| 摘要: |
| 支撑向量数据域描述(support vector data description,简称SVDD)作为一种已经得到广泛应用的核方法,研究主要集中在其性能和效率的提高上,然而该算法优化问题最优解性质的理论性质却没有得到足够的关注.,首先把SVDD 定义的原始优化问题等价转化为一个凸约束二次优化问题,然后从理论上证明了其构建的超球具有唯一性,然而超球半径在一定条件下却存在不唯一性,并且给出了半径存在不唯一性的充分必要条件.还从优化问题的角度分析了超球的圆心和半径性质,并且给出了SVDD 算法中在根据优化问题最优解构建超球半唯一情况下计算超球半径的方法.完善了该算法的理论和方法体系,从而为其更深入的研究和应用奠定了理础. |
| 关键词: 核方法 支撑向量数据域描述 凸优化 唯一性 |
| DOI：10.3724/SP.J.1001.2011.03856 |
| 分类号: |
| 基金项目:国家自然科学基金(60773206, 60903100, 60975027, 90820002); 江苏省自然科学基金(BK2009067) |
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| Theoretical Analysis for the Optimization Problem of Support Vector Data Description |
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WANG Xiao-Ming, WANG Shi-Tong
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School of Information, Jiangnan University, Wuxi 214122, China
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| Abstract: |
| A majority of previous research done on Support Vector Data Description (SVDD), which is one of the
excellent and applied widely to kernel methods, were directed toward efficient implementations and practical
applications. However, very few research attempts have been directed toward studying the properties of SVDD
solutions. In this work, the primal optimization of SVDD is first transformed into a convex constrained optimization
problem, and the uniqueness of the centre of ball is proved while the non-uniqueness of the radius is investigated.
This paper also investigates the property of the centre and radius from the perspective of the dual optimization
problem, and suggests a method to calculate the radius. The results of this paper complete the SVDD theory, and
contribute to further theoretical study and extensive applications. |
| Key words: kernel method support vector data description convex optimization uniqueness |
