A representative model in integrative analysis of two high-dimensional correlated datasets is to decompose each data matrix into a low-rank common matrix generated by latent factors shared across datasets, a low-rank distinctive matrix corresponding to each dataset, and an additive noise matrix. Existing decomposition methods claim that their common matrices capture the common pattern of the two datasets. However, their so-called common pattern only denotes the common latent factors but ignores the common pattern between the two coefficient matrices of these common latent factors. We propose a new unsupervised learning method, called the common and distinctive pattern analysis (CDPA), which appropriately defines the two types of data patterns by further incorporating the common and distinctive patterns of the coefficient matrices. A consistent estimation approach is developed for high-dimensional settings, and shows reasonably good finite-sample performance in simulations. Our simulation studies and real data analysis corroborate that the proposed CDPA can provide better characterization of common and distinctive patterns and thereby benefit data mining.
翻译:综合分析两个高维相关数据集的一个具有代表性的模式是,将每个数据矩阵分解成一个低层次的通用矩阵,即由各数据集共享的潜在因素产生的低层次共同矩阵、一个与每个数据集相对应的低层次特殊矩阵和一个添加噪音矩阵。现有的分解方法声称,它们的共同矩阵反映了两个数据集的共同模式。然而,它们所谓的共同模式只表示共同潜伏因素,而忽略了这些共同潜伏因素的两个系数矩阵之间的共同模式。我们提出了一种新的不受监督的学习方法,称为共同和独特的模式分析(CDPA),它通过进一步纳入系数矩阵的共同和独特模式,适当界定了两类数据模式。为高维设置制定了一致的估算方法,并显示了在模拟中相当良好的有限抽样性表现。我们的模拟研究和实际数据分析证实,拟议的CDPA能够更好地描述共同和独特模式,从而有利于数据挖掘。