  The fingerprint classification problem is to sort fingerprints into
pre-determined groups, such as arch, loop, and whorl. It was asserted in the
literature that minutiae points, which are commonly used for fingerprint
matching, are not useful for classification. We show that, to the contrary,
near state-of-the-art classification accuracy rates can be achieved when
applying topological data analysis (TDA) to 3-dimensional point clouds of
oriented minutiae points. We also apply TDA to fingerprint ink-roll images,
which yields a lower accuracy rate but still shows promise, particularly since
the only preprocessing is cropping; moreover, combining the two approaches
outperforms each one individually. These methods use supervised learning
applied to persistent homology and allow us to explore feature selection on
barcodes, an important topic at the interface between TDA and machine learning.
We test our classification algorithms on the NIST fingerprint database SD-27.
