The linear response of a photomultiplier tube (PMT) is a required property for photon counting and reconstruction of the neutrino energy. The linearity valid region and the saturation response of a PMT were investigated using a linear-alkylbenzene (LAB)-based liquid scintillator. A correlation was observed between the two different saturation responses, with pulse-shape distortion and pulse-area decrease. The observed pulse shape provides useful information for the estimation of the linearity region relative to the pulse area. This correlation-based diagnosis allows an in situ estimation of the linearity range, which was previously challenging. The measured correlation between the two saturation responses was employed to train an artificial neural network (ANN) to predict the decrease in pulse area from the observed pulse shape. The ANN-predicted pulse-area decrease enables a prediction of the ideal number of photoelectrons regardless of the saturation behavior. This pulse-shape-based machine-learning technique offers a novel method for restoring the saturation response of PMTs.