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The multivariate polynomial model provides an effective way to describe complex nonlinear input-output relationships since it is tractable for optimization, sensitivity analysis, and prediction of confidence intervals. However, for high-dimensional and high-order problems, multivariate polynomial regression becomes impractical due to its huge number of product terms. This is especially true for the case of a full interaction model. In this paper, we propose a reduced multivariate polynomial model to circumvent the dimensionality problem with some compromise in its approximation capability. In multimodal biometrics and many classifiers fusion applications, as individual classifiers to be combined would have attained a certain level of classification accuracy, this reduced multivariate polynomial model can be used to combine these classifiers in the next level of classification taking their outputs as the inputs to the reduced multivariate polynomial model. The model is first applied to a well-known pattern classification problem to illustrate its classification capability. The reduced multivariate polynomial model is then applied to combine two biometric verification systems with improved receiver operating characteristics performance as compared to an optimal weighing method and a few commonly used classifiers.