In materials, long-ranged interactions and short-ranged chemical interactions play important roles in phase stability and morphology. The total energies of a few coherent structures can be obtained by cluster expansion (CE) method. However, CE method such based on DFT is proven to be challenging for long-ranged strain interaction. By modeling the short- and long-ranged interactions in r- and k-space respectively, long-ranged strain interactions are incorporated in CE, which is called mixed-space cluster expansion (MSCE). The MSCE method owes the high accuracy, compared with r-space CE, to three aspects： (1) The long-ranged limit of the constituent strain energy due to size-mismatch are explicitly incorporated using the k-space formalism. (2) The attenuation of the long-ranged interactions accommodates for medium-ranged structures, which is the case for the majority of the structures in the training set. (3) The regularization of r-space effective cluster interactions allow to include much larger number of clusters, which enhances the fitting capability. In this work, Kang Wang et al. from the Department of Materials Science and Engineering, University of Virginia, used machine learning and generalized MSCE to systems with multiple sublattices by formulating compatible reciprocal space interactions and combined with a crystal-symmetry-agnostic algorithm for the calculation of constituent strain energy. This generalized approach was then demonstrated in a hypothetical HCP system and Mg-Zn alloys. The current MSCE can significantly improve the accuracy of the energy parameterization and account for all the fully relaxed structures regardless of lattice distortion. The generalized MSCE method makes it possible to simultaneously analyze the short- and long-ranged configuration-dependent interactions in crystalline materials with arbitrary lattices with the accuracy of typical first-principles methods. This work has promoted the applicability of MSCE method and is of great significance for the development of materials science.