稀疏保持投影(SPP)是一种基于l1图的新型降维算法, 它利用样本间的稀疏重构关系建图, 但是SPP为非监督算法, 分类效果受到限制。针对此问题, 本文提出了一种新的稀疏流形学习算法-稀疏鉴别嵌入(SDE)。该算法在利用样本的稀疏重构关系建图时引入了样本的类别信息, 并通过优化目标函数来得到投影矩阵, 使得不同类的数据点在低维嵌入空间中尽可能地分散开。SDE通过结合数据稀疏性及类间流形结构的优点, 不仅保留样本间的稀疏重构关系, 而且通过引入训练样本的类别信息实现稀疏鉴别特征提取, 更有利于分类。在Urban和Washington DC Mall数据集上的实验结果表明：SDE算法比其他算法的分类性能有明显的提升, 在每类随机选取16个训练样本的情况下, SDE算法的分类精度分别达到了73.47%和98.35%。

Sparsity Preserving Projection(SPP) is a new algorithm for reducing dimensions of dataset based on a weighted graph( l1-Graph), which reconstructs the weighted graph by the sparse relationship of train samples. However, SPP is an unsupervised learning method essentially, and it doesn’t employ any prior knowledge of class to extract identification features. For this issue, a novel algorithm, Sparsity Discriminant Embedding (SDE) is proposed. Unlike SPP, the SDE adopts the class information of train samples when it constructs weighted graph of sparse reconstruction relationship. The projection matrix of the SDE is obtained via optimizing objective function and making different kinds of data points separate in the low-dimensional embedding space via a projection. By combining both interclass manifold structure and sparse property, the SDE keeps the sparse reconstructive relationships of dataset, and employs the class information of train samples to increase the classification rate. The experimental results obtained from operations on Urban and Washington DC Mall datasets show that the classification efficiency of the SDE has improved greatly as compared to those of other algorithms. The obtained classification accuracy has been 73.47% and 98.35%, respectively, when 16 samples of each class are randomly selected for training.