  Persistent homology analysis provides means to capture the connectivity
structure of data sets in various dimensions. On the mathematical level, by
defining a metric between the objects that persistence attaches to data sets,
we can stabilize invariants characterizing these objects. We outline how so
called contour functions induce relevant metrics for stabilizing the rank
invariant. On the practical level, the stable ranks are used as fingerprints
for data. Different choices of contour lead to different stable ranks and the
topological learning is then the question of finding the optimal contour. We
outline our analysis pipeline and show how it can enhance classification of
physical activities data. As our main application we study how stable ranks and
contours provide robust descriptors of spatial patterns of atmospheric cloud
fields.
