We describe and compare two machine learning approaches for cell classification based on label-free quantitative phase imaging with transport of intensity equation methods. In one approach, we design a multilevel integrated machine learning classifier including various individual models such as artificial neural network, extreme learning machine and generalized logistic regression. In another approach, we apply a pretrained convolutional neural network using transfer learning for the classification. As a validation, we show the performances of both approaches on classification between macrophages cultured in normal gravity and microgravity with quantitative phase imaging. The multilevel integrated classifier achieves average accuracy 93.1%, which is comparable to the average accuracy 93.5% obtained by convolutional neural network. The presented quantitative phase imaging system with two classification approaches could be helpful to biomedical scientists for easy and accurate cell analysis.