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Support vector machines (SVM) are attractive for the classification of remotely sensed data with some claims that the method is insensitive to the dimensionality of the data and, therefore, does not require a dimensionality-reduction analysis in preprocessing. Here, a series of classification analyses with two hyperspectral sensor data sets reveals that the accuracy of a classification by an SVM does vary as a function of the number of features used. Critically, it is shown that the accuracy of a classification may decline significantly (at 0.05 level of statistical significance) with the addition of features, particularly if a small training sample is used. This highlights a dependence of the accuracy of classification by an SVM on the dimensionality of the data and, therefore, the potential value of undertaking a feature-selection analysis prior to classification. Additionally, it is demonstrated that, even when a large training sample is available, feature selection may still be useful. For example, the accuracy derived from the use of a small number of features may be noninferior (at 0.05 level of significance) to that derived from the use of a larger feature set providing potential advantages in relation to issues such as data storage and computational processing costs. Feature selection may, therefore, be a valuable analysis to include in preprocessing operations for classification by an SVM.