Projection-based reduced order modeling of parametric dynamical systems seeks to develop a small global basis to approximate physical behavior across system space, time, and parameters. The multiway relationships between dynamics and parameters have motivated recent developments in multilinear or tensor methods to capture informative global reduced bases. Despite the success of tensor-based approaches across scientific applications, fundamental linear algebra properties often break down in higher dimensions. Recent advances in matrix-mimetic tensor algebra in have made it possible to preserve linear algebraic properties and, as a result, to obtain optimal representations of multiway data. Matrix-mimeticity arises from interpreting tensors as t-linear operators, which in turn are parameterized by invertible linear transformations. The choice of transformation is critical to representation quality, and thus far, has been made heuristically. In this talk, we will learn data-dependent, orthogonal transformations by leveraging the optimality of matrix-mimetic representations. In particular, we will exploit the coupling between transformations and optimal tensor representations using variable projection. We will highlight the efficacy of our proposed approach on image compression and reduced order modeling tasks.