Kendall: Kendall's tau kernel

In kerntools: Kernel Functions and Tools for Machine Learning Applications

Kendall's tau kernel

Description

‘Kendall()' computes the Kendall’s tau, which happens to be a kernel function for ordinal variables, ranks or permutations.

Usage

Kendall(X, NA.as.0 = TRUE, samples.in.rows = FALSE, comp = "mean")

Arguments

X	When evaluating a single ordinal feature, X should be a numeric matrix or data.frame. If data is multivariate, X should be a list, and each ordinal/ranking feature should be placed in a different element of the list (see Examples).
NA.as.0	Should NAs be converted to 0s? (Defaults: TRUE).
samples.in.rows	If TRUE, the samples are considered to be in the rows. Otherwise, it is assumed that they are in the columns. (Defaults: FALSE).
comp	If X is a list, this argument indicates how the ordinal/ranking variables are combined. Options are: "mean" and "sum". (Defaults: "mean").

Value

Kernel matrix (dimension: NxN).

References

Jiao, Y. and Vert, J.P. The Kendall and Mallows kernels for permutations. International Conference on Machine Learning. PMLR, 2015. Link

Examples

# 3 people are given a list of 10 colors. They rank them from most (1) to least
# (10) favorite
color_list <-  c("black","blue","green","grey","lightblue","orange","purple",
"red","white","yellow")
survey1 <- 1:10
survey2 <- 10:1
survey3 <- sample(10)
color <- cbind(survey1,survey2,survey3) # Samples in columns
rownames(color) <- color_list
Kendall(color)

# The same 3 people are asked the number of times they ate 5 different kinds of
# food during the last month:
food <- matrix(c(10, 1,18, 25,30, 7, 5,20, 5, 12, 7,20, 20, 3,22),ncol=5,nrow=3)
rownames(food) <- colnames(color)
colnames(food) <- c("spinach", "chicken", "beef" , "salad","lentils")
# (we can observe that, for person 2, vegetables << meat, while for person 3
# is the other way around)
Kendall(food,samples.in.rows=TRUE)

# We can combine this results:
dataset <- list(color=color,food=t(food)) #All samples in columns
Kendall(dataset)

kerntools documentation built on April 3, 2025, 7:52 p.m.