According to Skolem’s conjecture, if an exponential Diophantine equation is not solvable, then it solvable modulo appropriately chosen modulus. Besides several concrete equations, the conjecture has only been proved for rather special cases. In

Most well-known supervised dimensionality reduction algorithms suffer from the curse of while handling high-dimensional sparse data due to ill-conditioned second-order statistics matrices. They also do not deal with multi-modal properly since they construct neighborhood graphs that discriminate between classes and single-modal ones. In this paper, a novel method mitigates above problems is prop...