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.
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