Abstract: The accuracy of Kriging interpolation is low with small amount of data. Semi-supervised learning which utilizes unlabeled samples in training is combined with Kriging interpolation model to improve the model’s performance. Self-Training Kriging interpolation model（STK） and Co-Training Kriging interpolation model（CTK） are proposed in this paper. The PM2.5 concentration data of April and May of 2017 in Beijing are used to verify the Kriging interpolation model, STK and CTK. The experimental results show that STK and CTK models have the advantage of semi-supervised learning which is adaptive to the situation where few labeled samples are available, as well as the capability of analyzing the distribution pattern of spatial phenomena. CTK adopts two models to carry out collaborative training to effectively diminish early errors on post-training and employs unlabeled samples to improve the model’s performance.

Key words: Kriging interpolation, semi-supervised learning, co-training, PM2.5

摘要： 针对数据量较小时，克里金插值精度低的问题，将克里金插值模型与半监督学习理论相结合，利用未标记样本参与训练改进模型性能，提出基于半监督学习的克里金插值模型，即自训练克里金插值模型（STK）和协同训练克里金插值模型（CTK）。以北京地区2017年4月和5月的PM2.5浓度数据作为实验数据，采用克里金插值模型、STK和CTK进行对比实验。实验结果表明，这两个模型既具有半监督学习的优点，适用于只有少量标记样本的情况，又可以分析空间现象的分布模式。其中CTK采用两个模型协同训练，有效削弱了早期误差对后期训练的影响，利用未标记样本提升了模型的性能。

关键词: 克里金插值, 半监督学习, 协同训练, PM2.5