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An Exact Penalty Method for Top-k Multiclass Classification Based on L0 Norm Minimization

Top-k multiclass classification is one of the central problems in machine learning and computer vision. It aims at classifying instances into one of three or more classes and allows k guesses to evaluate classifiers based on the top-k error. However, existing solutions either simply ignore the specific structure of the top-k error by directly solving the top-1 error minimization problem or consider convex relaxation approximation for the original top-k error model. In this paper, we formulate the top-k multiclass classification problem as an ℓ0 norm minimization problem. Although the model is NP-hard, we reformulate it as an equivalent mathematical program with equilibrium constraints and consider an exact penalty method to solve it. The algorithm solves a sequence of convex optimization problems to find a desirable solution for the original nonconvex problem. Finally, we demonstrate the efficacy of our method on some real-world data sets. As a result, our method achieves state-of-the-art performance in term of accuracy