Supervised machine learning-enabled mapping of the X-ray absorption near edge structure (XANES) spectra to local structural descriptors offers new methods for understanding the structure and function of working nanocatalysts. We briefly summarize a status of XANES analysis approaches by supervised machine learning methods. We present an example of an autoencoder-based, unsupervised machine learning approach for latent representation learning of XANES spectra. This new approach produces a lower-dimensional latent representation, which retains a spectrum-structure relationship that can be eventually mapped to physicochemical properties. The latent space of the autoencoder also provides a pathway to interpret the information content "hidden" in the X-ray absorption coefficient. Our approach (that we named latent space analysis of spectra, or LSAS) is demonstrated for the supported Pd nanoparticle catalyst studied during the formation of Pd hydride. By employing the low-dimensional representation of Pd K-edge XANES, the LSAS method was able to isolate the key factors responsible for the observed spectral changes.