Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 26, Issue 7, Pages 1403-1416Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2014.2342533
Keywords
Incremental learning; online learning; ordinal regression (OR); support vector machine (SVM)
Categories
Funding
- Priority Academic Program Development, Jiangsu Higher Education Institutions
- U.S. National Science Foundation [IIS-1115417]
- National Natural Science Foundation of China [61232016, 61202137]
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [1115417] Funding Source: National Science Foundation
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Support vector ordinal regression (SVOR) is a popular method to tackle ordinal regression problems. However, until now there were no effective algorithms proposed to address incremental SVOR learning due to the complicated formulations of SVOR. Recently, an interesting accurate on-line algorithm was proposed for training nu-support vector classification (nu-SVC), which can handle a quadratic formulation with a pair of equality constraints. In this paper, we first present a modified SVOR formulation based on a sum-of-margins strategy. The formulation has multiple constraints, and each constraint includes a mixture of an equality and an inequality. Then, we extend the accurate on-line nu-SVC algorithm to the modified formulation, and propose an effective incremental SVOR algorithm. The algorithm can handle a quadratic formulation with multiple constraints, where each constraint is constituted of an equality and an inequality. More importantly, it tackles the conflicts between the equality and inequality constraints. We also provide the finite convergence analysis for the algorithm. Numerical experiments on the several benchmark and real-world data sets show that the incremental algorithm can converge to the optimal solution in a finite number of steps, and is faster than the existing batch and incremental SVOR algorithms. Meanwhile, the modified formulation has better accuracy than the existing incremental SVOR algorithm, and is as accurate as the sum-of-margins based formulation of Shashua and Levin.
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