  Hierarchical classification problems are commonly seen in practice. However,
most existing methods do not fully utilize the hierarchical information among
class labels. In this paper, a novel label embedding approach is proposed,
which keeps the hierarchy of labels exactly, and reduces the complexity of the
hypothesis space significantly. Based on the newly proposed label embedding
approach, a new angle-based classifier is developed for hierarchical
classification. Moreover, to handle massive data, a new (weighted) linear loss
is designed, which has a closed form solution and is computationally efficient.
Theoretical properties of the new method are established and intensive
numerical comparisons with other methods are conducted. Both simulations and
applications in document categorization demonstrate the advantages of the
proposed method.

Methodology