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For classifier ensembles, an effective combination method is to combine the outputs of each classifier using a linearly weighted combination rule. There are multiple ways to linearly combine classifier outputs and it is beneficial to analyze them as a whole. We present a unifying framework for multiple linear combination types in this paper. This unification enables using the same learning algorithms for different types of linear combiners. We present various ways to train the weights using regularized empirical loss minimization. We propose using the hinge loss for better performance as compared to the conventional least-squares loss. We analyze the effects of using hinge loss for various types of linear weight training by running experiments on three different databases. We show that, in certain problems, linear combiners with fewer parameters may perform as well as the ones with much larger number of parameters even in the presence of regularization.