LASSO constraints can lead to a Gaussian mixture copula model that is more robust, better conditioned, and more reflective of the actual clusters in the training data. These qualities of the GMCM have been shown with data obtained from: digital images of fine needle aspirates of breast tissue for detecting cancer; email for detecting spam; two dimensional terrain data for detecting hills and valleys; and video sequences of hand movements to detect gestures. Using training data, a GMCM estimate can be produced and iteratively refined to maximize a penalized log likelihood estimate until sequential iterations are within a threshold value of one another. The GMCM estimate can then be used to classify further samples. The LASSO constraints help keep the analysis tractibe such that useful results can be found and used while the result is still useful.