AI 中文总结
本文针对高光谱图像分类的难点，提出LegoQ密度矩阵表示学习框架，通过谱-空间状态转移实现分类，在两个公开数据集上取得优于传统方法的分类性能。
AI 中文摘要
高光谱图像分类受混合像元、光谱歧义、类别不平衡及标注有限等因素影响，难度较大。当前多数分类器将单个像元或图像块编码为确定性向量，再应用线性或多层softmax分类头，虽具备判别能力，但该表示无法直接反映样本的混合程度或不确定性。本文提出LegoQ，一种用于高光谱图像的经典密度矩阵表示学习框架：将光谱波段划分为多个组，每组映射为半正定、厄米且迹归一化的矩阵状态；由光谱、空间及组间转移构成的可组合栈更新状态，同时反复将其投影回有效状态集。LegoQ不展平最终特征，而是聚合各组状态，通过Uhlmann保真度与可学习的类别原型密度矩阵进行比较；归一化本征谱、冯·诺依曼熵、纯度及原型保真度可提供传统向量分类头无法实现的样本级诊断。在Indian Pines数据集上，10次运行的总体精度为96.20±0.70%，平均精度为95.57±1.29%，卡帕系数为95.66±0.80%；在WHU-Hi-LongKou数据集上，10次运行的最佳结果达到97.52%的总体精度。分类图与特征投影表明，转移栈可生成更紧凑、分离度更高的类别结构，结果验证了约束矩阵状态学习可作为仅基于向量的高光谱分类的实用替代方案，无需量子硬件支持。
英文摘要
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.
