  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.
