aiqbench analysis
This paper proposes a supervised dimensionality reduction method that learns class centroids in the latent space while constraining their pairwise geometry, aiming to make embeddings more reproducible across training runs. It also introduces the Centroid Neighborhood Stability metric for measuring run-to-run consistency. For ML practitioners, the useful questions are whether the gains hold beyond the reported image and biological datasets and how much the explicit geometry constraint costs in practice.
Stable Dimensionality Reduction via Isometric Centroid-Encoder
arXiv:2610.33872v1 Announce Type: new Abstract: Many supervised dimensionality reduction methods promote intra-class compactness and inter-class separation but do not explicitly constrain class geometry, leading to variability in the relative arrangement of classes across independent runs. Such variability limits the reproducibility and interpretability of low-dimensional embeddings. We propose the Isometric Centroid-Encoder (ICE), a supervised dimensionality reduction framework in which class centroids are learned directly in the latent space while preserving a prescribed pairwise class-centroid geometry. Unlike existing centroid- or prototype-based methods that primarily encourage intra-class compactness, ICE explicitly regularizes the relative arrangement of latent class centroids. Unlike multidimensional scaling and many metric-learning approaches that preserve sample-level relationships, ICE operates on class centroids, preserving inter-class geometry without requiring large numbers of sample-pair or triplet constraints. We further show that the intrinsic dimensionality required to represent the centroid-distance configuration of $M$ classes is at most $M-1$, explaining the observed saturation of distance-preservation measures as the latent dimensionality increases. To quantify embedding reproducibility, we introduce the Centroid Neighborhood Stability (CNS) metric, which measures the consistency of class-level neighborhood topology across independent runs and complements existing embedding quality measures. Experiments on image and biological datasets demonstrate that ICE produces stable embeddings with improved preservation of class-centroid geometry while remaining computationally efficient. Additional analyses of optimization dynamics, sensitivity, and preprocessing further provide practical insights into latent dimensionality and explicit geometry modeling for supervised dimensionality reduction.
Abstract:Many supervised dimensionality reduction methods promote intra-class compactness and inter-class separation but do not explicitly constrain class geometry, leading to variability in the relative arrangement of classes across independent runs. Such variability limits the reproducibility and interpretability of low-dimensional embeddings. We propose the Isometric Centroid-Encoder (ICE), a supervised dimensionality reduction framework in which class centroids are learned directly in the latent space while preserving a prescribed pairwise class-centroid geometry. Unlike existing centroid- or prototype-based methods that primarily encourage intra-class compactness, ICE explicitly regularizes the relative arrangement of latent class centroids. Unlike multidimensional scaling and many metric-learning approaches that preserve sample-level relationships, ICE operates on class centroids, preserving inter-class geometry without requiring large numbers of sample-pair or triplet constraints. We further show that the intrinsic dimensionality required to represent the centroid-distance configuration of $M$ classes is at most $M-1$, explaining the observed saturation of distance-preservation measures as the latent dimensionality increases. To quantify embedding reproducibility, we introduce the Centroid Neighborhood Stability (CNS) metric, which measures the consistency of class-level neighborhood topology across independent runs and complements existing embedding quality measures. Experiments on image and biological datasets demonstrate that ICE produces stable embeddings with improved preservation of class-centroid geometry while remaining computationally efficient. Additional analyses of optimization dynamics, sensitivity, and preprocessing further provide practical insights into latent dimensionality and explicit geometry modeling for supervised dimensionality reduction.
Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV)
arXiv:2610.33872 [cs.LG]
(or arXiv:2610.33872v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.33872 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 324 words