Big datasets are becoming increasingly important in astrophysics due to new surveys continuously observing our night sky. A prominent example of an observatory that will produce a large data stream is Vera C. Rubin LSST, designed to simultaneously monitor the southern night sky in six colors. Unsupervised machine learning (ML), a method of learning from patterns within the data, is key for gaining insight into this expansive photometric data. We present our prototype classifier dedicated to classifying RR Lyrae variable stars into their relevant subclasses (RRab, RRc, and RRd). Using the RR Lyrae catalog of the ESA Gaia mission, we constructed training sets containing ~30,000 light curves using data from the Zwicky Transient Facility Catalog of Periodic Variable Stars (ZTF CPVS) and light curves extracted from full-frame images of the NASA TESS space telescope. Using a Variational Autoencoder (VAE), we project the processed light curves into a low-dimensional representation, which quantitatively describes the characteristic shape elements of the light curves. In preparation for Rubin LSST, we applied our pipeline to ZTF, a precursor facility for Rubin LSST. We show how the ML results are improved by including physical features such as period and variation amplitude. Through unsupervised clustering of this data representation, we identified the RR Lyrae subclasses in the ZTF data, which we anticipate to be easily adaptable to Rubin LSST.