Body-Machine Interfaces (BoMIs) provide a means to control various devices, enabling users to extend their motor capabilities by using the remaining redundancy in the musculoskeletal system after a neurological injury. Here, we considered a hybrid BoMI combining motion and muscle activities, measured respectively by inertial sensors and electromyography. We aimed to determine which algorithm for dimensionality reduction between a linear - principal component analysis (PCA) - and a non-linear one – nonlinear autoencoder (AE)- would allow for a more proficient control. We recruited fourteen healthy subjects and assessed their proficiency in controlling a computer cursor with either mapping. The subjects were randomly assigned to start with either PCA or AE mapping in a crossover study. We found that the hybrid BoMI with PCA led to better performance paving the way to further exploitation of linear dimensionality reduction algorithms in clinical approaches targeting simultaneously motion and muscle activations.