Missing data is a commonly occurring problem in practice. Many imputation methods have been developed to fill in the missing entries. However, not all of them can scale to high-dimensional data, especially the multiple imputation techniques. Meanwhile, the data nowadays tends toward high-dimensional. Therefore, in this work, we propose Principal Component Analysis Imputation (PCAI), a simple but versatile framework based on Principal Component Analysis (PCA) to speed up the imputation process and alleviate memory issues of many available imputation techniques, without sacrificing the imputation quality in term of MSE. In addition, the frameworks can be used even when some or all of the missing features are categorical, or when the number of missing features is large. Next, we introduce PCA Imputation - Classification (PIC), an application of PCAI for classification problems with some adjustments. We validate our approach by experiments on various scenarios, which shows that PCAI and PIC can work with various imputation algorithms, including the state-of-the-art ones and improve the imputation speed significantly, while achieving competitive mean square error/classification accuracy compared to direct imputation (i.e., impute directly on the missing data).

翻译：缺失数据是实践中普遍存在的问题。目前已开发出多种插补方法填补缺失条目，但并非所有方法都能扩展到高维数据，尤其是多重插补技术。然而，当前数据正呈现高维化趋势。为此，本文提出基于主成分分析的插补框架（PCAI）——一种简洁而通用的方法，通过主成分分析加速插补过程并缓解多种现有插补技术的内存压力，同时不牺牲均方误差层面的插补质量。该框架还可处理以下情形：部分或全部缺失特征为类别型变量，或缺失特征数量庞大。进一步地，我们引入主成分分析插补-分类框架（PIC），这是PCAI针对分类问题的改进应用。通过多场景实验验证，PCAI与PIC能够适配包括最先进方法在内的各类插补算法，在显著提升插补速度的同时，与直接插补（即对缺失数据直接插补）相比取得具有竞争力的均方误差/分类准确率。