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对于线性不可分的样本怎么办？ 非线性可分情形 如何找到正确的分类曲线和正确的超平面对此类情况分类? 非线性可分情形 关键点: 把 xi 变换到高维的特征空间 为什么要变换？ 通过加入一个新的特征xi，使得样本变成线性可分的，此时特征空间维数变高 Transform x ? ?(x) 例子 a x12+b x22=1 [w]1 z1+ [w]2z2 + [w]3 z3+ b =0 设训练集 ，其中 假定可以用 平面上的二次曲线来划分： 现考虑把2维空间 映射到6维空间的变换 上式可将2维空间上二次曲线映射为6维空间上的一个超平面： 非线性分类 可见，只要利用变换，把 x 所在的2维空间的两类输入点映射x 所在的6维空间，然后在这个6维空间中，使用线性学习机求出分划超平面： 最后得出原空间中的二次曲线： 非线性分类 如何选择到较高维空间的非线性映射？给定的检验元组，必须计算与每个支持向量的点积，出现形如 可以引入核函数（内积的回旋）来替代 需要求解的最优化问题 非线性分类 最后得到决策函数 或 为此，引进函数 理学院 武汉理工大学 8 We have seen a thorough overview of the BusinessObjects technology and benefits. What are the key points of this technology? Firstly, BusinessObjects is the recognized industry leader ?the safe choice, with over 150,000 users in over 40 different countries worldwide. BusinessObjects is the only fully integrated query, reporting and analysis solution. This means that it抯 the easiest tool for end users, who can drill straight on reports and so don抰 have to waste time swapping between tools and interfaces, and IS don抰 have to spend time and money transforming data manually. BusinessObjects is the most enterprise deployable tool, because of its central repository, advanced security controls and openness. Finally, BusinessObjects is a decision support tool that anyone in your organization can use, from full analysis users to 搑eport readers,?EIS-style interface users and even spreadsheet users using BusinessQuery for Excel. Thank you very much. We have seen a thorough overview of the BusinessObjects technology and benefits. What are the key points of this technology? Firstly, BusinessObjects is the recognized industry leader ?the safe choice, with over 150,000 users in over 40 different countries worldwide. BusinessObjects is the only fully integrated query, reporting and analysis solution. This means that it抯 the easiest tool for end users, who can drill straight on reports and so don抰