Luttrell S P, March 1993, The Markov chain theory of vector quantisers, DRA technical report (Malvern, UK), 4742
In this paper a rigorous approach will be taken, in which Bayesian methods are used to analyse some of the properties of a special type of Markov chain. The forward transitions through the chain are followed by inverse transitions (using Bayes' theorem) backwards through a copy of the same chain; this is called a folded Markov chain. If an appropriately defined Euclidean distortion (between the original input and its 'reconstruction' via Bayes theorem) is minimised in the space of Markov chain transition probabilities, then the theory of vector quantisers and topographic vector quantisers emerges, and the theory of self-supervision in multi-layer unsupervised networks also emerges. This approach is much more compelling than one in which these models are proposed as if they were logically independent constructs. Only the 2 and 3-layer cases are studied in this paper.