Principal component analysis of absorbing state phase transitions.

Abstract

We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes-directed bond percolation and branching and annihilating random walks with an even number of offspring. We find that the uncentered PCA of data sets storing various system's configurations can be successfully used to determine the critical properties of these nonequilibrium phase transitions. In particular, in both cases, we obtain good estimates of the critical point and the dynamical critical exponent of the models. For directed bond percolation, we are furthermore able to extract critical exponents associated with the correlation length and the order parameter. We discuss the relation of our analysis with low-rank approximations of data sets.