| 摘要: |
| 通过ISE 准则逼近真实密度差的L2-核分类器没有显式地考虑到分类间隔,在一定程度上不利于提高分类器精度;同时,权向量的求解最终转化为一个二次规划问题,导致L2-核分类器训练速度较慢,特别是对于较大样本.基于这两个问题,利用样本间的密度差构造了分类间隔并最大化此间隔,而此问题最终转化为一个对数优化问题,故称其为最大间隔对数向量机(maximum margin logistic vector machine,简称MMLVM),进而利用梯度下降法求解最优权.同时,分别从权的全局最优性、一般化误差界及算法复杂度这3 方面进行了理论分析.最后,人工和UCI,PIE 及USPS 数据集的实验结果表明,算法理论正确,解决了上述两个问题并获得了较好的效果. |
| 关键词: 分类 最大间隔 对数向量机 核分类器 密度差 |
| DOI：10.3724/SP.J.1001.2012.04209 |
| 分类号: |
| 基金项目:国家自然科学基金(61170122, 61272210); 江苏省自然科学基金(BK2011003, BK201141); 江苏省“333 专家”工程(BRA2011142); 江西省自然科学基金(20114BAB201022); 2011 年、2012 年江苏省普通高校研究生科研创新计划 |
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| Maximum Margin Logistic Vector Machine |
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HU Wen-Jun1,2, WANG Shi-Tong1, WANG Juan2, YAN Qi-Sheng1,3
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1.School of Digital Media, Jiangnan University, Wuxi 214122, China;2.School of Information and Engineering, Huzhou Teachers College, Huzhou 313000, China;3.School of Mathematics and Information Science, East China Institute of Technology, Fuzhou 344000, China
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| Abstract: |
| The L2-kernel classifier does not consider explicitly its classification margin when approximating the difference of densities (DoD) with the integrated squared error (ISE) criterion of probability densities, which is disadvantageous for improving the performance of classifiers to a certain extent. Its weights can simply be obtained by solving the corresponding QP problem which results in the comparatively slow training speed and is impractical especially for large datasets. With the aim of overcoming the above drawbacks, a new classification method is proposed in this paper, called the maximum margin logistic vector machine (MMLVM), which maximizes the DoDbased classification margin and finds the corresponding weight vector by solving a logistic optimization problem in gradient descent way. The theoretical analysis is provided in the globally optimal weights, the generalization error bound, and in the computational complexity of MMLVM. Experimental results on the artificial, UCI, PIE and USPS data sets demonstrate the effectiveness of the proposed approach in overcoming the drawbacks as above. |
| Key words: classification maximum margin logistic vector machine kernel classifier difference of densities |
