1. A computer-implemented method for detecting a wakeword in a spoken utterance using a trained classifier, the method comprising: determining, for each of a first plurality of audio feature dimensions, a respective utility of each audio feature dimension for classifying audio data as including or not including a wakeword; determining a second plurality of audio feature dimensions using the respective utilities, wherein the second plurality of audio feature dimensions is a subset of the first plurality of audio feature dimensions; configuring a first support vector machine (SVM) classifier to classify whether input audio data includes a wakeword, the first SVM classifier comprising a first plurality of support vectors, each of the first plurality of support vectors including a value for each of the second plurality of audio feature dimensions; determining a positive pair of support vectors in the first plurality of support vectors, each support vector of the positive pair of support vectors being on a positive side of a binary classification of the first SVM classifier; combining the positive pair of support vectors into a first combined support vector; determining a negative pair of support vectors in the first plurality of support vectors, each support vector of the negative pair of support vectors being on a negative side of the binary classification of the first SVM classifier; combining the negative pair of support vectors into a second combined support vector; creating additional combined support vectors by alternating between combining a positive pair of support vectors and combining a negative pair of support vectors; determining a second plurality of support vectors including at least the first combined support vector, the second combined support vector, and the additional combined support vectors; configuring a second SVM classifier comprising the second plurality of support vectors; and determining, using the second SVM classifier, that first audio data includes a representation of a first wakeword.