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

## TL;DR

This study applies Principal Component Analysis to hydrodynamic simulation data from heavy-ion collisions to identify flow patterns without human bias, revealing similarities and differences with traditional Fourier-based methods.

## Contribution

It demonstrates that PCA can effectively extract flow harmonics from collision data, offering a data-driven alternative to traditional Fourier analysis.

## Key findings

- PCA eigenvectors resemble Fourier bases but are not identical.
- Flow harmonics $v_n^ ext{'}$ are similar to $v_n$ for n=2,3, but differ for n≥4.
- Mode-coupling effects are reduced in PCA-defined flow harmonics.

## Abstract

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 $v_n^\prime$ are also similar to the traditional $v_n$ for $n=2$ and 3, but largely deviated from the Fourier ones for $n\geq 4$. 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.