  We apply principal component analysis to the study of event-by-event
fluctuations in relativistic heavy-ion collisions. This method brings out all
the information contained in two-particle correlations in a physically
transparent way. We present a guide to the method, and apply it to multiplicity
fluctuations and anisotropic flow, using ALICE data and simulated events. In
particular, we study elliptic and triangular flow fluctuations as a function of
transverse momentum and rapidity. This method reveals previously unknown
subleading modes in both rapidity and transverse momentum for the momentum
distribution as well as elliptic and triangular flows.
