Locally Non-linear Embeddings for Extreme Multi-label Learning

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 X1 classifier to address both limitations. The main technical contribution in X1 is a formulation for learning a small ensemble of local distance preserving embeddings which can accurately predict infrequently occurring (tail) labels. This allows X1 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 X1 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%). X1 can also scale efficiently to data sets with a million labels which are beyond the pale of leading embedding methods.