  It is increasingly common in many types of natural and physical systems
(especially biological systems) to have different types of measurements
performed on the same underlying system. In such settings, it is important to
align the manifolds arising from each measurement in order to integrate such
data and gain an improved picture of the system. We tackle this problem using
generative adversarial networks (GANs). Recently, GANs have been utilized to
try to find correspondences between sets of samples. However, these GANs are
not explicitly designed for proper alignment of manifolds. We present a new GAN
called the Manifold-Aligning GAN (MAGAN) that aligns two manifolds such that
related points in each measurement space are aligned together. We demonstrate
applications of MAGAN in single-cell biology in integrating two different
measurement types together. In our demonstrated examples, cells from the same
tissue are measured with both genomic (single-cell RNA-sequencing) and
proteomic (mass cytometry) technologies. We show that the MAGAN successfully
aligns them such that known correlations between measured markers are improved
compared to other recently proposed models.
