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Rank-Transformed Dissimilarity Profiles for High-Dimensional Classification

NeurIPS 2026 · Label-efficient and robust learning › Recognition and long-tail · approach: Learning from unlabeled and positive-unlabeled data

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Proposes a rank-transformed dissimilarity-profiling classifier that maps each observation to class-wise average ranks of squared Euclidean distances and classifies with QDA, with a distance-based surrogate analyzed theoretically.

Problem

High-dimensional low-sample-size classification, where the dominant signal (mean, scale, or other distributional differences) varies across applications and standard distance- or margin-based classifiers can fail.

Approach

Represent each observation by its class-wise profile of (rank-transformed) pairwise dissimilarities to training observations in each class, producing a k-dimensional representation that is classified with QDA; the rank transform gives robustness to outliers, and a distance-based surrogate is analyzed to show that profiles encode first, second and higher-order moment differences.

Key results

• On the Nutt glioma dataset the rank-profile method achieves 0.160 misclassification versus 0.193 for the next best (RP-Ensemble).
• On simulated two-class scenarios the method achieves the lowest or near-lowest error in most settings, e.g. S1 (mu0=6,a=1.1) 0.002 vs 0.003 for SVM.
• On network data (S8/S9 with Hamming distance) it has the lowest error in all six configurations, e.g. S8 a=4 0.326 vs 0.354 for gMADD.

Surprising findings

• The distance-based (non-rank) surrogate fails badly under outlier contamination (e.g. 0.325 vs 0.035 with 3 outliers in S12), while the rank version stays robust.
• The method is not uniformly best: on the Shipp dataset GLDA and MLP are as good or better, and gMADD wins in some heavy-tailed variance settings.

Limitations

• Gains are concentrated in simulations designed around the proposed setting; on real data the method is competitive but not uniformly best.
• Theory relies on a distance-based surrogate with banded structure conditions rather than the rank-transformed method itself.
• Multi-class and network comparisons omit several baselines (e.g., RP-Ensemble), limiting comparability.

Experimental setup

Datasets: Shipp et al. DLBCL gene expression Nutt et al. glioma gene expression simulated Gaussian/t5/chi-square two-class and four-class data simulated configuration-model random graphs

Benchmarks: Shipp DLBCL Nutt glioma simulated two-class scenarios S1-S4 simulated four-class scenarios S5-S7 simulated network scenarios S8-S9

Metrics: misclassification rate

Baselines: GLDA SVM random forests glmnet LightGBM MLP gMADD RP-Ensemble

Builds on: quadratic discriminant analysis gMADD RP-Ensemble

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