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Adaptive array algorithms based on sample matrix inversion (SMI) require the availability of a secondary data set to "train" the adaptive filter. Numerous data-independent rules have been proposed for selecting this training data. However, such rules often perform poorly in inhomogeneous environments. We present data-adaptive methodologies for selecting the training data. The techniques, called "Power Selected Training" and "Power Selected Deemphasis", use measurements of the interference environment to select training data. This work describes these algorithms and their performance on recorded radar data.