提出自适应多阶图正则化方法，提升高光谱解混精度与鲁棒性。
Adaptive Multi-Order Graph Regularized NMF with Dual Sparsity for Hyperspectral Unmixing
- 引入多阶图正则化，融合全局与局部信息增强数据结构建模
- 自适应学习图参数，避免人工调参，提升模型泛化能力
- 嵌入双稀疏约束，有效抑制噪声，适合真实场景高光谱数据
高光谱解混是遥感中的关键挑战。现有非负矩阵分解（NMF）方法多关注一阶或二阶邻近关系，常需人工调参，难以刻画数据内在结构。为此，本文提出一种新型自适应多阶图正则化NMF方法（MOGNMF），具有三大特点：首先，在NMF框架中引入多阶图正则化，全面利用全局与局部信息；其次，通过数据驱动方式自适应学习多阶图相关参数；第三，嵌入双稀疏约束，即丰度矩阵采用ℓ₁/₂-范数，噪声矩阵采用ℓ₂,₁-范数，以提升鲁棒性。为求解该模型，设计了具有显式解的交替最小化算法，保证有效性。在模拟与真实高光谱数据上的实验表明，该方法解混效果更优。
原文摘要 · Abstract (English)
Hyperspectral unmixing (HU) is a critical yet challenging task in remote sensing. However, existing nonnegative matrix factorization (NMF) methods with graph learning mostly focus on first-order or second-order nearest neighbor relationships and usually require manual parameter tuning, which fails to characterize intrinsic data structures. To address the above issues, we propose a novel adaptive multi-order graph regularized NMF method (MOGNMF) with three key features. First, multi-order graph regularization is introduced into the NMF framework to exploit global and local information comprehensively. Second, these parameters associated with the multi-order graph are learned adaptively through a data-driven approach. Third, dual sparsity is embedded to obtain better robustness, i.e., $\ell_{1/2}$-norm on the abundance matrix and $\ell_{2,1}$-norm on the noise matrix. To solve the proposed model, we develop an alternating minimization algorithm whose subproblems have explicit solutions, thus ensuring effectiveness. Experiments on simulated and real hyperspectral data indicate that the proposed method delivers better unmixing results.
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