  It is shown that Principal Component Analysis (PCA) applied to event-by-event
single-particle distributions in A-A collisions allows establishing the most
optimal basis for anisotropic flow studies from data itself, in contrast to
manual selection of the basis functions. PCA coefficients for azimuthal
particle distributions are identical to Fourier coefficients from a
conventional analysis techniques. PCA applied in longitudinal dimension reveals
optimal basis that is similar to Legendre polynomial series. Analysis in both
dimensions simultaneously allows studying the coupling of the longitudinal
structure of events with the azimuthal anisotropy of particle emission.
