Topological Mappings of Video and Audio Data

We review a new form of self-organizing map which is based on a nonlinear projection of latent points into data space, identical to that performed in the Generative Topographic Mapping (GTM).(1) But whereas the GTM is an extension of a mixture of experts, this model is an extension of a product of experts.(2) We show visualisation and clustering results on a data set composed of video data of lips uttering 5 Korean vowels. Finally we note that we may dispense with the probabilistic underpinnings of the product of experts and derive the same algorithm as a minimisation of mean squared error between the prototypes and the data. This leads us to suggest a new algorithm which incorporates local and global information in the clustering. Both ot the new algorithms achieve better results than the standard Self-Organizing Map.