Deep subspace learning is an important branch of self-supervised learning and has been a hot research topic in recent years, but current methods do not fully consider the individualities of temporal data and related tasks. In this paper, by transforming the individualities of motion capture data and segmentation task as the supervision, we propose the local self-expression subspace learning network. Specifically, considering the temporality of motion data, we use the temporal convolution module to extract temporal features. To implement the local validity of self-expression in temporal tasks, we design the local self-expression layer which only maintains the representation relations with temporally adjacent motion frames. To simulate the interpolatability of motion data in the feature space, we impose a group sparseness constraint on the local self-expression layer to impel the representations only using selected keyframes. Besides, based on the subspace assumption, we propose the subspace projection loss, which is induced from distances of each frame projected to the fitted subspaces, to penalize the potential clustering errors. The superior performances of the proposed model on the segmentation task of synthetic data and three tasks of real motion capture data demonstrate the feature learning ability of our model.