With the rapid development of wearable sensors and pervasive computing technologies including smartphones, acceleration-based human activity recognition is receiving increased attention for medical research applications. Motivated by the 'weightlessness' feature, here we apply a bidirectional feature during the feature extraction phase of activity recognition; however, since the bidirectional feature has two components, they cannot simply be concatenated into a long vector, but can be naturally treated as a second-order tensor. Therefore, we propose a new tensor-based feature selection method termed tensor manifold discriminant projections (TMDP). TMDP simultaneously considers: 1) applying an optimization criterion that can directly process the tensor spectral analysis problem, thereby decreasing the computational cost compared to traditional tensor-based feature selection methods; 2) extracting local rank information by finding a tensor subspace that preserves the rank order information of the within-class input samples; and 3) extracting discriminant information by maximizing the sum of distances between every sample and their interclass sample mean. Experiments on the naturalistic mobile devices-based human activity 2.0 dataset are performed to demonstrate the effectiveness and robustness of TMDP.