判定一点是否属于高维复杂形体的算法及其应用

Algorithms of Determining Whether or not One Point is Within a High Dimension Complicated Geometrical Body and Its Application

许多模式识别问题都可以归结为判定一点是否属于高维满意覆盖体的问题,在传统的解析几何框架内判定一点是否属于高维(数百维以上)凸包络的并的问题是不适定难题。把高维凸包络的并视为同类事物特征在高维空间中形成的复杂几何形体的满意覆盖,给出了判定一点是否属于高维凸包络的并的有效算法,变通地解决了一个在传统的解析几何框架内直接计算的不适定难题。模式识别应用实验结果显示,对以6 400个样本作为正确识别集的测试样本,识别率为99.87%,表明该算法实用有效。

Many pattern recognition problems can be reduced to determining whether or not one point is within a high dimension satisfied coverage. Deciding whether or not a high dimension （over 100 dimension） point is within the collection of convex envelope is a problem difficult to solve within the framework of the traditional analytic geometry. In this paper a collection of high dimension convex envelope is regarded as the satisfied coverage of the complicated geometrical body formed by characteristics of the same type things in high dimension space, and an effective algorithm of determining whether or not one point is within collection of high dimension convex envelope is given. The alternative algorithm solves the difficult problem of a direct calculation within the traditional analytic geometry. Pattern recognition experiments show that the recogniton is 99.87% for the 6 400 samples as the testing samples of the correct recognition set, so the algorithm is practical and effective.