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.