基于VB与MatrixVB的最优分类超球面实现

Realization of Optimal Separation Hypersphere Based on VB and MatrixVB

提出了一种基于共形几何代数最优分类超球面的表示方法;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;介绍了基于共形几何代数的分类超球面几何表示,并用此表示将二类最优分类超球面的可分问题转化为二次规划的训练学习问题,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。另外针对Visual Basic数值计算能力的不足,不利于系统开发,介绍了基于VB和MatrixVB实现最优分类超球面,该方法将Matlab的强大计算功能与VB的Windows用户界面的开发优势结合起来,充分发挥了各自的特点,缩短了软件的开发周期。软件测试结果表明,计算方法正确,计算速度快,系统资源消耗少,操作简便易行,能满足数据分类的要求。

An optimal separation hypersphere algorithm based on conformal geometric algebra is introduced. The proba bility and simplicity of using the conformal geometric algebra to design optimal separation hypersphere are discussed firstly. A geometrical representation of separating hypersphere is introduced based on conformal geometric algebra, by which the two- class optimal separation hypersphere separation problem may be transformed into the training problem based on quadratic pro- gramming. The algorithm not only kept the advantages of maximising the margin, but also generalized the optimal separating hyperplane to optimal separating hypersphere. According to the situation that Visual Basic is insufficient in numerical compu tation ability, and is weak in algorithm development, the realization of optimal separation hypersphere algorithm is introduced by incorporating VB and MatrixVB. The incorporated advances of Matlab＇s powerful calculation function and Visual Basic＇s friendly graphic user interface shorten the period of software development by taking the advantages of both. It has been demonstrated by the instance that the calculating procedure is accurate. The software interface is friendly. Beside this, the re source expenditure of computer is low and the calculating speed is quick, the software is convenient to use. It can fulfill the classification problem well.