我有如下曲线:
可以看出，上面有两条上下界曲线(大致可视化见下图!):
我试图通过以下代码找到下界:
lower_bound = rbind()
for(i in 2:(length(data[,1])-1))
{
if(data[i,2] < data[i+1,2] && data[i,2] < data[i-1,2])
{
lower_bound = rbind2(lower_bound, c(data[i,1], data[i,2]))
}
}
但是，问题是中间有一些局部极小值，所以结果不是我所期望的(如下所示)。
因此问题是如何在 R 中找到这种曲线的下界？有没有已知的算法可以找到下界？
关于最小的可重现示例，我在下面包含了 500 个数据(为了有意义):
structure(c(3.54246575342466, 5.75616438356164, 6.54246575342466,
9.73424657534247, 7.75616438356164, 9.75616438356164, 1.41917808219178,
2.75342465753425, 3.16986301369863, 2.27123287671233, 3.74520547945205,
5.74520547945205, 4.29315068493151, 3.37260273972603, 8.37534246575343,
3.33698630136986, 5.04657534246575, 6.92328767123288, 1.33972602739726,
6.34246575342466, 26.358904109589, 2.34794520547945, 4.35068493150685,
7.35342465753425, 27.3671232876712, 1.15068493150685, 2.14794520547945,
4.15342465753425, 6.15342465753425, 9.15616438356164, 19.1616438356164,
29.1698630136986, 2.58904109589041, 4.5972602739726, 9.6, 29.613698630137,
3.10684931506849, 8.11780821917808, 3.35068493150685, 8.37260273972603,
5.11506849315068, 28.1315068493151, 5.36986301369863, 28.386301369863,
4.87945205479452, 4.46027397260274, 5.35616438356164, 25.3698630136986,
25.8684931506849, 5.85479452054795, 1.85205479452055, 4.37260273972603,
6.37260273972603, 9.37534246575343, 19.3835616438356, 29.3890410958904,
18.3808219178082, 1.36986301369863, 8.37534246575343, 3.37260273972603,
5.85479452054795, 28.3890410958904, 2.87671232876712, 4.87945205479452,
7.37808219178082, 8.17260273972603, 28.186301369863, 4.29315068493151,
6.96164383561644, 26.3479452054795, 7.96438356164384, 1.53972602739726,
1.58630136986301, 5.04657534246575, 16.6356164383562, 18.4684931506849,
25.0602739726027, 15.6493150684932, 24.8547945205479, 25.3506849315068,
26.1068493150685, 16.0547945205479, 2.16712328767123, 19.2657534246575,
20.6849315068493, 1.04383561643836, 3.04383561643836, 23.0575342465753,
3.29315068493151, 4.13150684931507, 2.04383561643836, 22.0575342465753,
22.8904109589041, 2.87671232876712, 5.54246575342466, 25.5561643835616,
1.04931506849315, 6.05205479452055, 26.0657534246575, 2.09041095890411,
7.09315068493151, 27.1068493150685, 2.09041095890411, 4.09315068493151,
6.09315068493151, 9.0958904109589, 19.1013698630137, 29.1095890410959,
1.83287671232877, 1.42739726027397, 3.43013698630137, 9.3041095890411,
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23.4219178082192, 8.21095890410959, 3.20821917808219, 5.20821917808219,
18.8027397260274, 19.8054794520548, 21.7232876712329, 2.25205479452055,
22.8054794520548, 24.4301369863014, 4.41643835616438, 25.2684931506849,
5.25479452054795, 6.33698630136986, 26.3506849315068, 2.87671232876712,
4.29315068493151, 2.78630136986301, 1.2958904109589, 1.75890410958904,
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最佳答案
相对简单的实现，可以尝试如下:
考虑具有恒定宽度的连续数据切片。宽度必须大于最大间隙。
构造点的上下船体，使用Monotone Chain算法(不用排序，你的点已经是横坐标递增)。 https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain
对于切片中的中间横坐标，估计凸包上的两个纵坐标(通过识别特定横坐标处的包边缘)。通过扫掠，这将创建所需的曲线。在范围的两端，使用第一个和最后一个半切片中的所有横坐标。
在曲率高和/或窗口大的地方会有一个小的向下偏差，但没有人是完美的。
总运行时间将与点数和窗口宽度的乘积成正比。但我想增量版本可以做得更好。
关于r - 曲线的下界，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/47342502/