精确的增量式支持向量机的研究

Since Vapnik et al. proposed the the Support Vector Machines (SVMs) in the mid 1990s, SVMs have become a popular technique for solving classification, regression and other key problems in machine learning due to having many good characteristics (e.g., the generality, the robustness, the good generalization capacity and so on). However, in practical applications, the training data is usually provided one example at a time, which is the so called online scenario. If the size of the training data is very large, and the distribution of the data varies over time, batch algorithms will generally fail due to the recomputation for all training data. Bacause the exact incremental algorithm of Support Vector Machine will not only provide a feasible approach for tackling on-line learning of SVMs in practical applications, but also can offer an feasible method for addressing model selection, leave-one-out error estimation, resource constrained learning and other key problems of SVMs, the exact incremental algorithm of Support Vector Machine is more suitable for this case.This study will focuse on addressing the shortcomings of the robustness, the algorithm framework, the theoretical analysis and the range of problem-solving for the accurate incremental Support Vector Machines. Especially, the work of the theoretical analysis to verify the feasibility and finite convergence of the accurate incremental Support Vector Machines, will make the field researchers having a more comprehensive and in-depth understanding to the features of the accurate incremental SVMs. On this basis, we will further improve the algorithm framework of accurate incremental SVMs, and design the accurate incremental algorithms for the ν-Support Vector Classification, ν-Support Vector Regression, Multi-class Support Vector Machine and Ordinal Regression Support Vector Machine, respectively.

自Vapnik等人提出支持向量机以来，由于其通用性、鲁棒性以及良好推广性等特点，已经成为机器学习领域解决分类、回归等问题一种流行的技术。然而在实际问题环境中，训练数据大都在线提供，当数据量较大且数据分布随着时间变化而变化，批处理算法将因重新计算而失效，而精确增量式算法不仅可以有效解决实际环境中存在的在线支持向量机学习，还可以对支持向量机的模型选择、留一误差估计、资源受限学习等重要问题的解决提供一种可行的技术路线。本课题将致力于完善精确增量式支持向量机算法目前在健壮性、框架设计、理论分析以及求解问题范围方面上的缺失。特别是通过理论分析验证算法的可行性与有限收敛性，使领域研究者对精确增量式支持向量机的特性有更全面和深入的认识，在此基础上，进一步完善精确增量式支持向量机算法框架，并针对ν支持向量分类机，ν支持向量回归机，多类分类支持向量机以及有序回归支持向量机设计相应的精确增量式算法。

自Vapnik等人提出支持向量机以来，由于其通用性、鲁棒性以及良好推广性等特点，已经成为机器学习领域解决分类、回归等问题一种流行的技术。本课题主要针对在线环境，展开精确的增量式支持向量机学习的研究。主要研究结果：1）本课题首次针对ν支持向量回归机设计了相应的精确增量式算法；2）本课题首次针对有序回归问题给出了相应的精确增量式支持向量机；3）本课题首次针对代价敏感支持向量机给出了相应的精确增量式支持向量机；4）本课题针对一类分类支持向量机给出相应的增量式算法；5）本课题针对精确增量式算法给出算法的可行性与有限收敛性分析。相关的工作发表在国际主流机器学习期刊，在一定程度上促进了国际上相关学者对精确的增量式支持向量机算法的认识与理解，促进了增量式算法的使用范围。