Intrinsic Classification of Spatially Correlated Data

Intrinsic classification, or unsupervised learning of a classification, was the earliest application of what is now termed minimum message length (MML) or minimum description length (MDL) inference. The MML algorithm ‘Snob’ and its relatives have been used successfully in many domains. These algorithms treat the ‘things’ to be classified as independent random selections from an unknown population whose class structure, if any, is to be estimated. This work extends MML classification to domains where the ‘things’ have a known spatial arrangement and it may be expected that the classes of neighbouring things are correlated. Two cases are considered. In the first, the things are arranged in a sequence and the correlation between the classes of successive things modelled by a first-order Markov process. An algorithm for this case is constructed by combining the Snob algorithm with a simple dynamic programming algorithm. The method has been applied to the classification of protein secondary structure. In the second case, the things are arranged on a two-dimensional (2D) square grid, like the pixels of an image. Correlation is modelled by a prior over patterns of class assignments whose log probability depends on the number of adjacent mismatched pixel pairs. The algorithm uses Gibbs sampling from the pattern posterior and a thermodynamic relation to calculate message length.