| colAUC {caTools} | R Documentation |
Area Under ROC Curve (AUC) calculated for every column of the matrix.
auc = colAUC(X, y) p = colAUC(X, y, p.val=TRUE)
X |
A matrix or data frame. Rows contain samples and columns contain features/variables. |
y |
Class labels for the X data samples.
A response vector with one label for each row/component of X.
Can be either a factor, string or a numeric vector. |
p.val |
a boolean flag: if set to TRUE than "Wilcoxon rank sum test"
p-values (see wilcox.test) will be returned instead of AUC
values |
AUC is a very useful measure of similarity between two classes measuring area
under "Receiver Operating Characteristic" or ROC curve.
In case of data with no ties all sections of ROC curve are either horizontal
or vertical, in case of data with ties diagonal
sections can also occur. Area under the ROC curve is calculated using
trapz function. AUC is always in between 0.5
(two classes are statistically identical) and 1.0 (there is a threshold value
that can achieve a perfect separation between the classes).
This measure is very similar to Wilcoxon rank sum test (see
wilcox.test), which is also called
Mann-Whitney test. Wilcoxon-test's p-value can be calculated by
p=pnorm( n1*n2*(1-auc), mean=n1*n2/2, sd=sqrt(n1*n2*(n1+n2+1)/12) )
where n1 and n2 are numbers of elements in two classes being
compared.
The main purpose of this function was to calculate AUC's of large number of
features, fast. It is being used to help with classification of protein mass
spectra data
that often have up to 50K features, as a fast and dirty way of lowering
dimensionality of the data before applying standard classification algorithms
like nnet or svd.
An output is a single matrix with the same number of columns as X and
"n choose 2" ( n!/((n-2)! 2!) ) number of rows,
where n is number of unique labels in y list. For example, if y
contains only two unique class labels ( length(unique(lab))==2 ) than
output
matrix will have a single row containing AUC of each column. If more than
two unique labels are present than AUC is calculated for every possible
pairing of classes ("n choose 2" of them).
Jarek Tuszynski (SAIC) jaroslaw.w.tuszynski@saic.com
AUC from ROC package,
roc.area from verification package,
wilcox.test
# load MASS library with "cats" data set that have following columns: sex,
# body weight, hart weight
library(MASS)
data(cats)
colAUC(cats[,2:3], cats[,1])
# compare with examples from roc.area function: using Data from Mason and Graham (2002).
a<- (1981:1995)
b<- c(0,0,0,1,1,1,0,1,1,0,0,0,0,1,1)
c<- c(.8, .8, 0, 1,1,.6, .4, .8, 0, 0, .2, 0, 0, 1,1)
d<- c(.928,.576, .008, .944, .832, .816, .136, .584, .032, .016, .28, .024, 0, .984, .952)
A<- data.frame(a,b,c,d)
names(A)<- c("year", "event", "p1", "p2")
if (library(verification, logical.return=TRUE)) {
roc.area(A$event, A$p1) # for model with ties
roc.area(A$event, A$p2) # for model without ties
}
wilcox.test(p2~event, data=A)
# colAUC output is the same as roc.area's A.tilda values
colAUC(A[,3:4], A$event)
# colAUC output is the same as roc.area's and wilcox.test's p values
colAUC(A[,3:4], A$event, p.val=TRUE)
# example of 3-class data
data(iris)
colAUC(iris[,-5], iris[,5])