Hot sub-luminous stars represent a population of stripped and evolved red giants that is located on the extreme horizontal branch. Since they exhibit a wide range of variability due to pulsations or binary interactions, it is crucial to unveil their intrinsic and extrinsic variability to understand the physical processes of their formation. In the Hertzsprung-Russell diagram, they overlap with interacting binaries such as cataclysmic variables (CVs). By leveraging the most recent clustering algorithm tools, we investigate the variability of 1,576 candidate hot subdwarf variables using comprehensive data from Gaia DR3 multi-epoch photometry and Transiting Exoplanet Survey Satellite (TESS) observations. We present a novel approach that uses the t-distributed stochastic neighbour embedding and the uniform manifold approximation and projection dimensionality reduction algorithms to facilitate the identification and classification of different populations of variable hot subdwarfs and CVs in a large dataset. In addition to the publicly available Gaia time-series statistics table, we adopted additional statistical features that enhanced the performance of the algorithms. The clustering results led to the identification of 85 new hot subdwarf variables based on Gaia and TESS light curves and of 108 new variables based on Gaia light curves alone, including reflection-effect systems, HW Vir, ellipsoidal variables, and high-amplitude pulsating variables. A significant number of known CVs (140) distinctively cluster in the 2D feature space among an additional 152 objects that we consider candidates for new CVs. This study paves the way for more efficient and comprehensive analyses of stellar variability from ground- and space-based observations, and for the application of machine-learning classifications of candidate variable stars in large surveys.
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