Principal component analysis of formant transitions

Abstract

Formant transitions represent dynamic articulation processes and are useful to describe differences of articulation (e.g., normal and disordered speakers). Our method, considers the formant frequency change over time as a vector. We first reduce this vector to a single value which is plotted multi-dimensional space. Each dimension represents a data point in time and the position of the point of each dimension is the value of the formant frequency. Once the vector has been converted to a single point in the multi-dimensional space, principal component analysis is applied to reduce the dimensionality. These dimensions can then be applied to multi-variant statistical analysis. Additionally, the eigenvectors in each principal component can be used to plot the differences between sets of formant transitions through time. The eigenvectors are first weighted by calculating the Pythagorean distance in the multidimensional space of the first set of principle components and then each eigenvector is multiplied by the percentage of the variance explained by that principle component. Then, the eigenvectors are plotted and superimposed over the formant transitions. The change of height along the length of the curve represents areas along the transition of maximum and minimum differences between sets of transitions.