通过分析同类数据点在空间中的几何形态,从数据点集所构成几何形态的凹凸性着手,提出边界提取算法并对高维数据进行分类.针对现实生活中的高维数据,利用局部线性嵌入将数据进行降维处理,得到低维特征数据.在此基础上,对于单分类数据集,用数据集表面的点的近邻样本与过该点的切平面之间的关系寻找边界点;对于多分类数据集,利用贝叶斯后验概率来寻找边界重复的点,以此更快达到提取边界点的目的.由此可以粗略筛选出边界点.为去除不重要的边界点,降低分类误差,通过构造最优超平面和支持向量机对边界点赋予权重,并设置阈值去除不重要的边界点,由此达到用较少的边界点准确分类数据的目的.通过100个测试样本进行分类测试并计算其分类准确率,验证了此分类方法的可行性.%Based on the analysis on geometry of same data space and its concave-convex shape,the boundary extraction algorithm is proposed in order to classify high-dimensional data.Locally linear embedding is used to reduce high-dimensional data in real life into low dimension.For a single classification data set,relation between the neighboring points on the surface of data set with its tangent plane is used to determine the boundary point.For multi-classification data set,those overlap points are determined through Bayesian posterior probability so as to extract boundary point quickly.In this way,the boundary point is roughly dressed by screening.In order to remove unimportance boundary point and reduce classification error,weight is given to these boundary points by constructing optimal hyper-sphere and support vector machine.At the same time,a threshold is set to remove unimportance boundary point so as to obtain less boundary point data for the purpose of accurate classification.Finally,100 test samples are classified through this way and its feasibility is verified by calculating its classification accuracy.
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