Uncontrolled manifold method to speech production

Abstract

Speech production is a highly skilled sensorimotor activity defined by articulatory or acoustic coordinates. To compare the variabilities of those two conceptualizations, issues of dimension reduction, normalization, incompleteness of information, etc., need to be taken into account. Uncontrolled manifold (UCM) method analyzes high-dimensional movement dataset with respect to the outcomes that count as successful tasks. It divides the variability in the data into two parts: “bad” variability associated with motion within the controlled manifold (CM) that would lead to an error in the task and “good” variability within the uncontrolled manifold (UCM) that do not harm to the task. The smaller ratio indicates both tighter control (less variability in the CM) and greater flexibility (more variability in the UCM). The UCM method is applied to the Wisconsin X-ray microbeam data. We first constructed a neural-net-based forward mapping from articulators to acoustics. The inter-layer weight matrices and the outputs of each layer in the trained forward model are then used to compute the elements of this forward model’s Jacobian matrices; the Jacobians are then used to compute σCM/σUCM ratios. We further compare these ratios across data obtained in various linguistic conditions.