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Abstract:
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
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 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. The algorithm's 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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