sda.ranking {sda}

Shrinkage Discriminant Analysis 1: Predictor Ranking

Description

sda.ranking determines a ranking of predictors by computing CAT scores (correlation-adjusted t-scores) between the group centroids and the pooled mean.

plot.sda.ranking provides a graphical visualization of the top ranking features.

Usage

sda.ranking(Xtrain, L, lambda, lambda.var, lambda.freqs,
  ranking.score=c("entropy", "avg", "max"), 
  diagonal=FALSE, fdr=TRUE, plot.fdr=FALSE, verbose=TRUE)
## S3 method for class 'sda.ranking'
plot(x, top=40, arrow.col="blue", zeroaxis.col="red",
   ylab="Features", main, ...)

Arguments

Xtrain

A matrix containing the training data set. Note that the rows correspond to observations and the columns to variables.

L

A factor with the class labels of the training samples.

lambda

Shrinkage intensity for the correlation matrix. If not specified it is estimated from the data. lambda=0 implies no shrinkage and lambda=1 complete shrinkage.

lambda.var

Shrinkage intensity for the variances. If not specified it is estimated from the data. lambda.var=0 implies no shrinkage and lambda.var=1 complete shrinkage.

lambda.freqs

Shrinkage intensity for the frequencies. If not specified it is estimated from the data. lambda.freqs=0 implies no shrinkage (i.e. empirical frequencies) and lambda.freqs=1 complete shrinkage (i.e. uniform frequencies).

diagonal

Chooses between LDA (default, diagonal=FALSE) and DDA (diagonal=TRUE).

ranking.score

how to compute the summary score for each variable from the CAT scores of all classes - see Details.

fdr

compute FDR values and HC scores for each feature.

plot.fdr

Show plot with estimated FDR values.

verbose

Print out some info while computing.

x

An "sda.ranking" object – this is produced by the sda.ranking() function.

top

The number of top-ranking features shown in the plot (default: 40).

arrow.col

Color of the arrows in the plot (default is "blue").

zeroaxis.col

Color for the center zero axis (default is "red").

ylab

Label written next to feature list (default is "Features").

main

Main title (if missing, "The", top, "Top Ranking Features" is used).

...

Other options passed on to generic plot().

Details

For each predictor variable and centroid a shrinkage CAT scores of the mean versus the pooled mean is computed. If there are only two classes the CAT score vs. the pooled mean reduces to the CAT score between the two group means. Moreover, in the diagonal case (LDA) the (shrinkage) CAT score reduces to the (shrinkage) t-score.

The overall ranking of a feature is determine by computing a summary score from the CAT scores. This is controlled by the option ranking.score. The default setting (ranking.score="entropy") uses mutual information between the response and the respective predictors (ranking.score) for ranking. This is equivalent to a weighted sum of squared CAT scores across the classes. Another possibility is to employ the average of the squared CAT scores for ranking (as suggested in Ahdesm\"aki and Strimmer 2010) by setting ranking.score="avg". A third option is to use the maximum of the squared CAT scores across groups (similarly as in the PAM algorithm) via setting ranking.score="max". Note that in the case of two classes all three options are equivalent and lead to identical scores. Thus, the choice of ranking.score is important only in the multi-class setting. In the two-class case the features are simply ranked according to the (shrinkage) squared CAT-scores (or t-scores, if there is no correlation among predictors).

The current default approach is to use ranking by mutual information (i.e. relative entropy between full model vs. model without predictor) and to use shrinkage estimators of frequencies. In order to reproduce exactly the ranking computed by previous versions (1.1.0 to 1.3.0) of the sda package set the options ranking.score="avg" and lambda.freqs=0.

Calling sda.ranking is step 1 in a classification analysis with the sda package. Steps 2 and 3 are sda and predict.sda

See Zuber and Strimmer (2009) for CAT scores in general, and Ahdesm\"aki and Strimmer (2010) for details on multi-class CAT scores. For shrinkage t scores see Opgen-Rhein and Strimmer (2007).

Value

sda.ranking returns a matrix with the following columns:

idx

original feature number

score

sum of the squared CAT scores across groups - this determines the overall ranking of a feature

cat

for each group and feature the cat score of the centroid versus the pooled mean

If fdr=TRUE then additionally local false discovery rate (FDR) values as well as higher criticism (HC) scores are computed for each feature (using fdrtool).

Author(s)

Miika Ahdesm\"aki, Verena Zuber, Sebastian Gibb, and Korbinian Strimmer (https://strimmerlab.github.io).

References

Ahdesm\"aki, A., and K. Strimmer. 2010. Feature selection in omics prediction problems using cat scores and false non-discovery rate control. Ann. Appl. Stat. 4: 503-519. <DOI:10.1214/09-AOAS277>

Opgen-Rhein, R., and K. Strimmer. 2007. Accurate ranking of differentially expressed genes by a distribution-free shrinkage approach. Statist. Appl. Genet. Mol. Biol. 6:9. <DOI:10.2202/1544-6115.1252>

Zuber, V., and K. Strimmer. 2009. Gene ranking and biomarker discovery under correlation. Bioinformatics 25: 2700-2707. <DOI:10.1093/bioinformatics/btp460>

See Also

catscore, sda, predict.sda.

Examples

# load sda library
library("sda")

################# 
# training data #
#################

# prostate cancer set
data(singh2002)

# training data
Xtrain = singh2002$x
Ytrain = singh2002$y

######################################### 
# feature ranking (diagonal covariance) #
#########################################

# ranking using t-scores (DDA)
ranking.DDA = sda.ranking(Xtrain, Ytrain, diagonal=TRUE)
ranking.DDA[1:10,]

# plot t-scores for the top 40 genes
plot(ranking.DDA, top=40) 

# number of features with local FDR < 0.8 
# (i.e. features useful for prediction)
sum(ranking.DDA[,"lfdr"] < 0.8)

# number of features with local FDR < 0.2 
# (i.e. significant non-null features)
sum(ranking.DDA[,"lfdr"] < 0.2)

# optimal feature set according to HC score
plot(ranking.DDA[,"HC"], type="l")
which.max( ranking.DDA[1:1000,"HC"] ) 


##################################### 
# feature ranking (full covariance) #
#####################################

# ranking using CAT-scores (LDA)
ranking.LDA = sda.ranking(Xtrain, Ytrain, diagonal=FALSE)
ranking.LDA[1:10,]

# plot t-scores for the top 40 genes
plot(ranking.LDA, top=40) 

# number of features with local FDR < 0.8 
# (i.e. features useful for prediction)
sum(ranking.LDA[,"lfdr"] < 0.8)

# number of features with local FDR < 0.2 
# (i.e. significant non-null features)
sum(ranking.LDA[,"lfdr"] < 0.2)

# optimal feature set according to HC score
plot(ranking.LDA[,"HC"], type="l")
which.max( ranking.LDA[1:1000,"HC"] )