Display omitted •Characterizing high entropy alloys with machine learning and feature engineering.•Augmenting the dimensionality by non-linear combinations of original descriptors.•Linear machine learning model shows better generalization performance with non-linear descriptors. The prediction of the phase formation of high entropy alloys (HEAs) has attracted great research interest recent years due to their superior structure and mechanical properties of single phase. However, the identification of these single phase solid solution alloys is still a challenge. Previous studies mainly focus on trial-and-error experiments or thermodynamic criteria, the previous is time consuming while the latter depends on the descriptors quality, both provide unreliable prediction. In this study, we attempted to predict the phase formation based on feature engineering and machine learning (ML) with a small dataset. The descriptor dimensionality is augmented from original small dimension to high dimension by non-linear combinations to characterize HEAs. The results showed that this method could achieve higher accuracy in predicting the phase formation of HEAs than traditional methods. Except the prediction of HEAs, this method also can be applied to other materials with limited dataset.