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This paper presents a deterministic solution to an approximated classification-error based objectivefunction. In the formulation, we propose a quadratic approximation as the function for achieving smootherror counting. The solution is subsequently found to be related to the weighted least-squares wherebya robust tuning process can be incorporated. The tuning traverses between the least-squares estimateand the approximated total-error-rate estimate to cater for various situations of unbalanced attributedistributions. By adopting a linear parametric classifier model, the proposed classification-error basedlearning formulation is empirically shown to be superior to that using the original least-squares-errorcost function. Finally, it will be seen that the performance of the proposed formulation is comparableto other classification-error based and state-of-the-art classifiers without sacrificing the computationalsimplicity.
Pattern Classification, Classification Error Rate, Discriminant Functions, Polynomials andMachine Learning

K. Toh and H. Eng, "Between Classification-Error Approximation and Weighted Least-Squares Learning," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 30, no. , pp. 658-669, 2007.
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