Geometric programming for aggregation of binary classifiers

Multiclass classification problems are often decomposed into multiple binary problems that are solved by individual binary classifiers whose results are integrated into a final answer. We present a convex optimization-based method for aggregating results of binary classifiers in an optimal way to estimate class membership probabilities. We model the class membership probability as a softmax function whose input argument is a conic combination of discrepancies induced by individual binary classifiers. With this model, we formulate the ℓ1-regularized maximum likelihood estimation as a convex optimization that is solved by geometric programming. Numerical experiments on several UCI datasets demonstrate the high performance of our method, compared to existing methods.