DcPCA: A Deep Learning Model for Contrastive Analytics of Nonlinear Data

Principal component analysis (PCA) is one of the most fundamental techniques for Big Data analytics, capable of extracting the most essential information from a single dataset. However, when it encounters multiple datasets, PCA cannot reveal the specific inherent data structure hidden in one dataset relative to the other(s), which we term contrastive analytics in this paper. Although a number of proposals such as contrastive or discriminative PCA have been advocated, they require fine-tuning of hyper-parameters or cannot effectively deal with nonlinear data. In this paper, we advocate deep contrastive (Dc) PCA for nonlinear contrastive analytics, which leverages deep neural networks to learn the hidden nonlinear relationships in the datasets and further extracts the desired contrastive features. An alternating minimization algorithm is developed for simultaneously seeking the best nonlinear transformations for the data as well as the associated contrastive projections, tantamount to performing an eigenvalue decomposition and a back-propagation step. Experiments using both synthetic and real world datasetsare performed, which corroborate the superior adaptivity of DcPCA in dealing with nonlinear data relative to a set of competing alternatives.