Leakage-free evaluation of task-aware Nyström sampling for IoMT intrusion detection

Standard Nyström kernel approximation samples landmark points uniformly at random, ignoring that boundary-adjacent and minority-class samples often matter most for imbalanced intrusion detection. We propose a task-aware, importance-weighted Nyström landmark-selection mechanism that scores each training sample's classifier uncertainty, boundary distance, representativeness, and minority-class importance, with an optional quantum-amplitude reparameterization (QI-AWNS) shown to be algebraically equivalent to direct score-proportional sampling; the contribution is the importance scoring and its rigorous evaluation, not the amplitude framing or a quantum advantage. We benchmark QI-AWNS against uniform, K-means, and approximate ridge-leverage-score Nyström sampling, five tabular baselines, and a full-kernel RBF-SVM on two leakage-free IoMT benchmarks (ECU-IoHT, WUSTL-EHMS-2020) under a strict split-before-fit protocol, with each test partition evaluated once. Across 10 reseeded splits, per-split retuning of the importance weights improves QI-AWNS's stability relative to a frozen-weight configuration and yields a mean balanced-accuracy gain of 0.18 points over uniform sampling on ECU-IoHT. This is not significant after Holm correction for multiple comparisons (raw Wilcoxon p = 0.022, adjusted p = 0.129), and no advantage appears over K-means or approximate ridge-leverage-score sampling on either dataset. An 8-variant ablation and weight-search analysis shows that a validation-based ranking of two weight candidates reverses on WUSTL-EHMS-2020's test set. These findings show that task-aware landmark weighting offers limited, dataset-dependent benefit, and that single-split conclusions can overstate it.