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›› 2010, Vol. 25 ›› Issue (4): 699-708.

• Special Section on Advances in Machine Learning and Applications •

### Ordinal-Class Core Vector Machine

Bin Gu1(顾 彬), Jian-Dong Wang1(王建东), and Tao Li2(李 涛)

1. 1. Department of Computer Science and Engineering, Nanjing University of Aeronautics and Astronautics Nanjing 210016, China
2. College of Electronic and Information Engineering, Nanjing University of Information Science and Technology Nanjing 210044, China
• Received:2009-04-05 Revised:2010-01-18 Online:2010-07-09 Published:2010-07-09
• About author:
Bin Gu is currently a Ph.D. candidate in computer science in Nanjing University of Aeronautics and Astronautics. He received the B.S. degree in 2005 from Nanjing University of Aeronautics and Astronautics. In the same year, he was admitted to study for an M.Sc. degree in Nanjing University of Aeronautics and Astronautics without entrance examination. His research interests focus on machine learning and data mining.
Jian-Dong Wang graduated from Radio Department of Shanghai Jiaotong University in 1967. He is now a professor and Ph.D. supervisor of the College of Information Science and Technology, NUAA. His research interests include machine learning, data mining and information security.
Tao Li is currently a Ph.D. candidate in in computer science in Nanjing University of Aeronautics and Astronautics. He received his B.S. degree in computer science and M.S. degree in system analysis and integration from Nanjing University of Information Science and Technology, in 1999 and 2002 respectively. His research interests include recommender system and machine learning.
• Supported by:

This work was supported by the National High-Tech Research and Development 863 Program of China under Grant No. 2006AA12A106.

Ordinal regression is one of the most important tasks of relation learning, and several techniques based on support vector machines (SVMs) have also been proposed for tackling it, but the scalability aspect of these approaches to handle large datasets still needs much of exploration. In this paper, we will extend the recent proposed algorithm Core Vector Machine (CVM) to the ordinal-class data, and propose a new algorithm named as Ordinal-Class Core Vector Machine (OCVM). Similar with CVM, its asymptotic time complexity is linear with the number of training samples, while the space complexity is independent with the number of training samples. We also give some analysis for OCVM, which mainly includes two parts, the first one shows that OCVM can guarantee that the biases are unique and properly ordered under some situation; the second one illustrates the approximate convergence of the solution from the viewpoints of objective function and KKT conditions. Experiments on several synthetic and real world datasets demonstrate that OCVM scales well with the size of the dataset and can achieve comparable generalization performance with existing SVM implementations.

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