  A new semi-supervised machine learning method for the discovery of
structure-spectrum relationships is developed and demonstrated using the
specific example of interpreting X-ray absorption near-edge structure (XANES)
spectra. This method constructs a one-to-one mapping between individual
structure descriptors and spectral trends. Specifically, an adversarial
autoencoder is augmented with a novel rank constraint (RankAAE). The RankAAE
methodology produces a continuous and interpretable latent space, where each
dimension can track an individual structure descriptor. As a part of this
process, the model provides a robust and quantitative measure of the
structure-spectrum relationship by decoupling intertwined spectral
contributions from multiple structural characteristics. This makes it ideal for
spectral interpretation and the discovery of new descriptors. The capability of
this procedure is showcased by considering five local structure descriptors and
a database of over fifty thousand simulated XANES spectra across eight
first-row transition metal oxide families. The resulting structure-spectrum
relationships not only reproduce known trends in the literature, but also
reveal unintuitive ones that are visually indiscernible in large data sets. The
results suggest that the RankAAE methodology has great potential to assist
researchers to interpret complex scientific data, test physical hypotheses, and
reveal new patterns that extend scientific insight.
