kneedle

The goal of kneedle is to provide an easy to use implementation of the kneedle algorithm developed at https://raghavan.usc.edu/papers/kneedle-simplex11.pdf. The main functionality is to detect an inflection point, more commonly associated in continuous function, in discrete datasets.

Installation

You can install the development version from GitHub with:

install.packages("devtools")
devtools::install_github("etam4260/kneedle")

Example

This is a basic example:

library(kneedle)
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo

# The base function assumes the graph is both concave and increasing.
# First and second inputs must be vectors of integers or doubles.

plot(c(1,2,3,4,5,6), c(0,1,2,3,40,100), xlab = "x", ylab = "y", pch=21, col="blue", bg="lightblue", type = "b")

knee <- kneedle(c(1,2,3,4,5,6), c(0,1,2,3,40,100))
print(knee)
#> [1] 4 3

Parameters

This describes a few of the parameters that can be changed.

library(kneedle)
#Concavity parameter must be changed if the graph is convex. Furthermore, you 
#must specify if the y is increasing or decreasing as x increases. 

plot(c(1,2,3,4,5), c(0,20,40,41,42), xlab = "x", ylab = "y", pch=21, col="blue", bg="lightblue", type = "b")

knee <- kneedle(c(1,2,3,4,5), c(0,20,40,41,42), concave = FALSE, decreasing = FALSE)
print(knee)
#> [1]  3 40


plot(c(1,2,3,4,5), c(100,99,98,50,0), xlab = "x", ylab = "y", pch=21, col="blue", bg="lightblue", type = "b")

knee <- kneedle(c(1,2,3,4,5), c(100,99,98,50,0), concave = FALSE, decreasing = TRUE)
print(knee)
#> [1]  3 98

Sensitivity

This describes how the sensitivity parameter affects the output.

library(kneedle)
# Sensitivity defaults to 1 as per the referenced paper. However, you can adjust 
# it. A higher sensitivity make the rules more 'stringent' in classifying a 
# 'candidate knee' point as a knee. 

plot(c(1,2,3,4,5), c(0,1,2,40,60), xlab = "x", ylab = "y", pch=21, col="blue", bg="lightblue", type = "b")
knee <- kneedle(c(1,2,3,4,5), c(0,1,2,40,60), sensitivity = 1)
print(knee)
#> [1] 3 2

# In this case with sensitivity = 2, we see that that (3,2) is no longer considered a knee point. No
# other knees were detected.

plot(c(1,2,3,4,5), c(0,1,2,40,60), xlab = "x", ylab = "y", pch=21, col="blue", bg="lightblue", type = "b")

knee <- kneedle(c(1,2,3,4,5), c(0,1,2,40,60), sensitivity = 2)
print(knee)
#> numeric(0)