LegoQ: Density-Matrix Representation Learning with Spectral-Spatial State Transitions for Hyperspectral Classification

2026-07-30

AI Summary

This study addresses key challenges in hyperspectral image classification—such as mixed pixels, spectral ambiguity, class imbalance, and scarce annotations—by introducing density matrices to model spectral data. Unlike conventional vector representations that fail to capture sample uncertainty and mixture characteristics, the proposed method maps grouped spectral bands into physically constrained quantum states. It iteratively refines these states through a composable spectral-spatial-intergroup state transition module and performs classification by comparing states with learnable class prototypes via Uhlmann fidelity. The framework enables sample-level uncertainty quantification (e.g., von Neumann entropy and purity) and achieves quantum-inspired modeling without requiring quantum hardware. Evaluated on the Indian Pines and WHU-Hi-LongKou datasets, it attains overall accuracies of 96.20±0.70% and 97.52%, respectively, yielding more compact intra-class distributions and enhanced inter-class separability.

Abstract

Hyperspectral image classification is complicated by mixed pixels, spectral ambiguity, class imbalance, and limited annotations. Most current classifiers encode a pixel or patch as a deterministic vector and apply a linear or multilayer softmax head. Although effective for discrimination, this representation does not directly expose how mixed or uncertain a sample is. This paper presents \method, a classical density-matrix representation learning framework for hyperspectral images. The spectral bands are divided into groups and each group is mapped to a positive semi-definite, Hermitian, trace-normalized matrix state. A composable stack of spectral, spatial, and inter-group transitions then updates the states while repeatedly projecting them back to the valid state set. Instead of flattening the final features, \method\ aggregates the group states and compares them with learnable class-prototype density matrices through Uhlmann fidelity. The normalized eigenspectrum, von Neumann entropy, purity, and prototype fidelity provide sample-level diagnostics that are unavailable from a conventional vector head. On Indian Pines, ten runs yield an overall accuracy of $96.20\pm0.70\%$, an average accuracy of $95.57\pm1.29\%$, and a kappa coefficient of $95.66\pm0.80\%$. On WHU-Hi-LongKou, the best of ten runs reaches $97.52\%$ overall accuracy. Classification maps and feature projections show that the transition stack produces compact and better separated class structures. The results support constrained matrix-state learning as a practical alternative to vector-only hyperspectral classification without requiring quantum hardware.

Problem

• hyperspectral classification
• mixed pixels
• spectral ambiguity
• class imbalance
• limited annotations

Innovation

• density-matrix representation
• spectral-spatial state transitions
• Uhlmann fidelity
• von Neumann entropy
• hyperspectral classification