  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 can be considered as belonging to a middle ground
between the more commonly addressed semi-supervised manifold alignment problem
with some known correspondences between the two domains, and the purely
unsupervised case, where no known correspondences are provided. 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. By aligning two
distinct domains, MALI recovers a pairing and a common representation that
reveals related samples in both domains. Additionally, MALI can be used for the
transfer learning problem known as domain adaptation. We show that MALI
outperforms the current state-of-the-art manifold alignment methods across
multiple datasets.
