  In order to push the performance on realistic computer vision tasks, the
number of classes in modern benchmark datasets has significantly increased in
recent years. This increase in the number of classes comes along with increased
ambiguity between the class labels, raising the question if top-1 error is the
right performance measure. In this paper, we provide an extensive comparison
and evaluation of established multiclass methods comparing their top-k
performance both from a practical as well as from a theoretical perspective.
Moreover, we introduce novel top-k loss functions as modifications of the
softmax and the multiclass SVM losses and provide efficient optimization
schemes for them. In the experiments, we compare on various datasets all of the
proposed and established methods for top-k error optimization. An interesting
insight of this paper is that the softmax loss yields competitive top-k
performance for all k simultaneously. For a specific top-k error, our new top-k
losses lead typically to further improvements while being faster to train than
the softmax.
