  We apply principal component analysis (PCA) to a set of electrical output
signals from a commercially available superconducting nanowire single-photon
detector (SNSPD) to investigate their photon-number-resolving capability. We
find that the rising edge as well as the amplitude of the electrical signal
have the most dependence on photon number. Accurately measuring the rising edge
while simultaneously measuring the voltage of the pulse amplitude maximizes the
photon-number resolution of SNSPDs. Using an optimal basis of principle
components, we show unambiguous discrimination between one- and two-photon
events, as well as partial resolution up to five photons. This expands the
use-case of SNSPDs to photon-counting experiments, without the need of detector
multiplexing architectures.
