Cluster-Based Dimensionality Reduction by Nonparametric Distributional Screening

• URL: http://arxiv.org/abs/2609.06854v1
• Date: Sun, 06 Sep 2026 21:58:59 GMT
• Title: Cluster-Based Dimensionality Reduction by Nonparametric Distributional Screening
• Abstract summary: We consider dimensionality reduction for high-dimensional observations accompanied by a supplied partition into two or more clusters.<n>The proposed procedure compares the cluster-specific empirical distribution functions through a several-sample Kolmogorov-Smirnov separation statistic.<n>We formalize the resulting marginal cluster support and establish simultaneous finite-sample concentration over all coordinates.
• Score: 1.4773309126683776
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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