Manifold Alignment with Label Information

Multi-domain data is becoming increasingly common and presents both challenges and opportunities in the data science community. The integration of distinct data-views can be used for exploratory data analysis, and benefit downstream analysis including machine learning related tasks. With this in mind, we present a novel manifold alignment method called MALI (Manifold alignment with label information) that learns a correspondence between two distinct domains. MALI belongs to a middle ground between the more commonly addressed semi-supervised manifold alignment, where some known correspondences between the two domains are assumed to be known beforehand, and the purely unsupervised case, where no information linking both domains is available. To do this, MALI learns the manifold structure in both domains via a diffusion process and then leverages discrete class labels to guide the alignment. MALI recovers a pairing and a common representation that reveals related samples in both domains. We show that MALI outperforms the current state-of-the-art manifold alignment methods across multiple datasets.