arXiv:2607.28970cs.CV2026-07

用矩阵表示高光谱像素,让模型自动生成不确定性诊断。

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

论文配图:LegoQ: Density-Matrix Representation Learning with Spectral-Spatial State Transitions for Hyperspectral Classification
图 1 · 摘自论文原文
  • 将光谱分组并转为密度矩阵,通过谱空间变换更新状态
  • 在印第安纳波利斯数据集上达96.20%准确率,比传统方法更稳定
  • 可输出熵、纯度等诊断信息,适合需要可靠性评估的场景

高光谱图像分类受混合像元、光谱模糊、类别不平衡和标注有限等问题困扰。现有分类器通常将像素或块编码为确定性向量,并使用线性或多层Softmax头,虽有效但无法直接反映样本的混合程度或不确定性。本文提出 extmethod,一种基于密度矩阵的表征学习框架。将光谱波段分组,每组映射为正半定、厄米、迹归一化的矩阵状态,通过可组合的谱-空-组间转移栈更新状态,并反复投影回合法状态集。不采用展平最终特征,而是聚合组状态,通过乌尔曼保真度与可学习的类原型密度矩阵比较。归一化特征谱、冯诺依曼熵、纯度及原型保真度提供传统向量头无法获得的样本级诊断信息。在印度棕榈数据集上,十次运行整体精度达$96.20\pm0.70\%$,平均精度$95.57\pm1.29\%$,kappa系数$95.66\pm0.80\%$;在WHU-Hi-LongKou数据集上最佳结果达$97.52\%$整体精度。分类图与特征投影显示,转移栈生成了紧凑且分离更好的类别结构。结果支持约束矩阵态学习作为无需量子硬件的向量式分类实用替代方案。

原文摘要 · Abstract (English)

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.

高光谱分类密度矩阵不确定性建模

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