对于二维数据曲线拟合的问题是众所周知的（LOWESS等），但给出一组三维数据点，我怎么适合3D曲线（如：平滑/回归样条），以这个数据？

The curve-fitting problem for 2D data is well known (LOWESS, etc.) but given a set of 3D data points, how do I fit a 3D curve (eg. a smoothing/regression spline) to this data?

更多：我试图找到一条曲线，装修用向量X，Y，Z它们没有已知的关系提供的数据。从本质上讲，我有一个三维点云，并需要找到一个3D的趋势线。

MORE: I'm trying to find a curve, fitting the data provided by vectors X,Y,Z which have no known relation. Essentially, I have a 3D point cloud, and need to find a 3D trendline.

更多：我的含糊道歉。我试了几种方法（我还没有尝试过修改线性拟合）和随机NN似乎制定出最好的。也就是说，我随机选择的点云的点，找到它的邻国的心（内任意球），迭代。连接重心，形成光滑样条线已经被证明是困难的，但获得的重心还说得过去。

MORE: I apologize for the ambiguity. I tried several approaches (I still haven't tried modifying the linear fit) and a random NN seems to work out best. I.e., I randomly pick a point from the point cloud, find the centroid of it's neighbors (within an arbitrary sphere), iterate. Connecting the centroids to form a smooth spline is proving to be difficult but the centroids obtained is passable.

要弄清这个问题，数据不是一个时间序列，我正在寻找一个平滑的样条曲线最能说明点云也就是说，如果我是项目的任何2个变量构成的平面这款3D样条曲线中，预计花键（到2D）将投影点云的平滑贴合（到2D）。

To clarify the problem, the data is not a time series and I'm looking for a smooth spline which best describes the point cloud I.e., if I were to project this 3D spline on a plane formed by any 2 variables, the projected spline (onto 2D) will be a smooth fit of the projected point cloud (onto 2D).

IMG：我已经包含一个图像。红色点重新present从上述方法获得的质心。

IMG: I've included an image. The red points represent the centroid obtained from the aforementioned method.

推荐答案

您可以尝试添加剂（即单指数模型），因为GAM http://www-stat.stanford.edu/software/gam/index.html

You could try additive (i.e single index models), as GAM http://www-stat.stanford.edu/software/gam/index.html

这是一个贪婪的方法，可伸缩性非常大，在一些R封装以及实施

it's a greedy approach, very scalable, well implemented in several R packages