Abstract: In this paper, we study touch modality data collected by RHex robots in White Sands National Monument, New Mexico, United States. Inspired by the recent advances of partial information decomposition (PID), we make analysis of Interaction Information (II), and propose two new feature selection algorithms, namely Mutual Information and Interaction Information ($MI^3$) criterion and Mutual Information Difference (MID) criterion. We applied our $MI^3$ and MID algorithms to feature selection of the robots sensing data, and reduced 12 features to 7 features. Simulation results show that the selected 7 feature data could be successfully used for terrain classification using random forest classifier. Our $MI^3$ and MID feature selection algorithms perform better than the Mutual Information Maximization (MIM), Joint Mutual Information (JMI), and SVD-QR algorithms in terrain classification.