Research On Feature Extraction And Support Vector Machine Based On Geometric Algebra

Clifford algebra is an algebraic system which is deeply rooted in the geometry. It isnamed as geometric algebra by its founder. Geometric algebra (Clifford algebra) is acombination of inner product and cross product. As a mathematical discipline, Cliffordalgebra relate to geometry and physics. Now geometric algebra to solve the problem: fromquantum computing and the electromagnetic wave to satellite navigation, from neuralnetworks to camera geometry, image processing and robot, etc. Machine learning forhigh-dimensional space has always been the hot topic of research. This article is mainly tosolve the feature selection of geometric algebra and applied to pattern recognition andpattern classification. we do the following research work:First of all, it was proposed in this paper that using the combination of particle swarmalgorithm and geometric algebra to solve feature ranking and feature selection based ongeometric algebra feature. Using geometric product, geometry data sets will be transformfrom ascending dimensions to dimension reduction, which is feature selection. Forgeometric algebra feature ranking, we adopted the iris, glass, Breast-cancer-wisconsin,Pima-indians diabetes, wine, Bupa liver-disorders of the six groups of data in UCIdatabase for simulation experiments, the classification error rate:1.73%,28.9%,2.92%,0,23.4%,27.1%. For geometric algebra feature selection, classification error rate:1.93%,26.6%,2.93%,0,22.2%,26.8%. That results are better than just normalized features. Thusthis method was proved to be feasible.Second, real support vector machine mainly solve the classification problem. Themulti-class classification problem has become a key research object. Real support vectormachine (SVM) to solve many problems mainly constructs multiple classifier, thusinevitably exist many problems: calling quadratic programming function many times,anddecrease the complexity add complexity, and so on. This paper carry out that calling aquadratic programming function, decrease the complexity, and solve the problem ofmulti-class by using geometric algebra support vector machine (SVM) This paperconstructs the geometric algebra radial basis function, and realize classification problem of the nuclear space. Experimental results show that the proposed method and the realsupport vector machine reach the same level. So prove that methods are proposed in thispaper is feasible.