  Machine learning has played an important role in information retrieval (IR)
in recent times. In search engines, for example, query keywords are accepted
and documents are returned in order of relevance to the given query; this can
be cast as a multi-label ranking problem in machine learning. Generally, the
number of candidate documents is extremely large (from several thousand to
several million); thus, the classifier must handle many labels. This problem is
referred to as extreme multi-label classification (XMLC). In this paper, we
propose a novel approach to XMLC termed the Sparse Weighted Nearest-Neighbor
Method. This technique can be derived as a fast implementation of
state-of-the-art (SOTA) one-versus-rest linear classifiers for very sparse
datasets. In addition, we show that the classifier can be written as a sparse
generalization of a representer theorem with a linear kernel. Furthermore, our
method can be viewed as the vector space model used in IR. Finally, we show
that the Sparse Weighted Nearest-Neighbor Method can process data points in
real time on XMLC datasets with equivalent performance to SOTA models, with a
single thread and smaller storage footprint. In particular, our method exhibits
superior performance to the SOTA models on a dataset with 3 million labels.
