Curve Fitting 3D 数据集 [英] Curve Fitting 3D data set
问题描述
2D 数据的曲线拟合问题是众所周知的(LOWESS 等)，但给定一组 3D 数据点，我如何将 3D 曲线(例如平滑/回归样条)拟合到该数据?
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，拟合由没有已知关系的向量 X、Y、Z 提供的数据.本质上，我有一个 3D 点云，需要找到 3D 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.
MORE:对于含糊不清，我深表歉意.我尝试了几种方法(我还没有尝试修改线性拟合)，随机神经网络似乎效果最好.即，我从点云中随机选择一个点，找到它的邻居的质心(在任意球体内)，迭代.连接质心以形成平滑样条被证明是困难的，但获得的质心是可以通过的.
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.
为了澄清问题，数据不是时间序列，我正在寻找最能描述点云的平滑样条，即，如果我将此 3D 样条投影到由任意 2 个变量形成的平面上，则投影样条(到 2D 上)将是投影点云(到 2D 上)的平滑拟合.
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:我添加了一张图片.红点代表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.
3D 点云和局部质心 http://img510.imageshack.us/img510/2495/40670529.jpg
推荐答案
您可以尝试加法(即单索引模型)，如 GAMhttp://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
这是一种贪婪的方法，非常可扩展，在几个 R 包中得到了很好的实现
it's a greedy approach, very scalable, well implemented in several R packages
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