R: Elbow/knee points in Scatterplot

Question

I need to identify the two elbow points in a curve with R. The curve isn't a real curve, but consists out of three linear functions. The linear functions themselfes are unknown. I've already tried different approaches, but none of them was able to identfiy the correct points. Does anyone know a solution?

Answer 1

You could look at the slope of the line and see where it changes:

fake <- data.frame(x = c(1:9, 10*1:5, 50*2:5),
                   y = c(10:2, 0.1*10:6, 0.01*59:56))
plot(fake)

# diff compares each value to the prior row. Undefined for first row so I add NA at the start
fake$slope = c(NA, diff(fake$y)/diff(fake$x))
fake$slope_chg = c(NA, round(diff(fake$slope),5))
fake$change = ifelse(fake$slope_chg != 0, "change","")

Result

     x     y  slope slope_chg change
1    1 10.00     NA        NA   <NA>
2    2  9.00 -1e+00        NA   <NA>
3    3  8.00 -1e+00    0.0000       
4    4  7.00 -1e+00    0.0000       
5    5  6.00 -1e+00    0.0000       
6    6  5.00 -1e+00    0.0000       
7    7  4.00 -1e+00    0.0000       
8    8  3.00 -1e+00    0.0000       
9    9  2.00 -1e+00    0.0000       
10  10  1.00 -1e+00    0.0000       
11  20  0.90 -1e-02    0.9900 change
12  30  0.80 -1e-02    0.0000       
13  40  0.70 -1e-02    0.0000       
14  50  0.60 -1e-02    0.0000       
15 100  0.59 -2e-04    0.0098 change
16 150  0.58 -2e-04    0.0000       
17 200  0.57 -2e-04    0.0000       
18 250  0.56 -2e-04    0.0000