CCMP: Class-Conditional Multicollinearity Pruning for High-Dimensional Feature Selection

Abstract

In high-dimensional scientific measurements, many features in a single sample often capture the same underlying physical attributes, producing severe multicollinearity. Supervised feature selectors fit on the entire dataset, so a feature can be informative for classification overall while still redundant with another feature in the same class. Class-conditional selectors, by contrast, trade some accuracy for a narrower, per-class view, since they never see data outside one class, but this lets new classes be added without refitting the whole model. They still cannot determine, however, which feature to drop from a correlated group. To close this gap, we propose classconditional multicollinearity pruning (CCMP), which iteratively prunes one feature from every highly correlated pair, per class. Four theoretical guarantees establish explicit bounds on the error induced by pruning under stated assumptions. Across four benchmark datasets spanning spectroscopic and hyperspectral imaging modalities, CCMP retains as few as 42 of 1531 features (3%) and as many as 60 of 145 (41%), outperforms every classconditional baseline, and remains competitive with supervised methods.