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A new methodology for classifying multidimensional satellite remote-sensing data is proposed. This technique is based on the Gaussian mixture modelling of the feature vectors extracted from the satellite image and the Bayesian approach to pattern recognition. The key contribution is the optimisation of the Gaussian mixture model for each class based on the training data. An array of techniques are employed for this purpose, including attribute learning vector quantisation, minimum description length model selection, semi-tied covariance matrices, minimum-classification-error learning, fusion of classifiers and the genetic algorithm. Contextual analysis is also developed for recognition. Experimental results on thematic mapper satellite image data demonstrate that the proposed technique outperforms various existing methods for pattern learning and classification.