structures that are most similar to the chosen one, selected once by conventional descriptors (ConD) and once using persistent homology (PerH). To compare these two sets, we compute their average distances to the reference material, measured by the metric $D_{CS}$ of the conventional space as well as by the metric $D_{TS}$ of the barcode space (see SI sections \[methcomp\] and \[theo\] for details). Figure \[Compare\]a shows the average distances of the two sets for each of the 146 experimentally known zeolite structures accessible to methane taken. The distances are normalized by the largest pairwise distance in the database. The TDA approach provides what one would expect: when persistent homology is used to identify similar pore structures, small $D_{TS}$ correlates well with small $D_{CS}$. I.e., similar persistence diagrams describing the pore shapes correlate with similar conventional geometric measures. Figure \[4similar\]a shows that the relatively few zeolites for which there are no four structures very similar to a given one with respect to PerH (large $D_{TS}$), the first four structures chosen by PerH might or might not have similar conventional geometric descriptors (small or large $D_{CS}$). The conventional approach, however, gives a different result: for each reference structure we can find structures 