Detecting one or more inflection points in a simple numeric vector

Question

All,

I\'m looking for a reliable, unsupervised way to detect change points in a relatively short vector. Consider the following two examples:

v1 = c(0.         


        

Answer 1

So, this is a simple solution. You can modify the parameters to give you back different (more/fewer, sensitive/insensitive) inflection points (or areas, in the case of your data).

plot(v2, type="l", col="darkblue", lwd=2)
# v2 <- smooth(v2, kind="3")  # optional
lines(v2, lwd=1, col="red")
d2 <- diff(v2)
d2 <- d2>0
d2 <- d2*2 -1 
k <- 5
cutoff <- 10
scores <- sapply(k:(length(d2)-k), FUN=function(i){
  score <- abs(mean(-d2[ i-1:k ], na.rm=T) + mean(d2[ i+0:k ], na.rm=T))
})


scores <- sapply(k:(length(v2)-k), FUN=function(i){
  left <- (v2[sapply(i-1:k, max, 1) ]<v2[i])*2-1
  right <- (v2[sapply(i+1:k, min, length(v2)) ]<v2[i])*2-1

  score <- abs(sum(left) + sum(right))
})

inflections <- (k:(length(v2)-k))[scores>=cutoff]

plot(v2, type="l")
abline(v=inflections, col="red", lwd=3)
print(inflections) #  6 11 18 25 32 (missed 51, if you make cutoff=8 it'll catch it...)