The eigencages-the rows of V T ν (see Fig. )-are an orthonormal basis for the approximate lower dimensional subspace in which all 3D porosity images lay and are ordered in terms of importance. The eigencages are the directions in 3D porosity image space that account for the most variance among the 3D porosity images in the dataset. We visualize the first (and most important) six eigencages in Fig. . As eqn. 8 illustrates, the eigencages express deviations from the average 3D porosity image c, whose contours are shown in Fig. . Thus, the eigencages possess contours at both positive and negative values. The periphery of the first eigencage v 1 in Fig. exhibits radial symmetry; as Fig. .1 indicates, v 1 is used heavily to describe how the cavity diameter of a given cage differs from the average cage in Fig. . The second and third eigencages appear to capture windows to the cavities and moieties that protrude from the core of the cage molecule. The fifth and sixth eigencages possess lobes likely describing windows but are difficult to reconcile with our intuition of how to describe the shape of a cage molecule, highlighting that a human-engineered feature of porous organic cages is unlikely to be optimal in compressing the information about a cage cavity into a low-dimensional representation.