Abstract: In view of the problem of “dimension disaster” in hyperspectral images, this paper proposes a Global discriminant and Local Sparse preserving Semi-supervised Feature Extraction algorithm（GLSSFE）. The algorithm exploits the divergence matrix of LDA algorithm to preserve the global intra-class discriminant information and the global inter-class discriminant information of the labeled data. It utilizes semi-supervised PCA to preserve global structure of the labeled data and the unlabeled data. It uses sparse representation optimization model to find the nonlinear structure of data adaptively. Local discriminant weight of intra-class and local discriminant weight of inter-class are embedded in semi-supervised LPP algorithm to store the local structure of data, so as to maximize the similarities of the same class objects and differences of the different class objects. In this paper, the validity of the proposed feature extraction method is verified by 1-NN and SVM classifiers. With two public hyperspectral image datasets of Indian Pines and Pavia University, the proposed feature extraction method is verified effectively. The experimental results of GLSSFE show that the highest overall classification reaches 89.10% and 92.09% respectively. It is superior to the existing feature extraction algorithm, effectively mining global features and local features of hyperspectral images, enhancing object classification effect.

Key words: hyperspectral images, semi-supervised global discriminant analysis, semi-supervised local sparse preserving, feature extraction, spatial correlation

摘要： 针对高光谱图像存在“维数灾难”的问题，提出一种全局判别与局部稀疏保持的高光谱图像半监督特征提取算法（GLSSFE）。该算法通过LDA算法的散度矩阵保存有类标样本的全局类内判别信息和全局类间判别信息，结合利用半监督PCA算法对有类标和无类标样本进行主成分分析，保存样本的全局结构；利用稀疏表示优化模型自适应揭示样本数据间的非线性结构，将局部类间判别权值和局部类内判别权值嵌入半监督LPP算法保留样本数据的局部结构，从而最大化同类样本的相似性和异类样本的差异性。通过1-NN和SVM两个分类器分别对Indian Pines和Pavia University两个公共高光谱图像数据集进行分类，验证所提特征提取方法的有效性。实验结果表明，该GLSSFE算法最高总体分类精度分别达到89.10%和92.09%，优于现有的特征提取算法，能有效地挖掘高光谱图像的全局特征和局部特征，极大地提升高光谱图像的地物分类效果。

关键词: 高光谱图像, 半监督全局判别分析, 半监督局部稀疏保持, 特征提取, 空间相关性