Principal Component Analysis of collective flow in Relativistic Heavy-Ion Collisions

In this paper, we implement Principal Component Analysis (PCA) to study the single particle distributions generated from thousands of {\tt VISH2+1} hydrodynamic simulations with an aim to explore if a machine could directly discover flow from the huge amount of data without explicit instructions from human-beings. We found that the obtained PCA eigenvectors are similar to but not identical with the traditional Fourier bases. Correspondingly, the PCA defined flow harmonics $v_n^{\mathrm{\prime }}$ are also similar to the traditional $v_n$ for $n=2$ and 3, but largely deviated from the Fourier ones for $n\ge 4$. A further study on the symmetric cumulants and the Pearson coefficients indicates that mode-coupling effects are reduced for these flow harmonics defined by PCA.