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When building a classifier from clean training data for a particular test environment, knowledge about the environmental noise and channel should be taken into account. We propose training a support vector machine (SVM) classifier using a modified kernel that is the expected kernel with respect to a probability distribution over channels and noise that might affect the test signal. We compare the proposed expected SVM to an SVM that ignores the environment, to an SVM that trains with multiple random samples of the environment, and to a quadratic discriminant analysis classifier that takes advantage of environment statistics (Joint QDA). Simulations classifying narrowband signals in a noisy acoustic reverberation environment indicate that the expected SVM can improve performance over a range of noise levels.