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Machine learning (ML) can process large sets of data generated from complexsystems, which is ideal for classification tasks as often appeared in criticalphenomena. Meanwhile ML techniques have been found effective in detectingcritical points, or in a broader sense phase separation, and extractingcritical exponents. But there are still many unsolved issues with the ML, oneof which is the meaning of hidden variables of unsupervised learning. Some saythat the hidden variables and the principal component may contain basicinformation regarding the order parameter of the system of interest, whichsounds plausible but lacks evidence. This study aims at searching for evidencesupporting the conjecture that the autoencoder's (AE) single latent variableand PCA's first principal component can only serve as signals related toparticle density, which happens to be the order parameter of thenon-equilibrium DP model. Indeed, in some phase transition (PT) models theorder parameter is the particle density, whereas in some PT models it is not.Having conducted a certain degree of random shuffling on the DP configurations,which are then fed to the neural networks as input, we find that AE's singlelatent variable and PCA's first principal component can indeed representparticle density. It is found that shuffling does affect the size of maximumcluster in the system, which suggests that the second principal component ofthe PCA is related to the maximal cluster. This has been supported by changesin the correlation length of the transition system with variations in theshuffle ratio.

Machine learning of (1+1)-dimensional directed percolation based on raw and shuffled configurations