  Capturing patterns of variation present in a dataset is important in
exploratory data analysis and unsupervised learning. Contrastive dimension
reduction methods, such as contrastive principal component analysis (cPCA),
find patterns unique to a target dataset of interest by contrasting with a
carefully chosen background dataset representing unwanted or uninteresting
variation. However, such methods typically require a tuning parameter that
governs the level of contrast, and it is unclear how to choose this parameter
objectively. Furthermore, it is frequently of interest to contrast against
multiple backgrounds, which is difficult to accomplish with existing methods.
We propose unique component analysis (UCA), a tuning-free method that
identifies low-dimensional representations of a target dataset relative to one
or more comparison datasets. It is computationally efficient even with large
numbers of features. We show in several experiments that UCA with a single
background dataset achieves similar results compared to cPCA with various
tuning parameters, and that UCA with multiple individual background datasets is
superior to both cPCA with any single background data and cPCA with a pooled
background dataset.
