A Systematic Interaction Analysis of Distance Measures and Feature Representations in Mammography

Abstract

Distance-based classifiers such as k -nearest neighbors remain widely used in mammographic computer-aided diagnosis and image retrieval, yet distance measure selection is rarely evaluated systematically. This paper investigates how the interaction between feature representation and distance formulation shapes mammographic lesion classification, evaluating 20 distance measures across 13 feature sets (handcrafted, deep, hybrid), three datasets (MIAS, CBIS-DDSM, INbreast), and two classifiers ( k -NN, nearest mean-distance), spanning 13,260 configurations under 5-fold cross-validation. Five findings emerge. First, distance choice significantly affects performance (Friedman χ²=1901 , p≈0 ; best–worst AUC gap = 0.079). Second, the optimal measure depends on feature type: handcrafted features favor Learned Mahalanobis, deep features favor Adaptive Weighted Euclidean, and hybrid features favor the proposed CCFCD (AUC = 0.712). Third, measure rankings are dataset-specific (cross-dataset ρ as low as −0.10). Fourth, k -NN and NMD agree at the configuration level ( ρ=0.94 ) but not at the measure level ( ρ=0.077 ). Fifth, increasing k improves AUC while reducing sensitivity from 0.40 to 0.14; 11.6% of configurations achieve accuracy above 80% with sensitivity below 10%, showing that AUC and accuracy alone are insufficient for clinical assessment. A computational complexity analysis shows that per-pair costs range from O(d) for most measures to O(d²) for Mahalanobis, with the top-performing adaptive measures remaining tractable. These findings demonstrate that distance-based mammographic classification is governed by a coupled interaction among feature type, distance formulation, classifier, neighborhood size, and evaluation metric. Adaptive and class-aware measures consistently outperform conventional defaults when matched to the feature space.