Determining Functional Units of Tongue Motion via Graphregularized Sparse Nonnegative Matrix Factorization
Determining Functional Units of Tongue Motion via Graphregularized Sparse Nonnegative Matrix Factorization
Introduction
The relationship between the structural and functional components of the tongue is poorly understood partly due to complex tongue anatomy and muscle interactions. Despite advances that have been made due to tMRI studies on understanding internal tissue motion, there has been very little research on its analysis to determine functional units. Motion clustering during tongue motion can be used to reveal the tongue’s intrinsic functional organization. In this work we assume a Riemannian manifold of the data within an NMF approach, which thereby captures the intrinsic geometric of the motion features derived from tMRI. In paticular, we propose a new approach to determine functional units of tongue motion from tMRI using graphregularized sparse NMF with spectral clustering, termed GSNMFS.
Method
Consider a set of P internal tongue tissue points each with n scalar quantities tracked through F time frames. These quantities characterized each point and are used to group them into functional units. The location of the pth tissue point at the fth time frame can be writtens as (). The tongue motion can the be represented by spatiotemporal feature matrix , where the pth column is given by

We cast the problem of determining the functional units as motion clustering problem. Thus the goal is to determine a permutation of the columns to form , where the submatrix comprises point tracks associated with the ith submotion, i.e. the ith functional unit. The overall algorithm is shown below:

Results
We used 2D datasets to demonstrate the clustering performance of the proposed method. In order to compare the performance of the different algorithms, we used a Kmeans clustering method (Kmeans), a normalized cut method (NCut) [Shi et. al.], standard NMF with Kmeans clustering (NMFK), graphregularized NMF with Kmeans clustering (GNMFK) [Cai et. al.], graph regularized sparse NMF with Kmeans clustering (GSNMFK) and our method (GSNMFS). The metrics we used to measure the performance of these algorithms are the Normalized Mutual Information (NMI) and the Accuracy (AC). Table 1 lists these values for all the algorithms.

We also tested our method using a simple nonspeech protrusion task and a speech task. Figure 1 shows the protrusion task and figure two shows part of the speech task. Note that the three clusters better represent the motions of the tongue. These motions include the backward motion of the tongue tip (blue), upward motion of the tongue body (green) and forward motion of the posterior tongue (red).


Conclusion
In this work we presented a novel method for determining functional units from tMRI. Unlike previous algorithms, this one aims at identifying the internal, coherent manifold structure of highdimensional motion data to determine functional units. The proposed method gives a principled method for defining subject/taskspecific functional units, which can be potentially used to elucidate speechrelated disorders.
Publications
 V. Parthasarathy, J.L. Prince, M. Stone, E.Z. Murano, and M. NessAiver, "Measuring tongue motion from tagged cineMRI using harmonic phase (HARP) processing", The Journal of the Acoustical Society of America, 121(1): 491504, 2007.
 M. NessAiver and J.L. Prince, "Magnitude image CSPAMM reconstruction (MICSR)", Magnetic resonance in medicine, 50(2):331342, 2003.
 F. Xing, J. Woo, E.Z. Murano, J. Lee, M. Stone, and J.L. Prince, "3D tongue motion from tagged and cine MR images", Medical Image Computing and ComputerAssisted Intervention Springer, 4148, 2013.
References
 J. Shi, and J. Malik, "Normalized cuts and image segmentation", IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8): 888905, 2000.
 D. Cai, X. He, J. Han, and T.S. Huang, "Graph regularized nonnegative matrix factorization for data representation", IEEE Transaction on Pattern Analysis and Machine Intelligence, 33(8): 15481560, 2011.