Hierarchical classification is critical to knowledge management and exploration, as is gene function prediction and document categorization. In hierarchical classification, an input is classified according to a structured hierarchy. In such a situation, the central issue is how to effectively utilize the interclass relationship to improve the generalization performance of flat classification ignoring such dependency. In this article, we propose a novel large margin method through constraints characterizing a multipath hierarchy, where class membership can be nonexclusive. The proposed method permits a treatment of various losses for hierarchical classification. For implementation, we focus on the symmetric difference loss and two large margin classifiers: support vector machines and ψ-learning. Finally, theoretical and numerical analyses are conducted, in addition to an application to gene function prediction. They suggest that the proposed method achieves the desired objective and outperforms strong competitors in the literature.
Bibliographical noteFunding Information:
Junhui Wang is Assistant Professor, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607 (E-mail: email@example.com). Xiaotong Shen is Professor, School of Statistics, University of Minnesota, Minneapolis, MN 55455 (E-mail: firstname.lastname@example.org). Wei Pan is Professor, Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455 (E-mail: email@example.com). The authors thank the editor, the associate editor, and two referees for their helpful comments and suggestions. This work is supported in part by NSF grant DMS-0604394, NIH grant 1R01GM081535-01 and the Supercomputing Institute at University of Minnesota.
- Directed acyclic graph
- Functional genomics
- Structured learning