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We consider a supervised classification of hyperspectral data using AdaBoost with stump functions as base classifiers. We used the bootstrap method without replacement to improve stability and accuracy and to reduce overtraining. We randomly split a data set into two subsets: one for training and the other one for validation. Subsampling and training/validation steps were repeated to derive the final classifier by the majority vote of the classifiers. This method enabled us to estimate variable relevance to the classification. The relevance measure was used to estimate prior probabilities of the variables for random combinations. In numerical experiments with multispectral and hyperspectral data, the proposed method performed extremely well and showed itself to be superior to support vector machines, artificial neural networks, and other well-known classification methods.