataset.