中文摘要：

提出了一种半监督算法用于学习高斯过程分类器,其通过结合非参数的半监督核向分类器提供未标记数据信息.该算法主要包括以下几个方面：1）通过图拉普拉斯的谱分解获得核矩阵,其联合了标记数据和未标记数据信息;2）采用凸最优化方法学习核矩阵特征向量的最优权值,构建非参数的半监督核;3）把半监督核整合到高斯过程模型中,构建所提出的半监督学习算法.该算法的主要特点是：把基于整个数据集的非参数半监督核应用于高斯过程模型,该模型有着明确的概率描述,可以方便地对数据之间的不确定性进行建模,并能够解决复杂的推论问题.通过实验结果表明,该算法与其他方法相比具有更高的可靠性.

英文摘要：

In this paper, we present a semi-supervised algorithm to learn Gaussian process classifiers, which is combined with nonparametric semi-supervised kernels in the presence of unlabeled data. This algorithm mainly includes the following aspects： 1） The spectral decomposition of graph Laplacians is used to obtain kernel matrices incorporating labeled and unlabeled data; 2） The convex optimization method is employed to learn the optimal weights of kernel matrix eigenvectors, which construct the nonparametric semi-supervised kernels; 3） The proposed semi-supervised learning algorithm is obtained by incorporating semi-supervised kernels into Gaussian process model. The main characteristic of the proposed algorithm is that we employ the nonparametric semi-supervised kernels based on the entire dataset into the Gaussian process model, which has an explicit probabilistic interpretation, and can model the uncertainty among the data and solve the complex non-linear inference problems. The effectiveness of the proposed algorithm is demonstrated by the experimental results in comparison with other related works in the literature.