Unsupervised machine learning of phase transition in percolation

Abstract

Machine learning is a powerful tool to find and recognize the intricate structures in large data set. By using the principal component analysis with the preprocessing treatment of the unpercolating clusters, we show that one may identify phase transition in percolation from raw data under unsupervised machine learning. The first principal component plays an important role and may be considered as an indicator of different phases. Based on the first principal component as the order parameter, we calculated the percolating threshold value and the critical exponents by using finite-size scaling method. The consistency of the obtained results with the classical values indicates that the first principal component has caught the basic features and the critical behaviors of phase transition in percolation. Our above scheme provides an alternative way to analyze the percolation model in the framework of the unsupervised machine learning.