Semi-supervised learning is a new challenge that exploits the information of unlabeled instances. In this paper, we propose a novel Laplacian pair-weight vector projection (LapPVP) algorithm for semi-supervised classification. LapPVP consists of two stages: projection and classification. In the projection stage, LapPVP integrates a within-class scatter, a between-class scatter and a Laplacian regularization together and formulates a pair of optimization problems. The goal of LapPVP is to maximize the between-class scatter and minimize the within-class scatter on the basis of labeled data, and simultaneously maintain the geometric structure of labeled and unlabeled data in the projected subspace. The optimization problems of LapPVP are identical to generalized eigenvalue ones. Thus, it is easy to obtain the optimal solutions to LapPVP. In the classification stage, LapPVP adopts a minimal distance classifier to implement tasks in the projected subspace. The proposed LapPVP can find a better separability using the geometric information embedded in labeled and unlabeled instances and the discriminative information embedded in labeled instance. Experiments on artificial datasets and UCI datasets validate the feasibility and effectiveness of the proposed algorithm.

半监督学习是一种利用未标记实例信息的新挑战。在本文中，我们提出了一种用于半监督分类的新型拉普拉斯对权重向量投影（LapPVP）算法。LapPVP 包括两个阶段：投影和分类。在投影阶段，LapPVP 将类内散布、类间散布和拉普拉斯正则化集成在一起，并制定了一对优化问题。LapPVP 的目标是在标记数据的基础上最大化类间散度和最小化类内散度，同时保持投影子空间中标记和未标记数据的几何结构。LapPVP 的优化问题与广义特征值相同那些。因此，很容易获得 LapPVP 的最优解。在分类阶段，LapPVP 采用最小距离分类器在投影子空间中实现任务。所提出的 LapPVP 可以使用嵌入在标记和未标记实例中的几何信息以及嵌入在标记实例中的判别信息来找到更好的可分离性。在人工数据集和 UCI 数据集上的实验验证了所提出算法的可行性和有效性。