We now leverage the singular value decomposition to learn from the set of 3D porosity images of the cages in Fig. an approximate, lower-dimensional subspace in which the 3D porosity images of porous cage molecules lay. The eigencages are a set of orthonormal vectors that span this lower-dimensional subspace; they are ordered in terms of which directions, in the space of all 3D porosity images, account for the most variance among the 3D porosity images of the cages in Fig. . Expressing a 3D porosity image as a combination of the eigencages then lends a latent representation of the cage.