Cluster-Based Dimensionality Reduction by Nonparametric Distributional Screening
Abstract
We consider dimensionality reduction for high-dimensional observations accompanied by a supplied partition into two or more clusters. The objective is not to construct a low-rank projection, but to retain an interpretable subset of the original coordinates that preserves the distributional information distinguishing the clusters. For each coordinate, the proposed procedure compares the cluster-specific empirical distribution functions through a several-sample Kolmogorov-Smirnov separation statistic. We formalize the resulting marginal cluster support and establish simultaneous finite-sample concentration over all coordinates, explicit bounds for false inclusions and omissions, and exact support recovery when the minimum distributional separation dominates the high-dimensional stochastic error. We also quantify the dimension inflation induced by using an unadjusted testing level and give a familywise-error-controlled version. Under a conditional sufficiency condition, sure screening preserves the full-data posterior cluster probabilities, mutual information, and Bayes risk; an additional result characterizes robustness to imperfectly estimated cluster labels. The procedure is invariant to strictly increasing coordinate transformations and can retain low-variance cluster signals that principal components may discard. We further develop average dual information, a criterion combining partition agreement after transformation with structural coverage of cluster-relevant coordinates, and derive its basic properties and consistency. Simulations illustrate the theory, the interpretability of the selected coordinates, and the distinction between cluster-directed screening and variance-directed projection.
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BibTeX
@misc{jha2026clusterbased,
title = {{Cluster-Based Dimensionality Reduction by Nonparametric Distributional Screening}},
author = {Sanoja Jha and Rishikesh Muralimohan and Praveen Athauda Arachchi and Abhishek Bhattacharjee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06854},
eprint = {2609.06854},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06854},
}
RIS
TY - UNPB
TI - Cluster-Based Dimensionality Reduction by Nonparametric Distributional Screening
AU - Sanoja Jha
AU - Rishikesh Muralimohan
AU - Praveen Athauda Arachchi
AU - Abhishek Bhattacharjee
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06854
UR - https://arxiv.org/abs/2609.06854
AB - We consider dimensionality reduction for high-dimensional observations accompanied by a supplied partition into two or more clusters. The objective is not to construct a low-rank projection, but to retain an interpretable subset of the original coordinates that preserves the distributional information distinguishing the clusters. For each coordinate, the proposed procedure compares the cluster-specific empirical distribution functions through a several-sample Kolmogorov-Smirnov separation statistic. We formalize the resulting marginal cluster support and establish simultaneous finite-sample concentration over all coordinates, explicit bounds for false inclusions and omissions, and exact support recovery when the minimum distributional separation dominates the high-dimensional stochastic error. We also quantify the dimension inflation induced by using an unadjusted testing level and give a familywise-error-controlled version. Under a conditional sufficiency condition, sure screening preserves the full-data posterior cluster probabilities, mutual information, and Bayes risk; an additional result characterizes robustness to imperfectly estimated cluster labels. The procedure is invariant to strictly increasing coordinate transformations and can retain low-variance cluster signals that principal components may discard. We further develop average dual information, a criterion combining partition agreement after transformation with structural coverage of cluster-relevant coordinates, and derive its basic properties and consistency. Simulations illustrate the theory, the interpretability of the selected coordinates, and the distinction between cluster-directed screening and variance-directed projection.
ER -