Pseudo-Boolean polynomial anomaly scoring for intelligent multisensor environmental monitoring

Abstract

Air quality sensor networks need anomaly detection that works from day one—without training data, without historical baselines, and with results an operator can actually interpret. Existing methods (Isolation Forest, One-Class SVM, LOF) require representative “normal” data for training, which makes them brittle when environmental conditions shift across seasons. We propose a training-free anomaly scoring method based on pseudo-Boolean polynomial (PBP) reduction with multi-threshold binarization. Sensor windows are converted to binary exceedance matrices at quantile thresholds (Q25– Q95); PBP coefficient features then serve as interpretable anomaly indicators. Two variants are introduced: full-window PBP applied to the w × s sensor matrix, and sensor-pair PBP applied to w × 2 sub-matrices isolating pairwise sensor interactions. On the UCI Air Quality dataset (6,941 readings, 8 sensor channels), sensor-pair PBP achieves AUC 0.881— exceeding One-Class SVM (0.877) and LOF (0.870)—with no training data at all. The real test is temporal robustness: under a strict chronological split (thresholds from the first half, evaluation on the second), PBP maintains AUC 0.865 while LOF collapses to 0.708 and OC-SVM drops to 0.833.