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中文摘要：
提出一种基于共形几何代数与二次规划的分类器设计方法。从新的角度出发,讨论了运用共形几何代数理论来构造最优分类超球可分问题的可行性和简便性,首先介绍了基于共形几何代数的分类超球面的几何表示,并用此表示将二类最优分类超球面的可分问题转化二次规划的训练学习问题,在此基础上分析了多类分类器的设计和训练方法。该算法保留了最大分类间隔理论的优点,将二类最优平面可分推广到最优超球可分,简化了其运算复杂度,仿真实验表明,该学习算法简洁明确,对于算法的集成,提高效率有着很重要的意义。
英文摘要：
A classifier design method based on conformal geometric algebra and quadratic programming is proposed.From a new point of view,the probability and simplicity of using the conformal geometric algebra to design optimal separation hyersphere is discussed.A geometrical representation of separating hypersphere is firstly introduced based on conformal geometric algebra,by which the two-class optimal separation hyersphere separation problem may be transformed into the training problem based on quadratic programming.According to this,the design and training of multi-class classifier are analyzed.The algorithm not only keeps the advantages of maximizing the margin,generalizing the optimal separating hyperplane to optimal separating hypersphere,but also simplifies computational complexity.Simulation results show that the algorithm is compact and explicit,and the integrations of algorithm have an important significance in the improvement of efficiency.
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