The dimensionality reduction of the unbalanced semi-supervised problem is difficult because there are too few labeled samples. In this paper, we propose a new dimensionality reduction method for the unbalanced semi-supervised problem, called sparse locality preserving projection (SLPP for short). In the past work of solving the semi-supervised dimensionality reduction problems, they either abandon some unlabeled samples or do not utilize the implicit discriminant information of unlabeled samples. While, SLPP learns the optimal projection matrix with the full use of the discriminant information and the geometric structure of the unlabeled samples. Here, we preserve the geometric structure of the rest unlabeled samples and their k-nearest neighbors after increasing the number of labeled samples by label propagation. The optimization problem of SLPP can be easily solved by a generalized eigenvalue problem. Results on various data sets from UCI machine learning repository and two hyperspectral data sets demonstrate that SLPP is superior to other conventional reduction methods.

中文翻译：

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通过稀疏局部保留投影进行半监督降维

不平衡的半监督问题的降维很困难，因为标记的样本太少了。本文针对不平衡的半监督问题提出了一种新的降维方法，称为稀疏局部保留投影（简称SLPP）。在过去解决半监督降维问题的工作中，他们要么放弃一些未标记的样本，要么不使用未标记的样本的隐式判别信息。同时，SLPP充分利用判别信息和未标记样本的几何结构来学习最佳投影矩阵。在这里，在通过标签传播增加标记样本的数量之后，我们保留了其余未标记样本及其k近邻的几何结构。SLPP的优化问题可以通过广义特征值问题轻松解决。来自UCI机器学习存储库的各种数据集和两个高光谱数据集的结果表明，SLPP优于其他常规的归约方法。