An Annealed Self-Organizing Map for Source Channel Coding

We derive and analyse robust optimization schemes for noisy vector quantization on the basis of deterministic annealing. Starting from a cost function for central clustering that incorporates distortions from channel noise we develop a soft topographic vector quantization al(cid:173) gorithm (STVQ) which is based on the maximum entropy principle and which performs a maximum-likelihood estimate in an expectation(cid:173) maximization (EM) fashion. Annealing in the temperature parameter f3 leads to phase transitions in the existing code vector representation dur(cid:173) ing the cooling process for which we calculate critical temperatures and modes as a function of eigenvectors and eigenvalues of the covariance matrix of the data and the transition matrix of the channel noise. A whole family of vector quantization algorithms is derived from STVQ, among them a deterministic annealing scheme for Kohonen's self-organizing map (SOM). This algorithm, which we call SSOM, is then applied to vector quantization of image data to be sent via a noisy binary symmetric channel.