This paper presents a computational approach to derive interpretable movement primitives from speech articulation data. It puts forth a convolutive Nonnegative Matrix Factorization algorithm with sparseness constraints (cNMFsc) to decompose a given data matrix into a set of spatiotemporal basis sequences and an activation matrix. The algorithm optimizes a cost function that trades off the mismatch between the proposed model and the input data against the number of primitives that are active at any given instant. The method is applied to both measured articulatory data obtained through electromagnetic articulography as well as synthetic data generated using an articulatory synthesizer. The paper then describes how to evaluate the algorithm performance quantitatively and further performs a qualitative assessment of the algorithm's ability to recover compositional structure from data. This is done using pseudo ground-truth primitives generated by the articulatory synthesizer based on an Articulatory Phonology frame-work [Browman and Goldstein (1995). "Dynamics and articulatory phonology," in Mind as motion: Explorations in the dynamics of cognition, edited by R. F. Port and T.van Gelder (MIT Press, Cambridge, MA), pp. 175-194]. The results suggest that the proposed algorithm extracts movement primitives from human speech production data that are linguistically interpretable. Such a framework might aid the understanding of longstanding issues in speech production such as motor control and coarticulation.