Visualization Classifier Based On Geometric Algebra

In the process of pattern recognition, the most important problem is classifier design, in this problem we have to consider the decision function selection and parameter acquisition which may have influence on classification result. So in this paper, it is researched visualization classifier based on geometric algebra which is according to the property of the geometric product to solve the above questions.Firstly, it is studyed trigonometric classifier. This classifier makes use of the outer product to judge a point’s category, and without parameters’effects. This method is applied to four groups datasets of UCI Dataset, and then compared with other commonly used classifiers. Experiments show that proposed trigonometric classifier has better effect of classifying, especially under the premise of using the same projection mode.Secondly, trigonometric classifier is extended to3D space. In3D space, the outer product of geometric algebra is formed an oriented volume, usually referred to as handedness. The four groups datasets of UCI Dataset is still used in this experiment, and the results show that accodding to the characteristics of the distribution of datasets, because of the data in3D space has more comprehensive information than that in2D space, and so that makes the classifier in3D space and2D space has different performance.Finally, put the visual classifier based on geometric algebra to the brain computer interface technology. Geometric algebra has been successfully extended to signal processing, feature extraction and pattern recognition, and in this paper, it is the first applied geometric algebra to brain computer interface. This method is applied to three groups datasets of BCI Competition Dataset, which were BCI Ⅰ, BCⅠⅡ_Ⅳ, BCI Ⅲ₃a, experiments show that the result of the visual classifier based on geometric algebra is the same as other common classifiers, and particular for BCI Ⅲ₃a, solves over-fitting compared with logistic linear classifier.