  Intelligible speech is produced by creating varying internal local muscle
groupings -- i.e., functional units -- that are generated in a systematic and
coordinated manner. There are two major challenges in characterizing and
analyzing functional units.~First, due to the complex and convoluted nature of
tongue structure and function, it is of great importance to develop a method
that can accurately decode complex muscle coordination patterns during speech.
Second, it is challenging to keep identified functional units across subjects
comparable due to their substantial variability. In this work, to address these
challenges, we develop a new deep learning framework to identify common and
subject-specific functional units of tongue motion during speech.~Our framework
hinges on joint deep graph-regularized sparse non-negative matrix factorization
(NMF) using motion quantities derived from displacements by tagged Magnetic
Resonance Imaging. More specifically, we transform NMF with sparse and graph
regularizations into modular architectures akin to deep neural networks by
means of unfolding the Iterative Shrinkage-Thresholding Algorithm to learn
interpretable building blocks and associated weighting map. We then apply
spectral clustering to common and subject-specific weighting maps from which we
jointly determine the common and subject-specific functional units. Experiments
carried out with simulated datasets show that the proposed method achieved on
par or better clustering performance over the comparison methods. Experiments
carried out with in vivo tongue motion data show that the proposed method can
determine the common and subject-specific functional units with increased
interpretability and decreased size variability.
