稀疏流形聚类和嵌入算法通过仿射空间中的稀疏表示获得稀疏系数, 并能由稀疏系数自适应地选取来自同一流形的数据点.但稀疏流形聚类和嵌入算法没有直接的投影矩阵, 且为非监督学习方法.针对稀疏流形聚类和嵌入算法算法的不足, 提出一种新的监督稀疏流形嵌入算法.该方法首先在仿射空间中采用稀疏优化法得到稀疏系数, 然后根据稀疏系数构建相似权值, 并在权值中嵌入样本类别信息, 增加同类数据间的聚集性, 并在低维嵌入空间中保持这种相似性不变, 提取鉴别特征来提升分类性能.实验结果表明: 该文方法不仅能保持数据的稀疏特性, 而且通过利用样本数据的类别信息使同类数据在低维空间尽可能聚集, 提取鉴别特征, 进而改善高光谱影像的地物分类效果.

Sparse Manifold Clustering and Embedding (SMCE) can adaptively select nearby points that lie in the same manifold based on sparse representation. However, there is no explicit project matrix in SMCE, and the unsupervised nature restricts its discriminating capability. Supervised Sparse Manifold Embedding (SSME) was proposed for dimensionality reduction of hyperspectral data. At first, the SSME method finds the sparse coefficients in affine subspace by solving a sparse optimization problem. It constructs the similarity weight matrix using the sparse coefficients, and naturally incorporates the label information into the weights. Then, it tries to extract discriminative features by increasing the compactness between homogeneous data in a low-dimensional embedding space. The experiments show that the SSME method not only inherits the merits of the sparsity property but also improves the severability of data points from different classes.