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- M. Burger, T. Graepel, and
K. Obermayer. An Annealed Self-Organizing Map for Source Channel Coding.
.
In Advances in Neural Information Processing Systems 10, pages
430-436, Cambridge, Massachusetts, 1998. MIT Press.
(FTP Gzipped PostScript, 7 pages, 584 kb)
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 algorithm (STVQ)
which is based on the maximum entropy principle and which performs a
maximum-likelihood estimate in an expectation-maximization (EM) fashion.
Annealing in the temperature parameter beta leads to phase transitions in the
existing code vector representation during 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 Kohonens
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. The algorithms performance is compared to those of LBG
and STVQ. While it is naturally superior to LBG, which does not take into
account channel noise, its results compare very well to those of STVQ, which
is computationally much more demanding.
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