Abstract: Quaternion has become one of the most widely used representations for rotational transformations in 3D graphics for decades. Due to the sparse nature of human motion in both the spatial domain and the temporal domain, an unexplored yet challenging research problem is how to directly represent intrinsically sparse human motion data in quaternion space. In this paper we propose a novel quaternion space sparse decomposition (QSSD) model that decomposes human rotational motion data into two meaningful parts (namely, the dictionary part and the weight part) with the sparseness constraint on the weight part. Specifically, a linear combination (addition) operation in Euclidean space is equivalently modeled as a quaternion multiplication operation, and the weight of linear combination is modeled as a power operation on quaternion. Besides validations of the robustness, convergence, and accuracy of the QSSD model, we also demonstrate its two selected applications: human motion data compression and content-based human motion retrieval. Through numerous experiments and quantitative comparisons, we demonstrate that the QSSD-based approaches can soundly outperform existing state-of-the-art human motion compression and retrieval approaches.