  Class ambiguity is typical in image classification problems with a large
number of classes. When classes are difficult to discriminate, it makes sense
to allow k guesses and evaluate classifiers based on the top-k error instead of
the standard zero-one loss. We propose top-k multiclass SVM as a direct method
to optimize for top-k performance. Our generalization of the well-known
multiclass SVM is based on a tight convex upper bound of the top-k error. We
propose a fast optimization scheme based on an efficient projection onto the
top-k simplex, which is of its own interest. Experiments on five datasets show
consistent improvements in top-k accuracy compared to various baselines.
