Hyperbolic Prototype Learning for Open-Set Joint HSI–LiDAR Classification

Abstract

Joint classification of hyperspectral and light detection and ranging (LiDAR) data in open-set scenarios is difficult, requiring models to classify known classes while rejecting unknowns. Existing reconstruction-based methods operate in Euclidean space and rely solely on reconstruction error, ignoring latent space geometry and cross-modal consistency. We propose a hyperbolic-physics-enhanced framework with two mechanisms: latent representations are projected onto a Poincaré ball, where known classes cluster near the origin and unknowns are pushed to the boundary; and a counterfactual modal mismatch detector flags implausible spectral-elevation combinations as potential unknowns. A multiscore fusion strategy combines reconstruction error, hyperbolic boundary distance, and modal consistency into a unified decision rule. Experiments on MUUFL and Houston datasets show state-of-the-art unknown detection while preserving known-class accuracy. The code is available at github.com/amir-khb/HPLOSR/