Rank-Transformed Dissimilarity Profiles for High-Dimensional Classification

Abstract

Despite advances in representation learning, high-dimensional classification remains challenging in low-sample-size regimes, where the dominant signal may vary across applications and labeled data are often limited. We propose a dissimilarity-profiling classification framework that represents each observation by its class-wise dissimilarity profile, transforming the original feature space into a low-dimensional representation that summarizes how the observation relates to each class. The key idea is to turn a consequence of the curse of dimensionality into signal: high-dimensional geometry can induce systematic within-class and between-class dissimilarity patterns under location, scale, or other distributional changes, and these patterns are captured by the class-wise profiles. Building on this representation, we introduce a rank-transformed algorithm that converts dissimilarities into class-wise rank profiles, yielding a compact representation for classification. The proposed method delivers competitive or improved performance relative to commonly used classifiers on two-class, multi-class, network, and real high-dimensional low-sample-size datasets. To provide insight into the mechanism underlying the method, we analyze a distance-based surrogate and show that the resulting profiles encode differences in first, second, and higher-order moments, while the rank transformation improves robustness to outliers. Together, these results show that rank-transformed dissimilarity profiles provide an adaptive representation for high-dimensional classification when the signal structure is unknown.