tauAP {ircor}

AP Rank Correlation Coefficients

Description

tauAP is the AP rank correlation coefficient by Yilmaz et al., where neither vector can contain tied items. tauAP_a and tauAP_b are the versions developed by Urbano and Marrero to cope with ties under the scenarios of accuracy and agreement, respectively. See the references for details.

Usage

tauAP(x, y, decreasing = TRUE)

tauAP_a(x, y, decreasing = TRUE)

tauAP_b(x, y, decreasing = TRUE)

Arguments

x

a numeric vector. In tauAP_a this is the vector of true scores.

y

a numeric vector of the same length as x. In tauAP_a this is the vector of estimated scores.

decreasing

logical. Should the sort order be increasing or decreasing (default)?

Details

Note that the sorting order is decreasing by default, as should be for instance if the scores represent the effectiveness of systems. When the sorting order is ascending, as is for instance when the vectors represent ranks, the parameter decreasing must be set to FALSE.

Value

The correlation coefficient.

References

E. Yilmaz, J.A. Aslam and S. Robertson (2008). A New Rank Correlation Coefficient for Information Retrieval. ACM SIGIR.

J. Urbano and M. Marrero (2017). The Treatment of Ties in AP Correlation. ACM ICTIR.

See Also

tau for Kendall correlation coefficients.

Examples

# No ties
x <- c(0.67, 0.45, 0.29, 0.12, 0.57, 0.24, 0.94, 0.75, 0.08, 0.54)
y <- c(0.48, 0.68, 0.32, 0.09, 0.06, 0.61, 0.87, 0.22, 0.44, 0.84)
tauAP(x, y)
tauAP_a(x,y) # same as tauAP

# Ties in y
y <- round(y, 1)
tauAP_a(x, y)
tauAP_b(x, y)

# Ties in x too
x <- round(x, 1)
tauAP_b(x, y)

# Set decreasing to FALSE when x and y already represent ranks
x <- rank(-x)
y <- rank(-y)
tauAP_b(x, y, FALSE) # same as above