Stable Dimensionality Reduction via Isometric Centroid-Encoder

Tomojit Ghosh, Siva Rama Krishna Prasad Changala, Prathyusha Kanakamalla, Harigovind Harikumar

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…