High-dimensional multi-source data are encountered in many fields. Despite recent developments on the integrative dimension reduction of such data, most existing methods cannot easily accommodate data of multiple types (e.g. binary or count-valued). Moreover, multi-source data often have block-wise missing structure, i.e. data in one or more sources may be completely unobserved for a sample. The heterogeneous data types and presence of block-wise missing data pose significant challenges to the integration of multi-source data and further statistical analyses. In this article, we develop a low-rank method, called generalized integrative principal component analysis (GIPCA), for the simultaneous dimension reduction and imputation of multi-source block-wise missing data, where different sources may have different data types. We also devise an adapted Bayesian information criterion (BIC) criterion for rank estimation. Comprehensive simulation studies demonstrate the efficacy of the proposed method in terms of rank estimation, signal recovery, and missing data imputation. We apply GIPCA to a mortality study. We achieve accurate block-wise missing data imputation and identify intriguing latent mortality rate patterns with sociological relevance.

中文翻译：

---

具有分块缺失结构的多类型数据的广义综合主成分分析。

在许多领域都遇到高维多源数据。尽管最近在减少此类数据的集成维方面取得了进展，但是大多数现有方法仍无法轻松容纳多种类型的数据（例如，二进制或计数值）。而且，多源数据通常具有逐块丢失的结构，即一个或多个源中的数据对于样本可能是完全不可见的。异构数据类型和逐块丢失数据的存在对多源数据的集成和进一步的统计分析提出了重大挑战。在本文中，我们开发了一种低阶方法，称为广义综合主成分分析（GIPCA），用于同时缩小和插补多源逐块丢失数据的维度，其中不同源可能具有不同的数据类型。我们还设计了一种适用于秩估计的贝叶斯信息准则（BIC）准则。全面的仿真研究证明了该方法在秩估计，信号恢复和丢失数据归因方面的有效性。我们将GIPCA应用于死亡率研究。我们实现了准确的逐块缺失数据估算，并确定了与社会学相关的有趣的潜在死亡率模式。