Buried threat detection algorithms in Ground Penetrating Radar (GPR) measurements often utilize a statistical classifier to model target responses. There are many different target types with distinct responses and all are buried in a wide range of conditions that distort the target signature. Robust performance of this classifier requires it to learn the distinct responses of target types while accounting for the variability due to the physics of the emplacement. In this work, a method to reduce certain sources of excess variation is presented that enables a linear classifier to learn distinct templates for each target type's response despite the operational variability. The different target subpopulations are represented by a Gaussian Mixture Model (GMM). Training the GMM requires jointly extracting the patches around target responses as well as learning the statistical parameters as neither are known a priori. The GMM parameters and the choice of patches are determined by variational Bayesian methods. The proposed method allows for patches to be extracted from a larger data-block that only contain the target response. The patches extracted from this method improve the ROC for distinguishing targets from background clutter compared to the patches extracted using other patch extraction methods aiming to reduce the operational variability.