  For the first time a principle-component analysis is used to separate out
different orthogonal modes of the two-particle correlation matrix from heavy
ion collisions. The analysis uses data from sqrt(s[NN]) = 2.76 TeV PbPb and
sqrt(s[NN]) = 5.02 TeV pPb collisions collected by the CMS experiment at the
LHC. Two-particle azimuthal correlations have been extensively used to study
hydrodynamic flow in heavy ion collisions. Recently it has been shown that the
expected factorization of two-particle results into a product of the
constituent single-particle anisotropies is broken. The new information
provided by these modes may shed light on the breakdown of flow factorization
in heavy ion collisions. The first two modes ("leading" and "subleading") of
two-particle correlations are presented for elliptical and triangular
anisotropies in PbPb and pPb collisions as a function of pt over a wide range
of event activity. The leading mode is found to be essentially equivalent to
the anisotropy harmonic previously extracted from two-particle correlation
methods. The subleading mode represents a new experimental observable and is
shown to account for a large fraction of the factorization breaking recently
observed at high transverse momentum. The principle-component analysis
technique has also been applied to multiplicity fluctuations. These also show a
subleading mode. The connection of these new results to previous studies of
factorization is discussed.
