  Top-k error is currently a popular performance measure on large scale image
classification benchmarks such as ImageNet and Places. Despite its wide
acceptance, our understanding of this metric is limited as most of the previous
research is focused on its special case, the top-1 error. In this work, we
explore two directions that shed more light on the top-k error. First, we
provide an in-depth analysis of established and recently proposed single-label
multiclass methods along with a detailed account of efficient optimization
algorithms for them. Our results indicate that the softmax loss and the smooth
multiclass SVM are surprisingly competitive in top-k error uniformly across all
k, which can be explained by our analysis of multiclass top-k calibration.
Further improvements for a specific k are possible with a number of proposed
top-k loss functions. Second, we use the top-k methods to explore the
transition from multiclass to multilabel learning. In particular, we find that
it is possible to obtain effective multilabel classifiers on Pascal VOC using a
single label per image for training, while the gap between multiclass and
multilabel methods on MS COCO is more significant. Finally, our contribution of
efficient algorithms for training with the considered top-k and multilabel loss
functions is of independent interest.
