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Method and apparatus for functional relationship approximation through nonparametric regression using R-functions

机译:使用R函数通过非参数回归进行函数关系近似的方法和装置

摘要

One embodiment of the present invention provides a system that constructs a functional relationship approximation from a set of data points through nonparametric regression. During operation, the system receives a training data set in an n-dimensional space. Next, the system defines a set of regression primitives in the n-dimensional space, wherein a regression primitive in the set passes through N data points in the training data set, wherein N≧n. The system then logically combines the set of regression primitives to produce a convex envelope F, such that for each point p in the n-dimensional space: (1) F(p)=0, if p is on the convex envelope; (2) F(p)0, if p is inside the convex envelope; and (3) F(p)0, if p is outside the convex envelope. The system next obtains the functional relationship approximation by computing an argument of the minimum of F in the n-dimensional space. The system subsequently uses the functional relationship approximation to classify data.
机译:本发明的一个实施例提供了一种通过非参数回归从一组数据点构造函数关系近似的系统。在操作过程中,系统会在n维空间中接收训练数据集。接下来,系统在n维空间中定义一组回归原语,其中该组中的回归原语穿过训练数据集中的N个数据点,其中N≥n。然后,系统在逻辑上组合回归图元集以生成凸包络F,从而对于n维空间中的每个点p:(1)F(p)= 0,如果p在凸包络上; (2)如果p在凸包络线内,则F(p)<0; (3)如果p在凸包络线之外,则F(p)> 0。接下来,系统通过计算n维空间中F的最小值的参数来获得函数关系近似值。系统随后使用函数关系近似对数据进行分类。

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