Tongue pellet data analysis by singular-value decomposition approac

Abstract

In order to obtain tongue trajectory information during speech, three or four pellets attached to the tongue of subjects are tracked in real time by the University of Wisconsin x-ray microbeam system. For each pellet, two time series are produced that correspond to x and y pellet coordinates, respectively. These data are being used to build a model of vocal tract acoustics. The singular-value decomposition (SVD) method has been found to be a good way to approach the following questions (1) Are the data redundant? (2) Can we find a better way to represent the data set? (3) Can relationships among the different pellets be discerned? In this experiment, six data series are organized into a data matrix and decomposed by SVD into two orthogonal matrices and one diagonal matrix. The diagonal matrix, called the singular-value matrix, indicates the redundancy of the original data set. Different deductions of the singular-value matrix were tested for five data sets. It is found that three transformed orthogonal data vectors can represent the original six data series at a 98% level of approximation. This work indicates that the orthogonal data matrices are well suited for model construction because: (1) the data size is decreased; (2) ambiguity is reduced for mapping work (e.g., to the terminal acoustic characteristics); and (3) relationships among the pellets can be found from the orthogonal matrices. These results and some other related issues will be discussed. [Work supported by NIH Grant NS-16373.]