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Issues in the quadratic discriminant functions (QDF) are discussed and two types of modified quadratic disriminant functions (MQDF1, MQDF2) which are less sensitive to the estimation error of the covariance matrices are proposed. The MQDF1 is a function which employs a kind of a (pseudo) Bayesian estimate of the covariance matrix instead of the maximum likelihood estimate ordinarily used in the QDF. The MQDF2 is a variation of the MQDF1 to save the required computation time and storage. Two discriminant functions were applied to Chinese character recognition to evaluate their effectiveness, and remarkable improvement was observed in their performance.