  The objective in extreme multi-label learning is to train a classifier that
can automatically tag a novel data point with the most relevant subset of
labels from an extremely large label set. Embedding based approaches make
training and prediction tractable by assuming that the training label matrix is
low-rank and hence the effective number of labels can be reduced by projecting
the high dimensional label vectors onto a low dimensional linear subspace.
Still, leading embedding approaches have been unable to deliver high prediction
accuracies or scale to large problems as the low rank assumption is violated in
most real world applications.
  This paper develops the X-One classifier to address both limitations. The
main technical contribution in X-One is a formulation for learning a small
ensemble of local distance preserving embeddings which can accurately predict
infrequently occurring (tail) labels. This allows X-One to break free of the
traditional low-rank assumption and boost classification accuracy by learning
embeddings which preserve pairwise distances between only the nearest label
vectors.
  We conducted extensive experiments on several real-world as well as benchmark
data sets and compared our method against state-of-the-art methods for extreme
multi-label classification. Experiments reveal that X-One can make
significantly more accurate predictions then the state-of-the-art methods
including both embeddings (by as much as 35%) as well as trees (by as much as
6%). X-One can also scale efficiently to data sets with a million labels which
are beyond the pale of leading embedding methods.
