RRF Manual
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Package ‘RRF’
July 17, 2018
Title Regularized Random Forest
Version 1.9
Date 2018-07-16
Depends R (>= 2.5.0), stats
Suggests RColorBrewer, MASS
Author Fortran original by Leo Breiman and Adele Cutler, R port by
Andy Liaw and Matthew Wiener, Regularized random forest for classification by
Houtao Deng. Regularized random forest for regression by Xin Guan.
Description Feature Selection with Regularized Random Forest. This
package is based on the 'randomForest' package by Andy Liaw.
The key difference is the RRF() function that builds a
regularized random forest.
Maintainer Houtao Deng <softwaredeng@gmail.com>
License GPL (>= 2)
URL https://sites.google.com/site/houtaodeng/rrf
Repository CRAN
Date/Publication 2018-07-16 12:08:05
NeedsCompilation yes
RoxygenNote 5.0.1
Rtopics documented:
classCenter ......................................... 2
combine........................................... 3
getTree ........................................... 4
grow............................................. 5
importance ......................................... 6
imports85 .......................................... 7
margin............................................ 8
MDSplot .......................................... 9
na.roughfix ......................................... 10
outlier............................................ 11
partialPlot.......................................... 11
plot.RRF........................................... 13
predict.RRF......................................... 14
1
2classCenter
RRF............................................. 16
rrfcv............................................. 20
rrfImpute .......................................... 21
rrfNews ........................................... 23
treesize ........................................... 23
tuneRRF........................................... 24
varImpPlot ......................................... 25
varUsed ........................................... 26
Index 27
classCenter Prototypes of groups.
Description
Prototypes are ‘representative’ cases of a group of data points, given the similarity matrix among
the points. They are very similar to medoids. The function is named ‘classCenter’ to avoid conflict
with the function prototype in the methods package.
Usage
classCenter(x, label, prox, nNbr = min(table(label))-1)
Arguments
xa matrix or data frame
label group labels of the rows in x
prox the proximity (or similarity) matrix, assumed to be symmetric with 1 on the
diagonal and in [0, 1] off the diagonal (the order of row/column must match that
of x)
nNbr number of nearest neighbors used to find the prototypes.
Details
This version only computes one prototype per class. For each case in x, the nNbr nearest neighors
are found. Then, for each class, the case that has most neighbors of that class is identified. The pro-
totype for that class is then the medoid of these neighbors (coordinate-wise medians for numerical
variables and modes for categorical variables).
This version only computes one prototype per class. In the future more prototypes may be computed
(by removing the ‘neighbors’ used, then iterate).
Value
A data frame containing one prototype in each row.
Author(s)
Andy Liaw
combine 3
See Also
RRF,MDSplot
Examples
data(iris)
iris.rf <- RRF(iris[,-5], iris[,5], prox=TRUE)
iris.p <- classCenter(iris[,-5], iris[,5], iris.rf$prox)
plot(iris[,3], iris[,4], pch=21, xlab=names(iris)[3], ylab=names(iris)[4],
bg=c("red", "blue", "green")[as.numeric(factor(iris$Species))],
main="Iris Data with Prototypes")
points(iris.p[,3], iris.p[,4], pch=21, cex=2, bg=c("red", "blue", "green"))
combine Combine Ensembles of Trees
Description
Combine two more more ensembles of trees into one.
Usage
combine(...)
Arguments
... two or more objects of class RRF, to be combined into one.
Value
An object of class RRF.
Note
The confusion,err.rate,mse and rsq components (as well as the corresponding components in
the test compnent, if exist) of the combined object will be NULL.
Author(s)
Andy Liaw <andy\_liaw@merck.com>
See Also
RRF,grow
Examples
data(iris)
rf1 <- RRF(Species ~ ., iris, ntree=50, norm.votes=FALSE)
rf2 <- RRF(Species ~ ., iris, ntree=50, norm.votes=FALSE)
rf3 <- RRF(Species ~ ., iris, ntree=50, norm.votes=FALSE)
rf.all <- combine(rf1, rf2, rf3)
print(rf.all)
4getTree
getTree Extract a single tree from a forest.
Description
This function extract the structure of a tree from a RRF object.
Usage
getTree(rfobj, k=1, labelVar=FALSE)
Arguments
rfobj aRRF object.
kwhich tree to extract?
labelVar Should better labels be used for splitting variables and predicted class?
Details
For numerical predictors, data with values of the variable less than or equal to the splitting point go
to the left daughter node.
For categorical predictors, the splitting point is represented by an integer, whose binary expansion
gives the identities of the categories that goes to left or right. For example, if a predictor has
four categories, and the split point is 13. The binary expansion of 13 is (1, 0, 1, 1) (because
13 = 1 ∗20+ 0 ∗21+ 1 ∗22+ 1 ∗23), so cases with categories 1, 3, or 4 in this predictor get sent
to the left, and the rest to the right.
Value
A matrix (or data frame, if labelVar=TRUE) with six columns and number of rows equal to total
number of nodes in the tree. The six columns are:
left daughter the row where the left daughter node is; 0 if the node is terminal
right daughter the row where the right daughter node is; 0 if the node is terminal
split var which variable was used to split the node; 0 if the node is terminal
split point where the best split is; see Details for categorical predictor
status is the node terminal (-1) or not (1)
prediction the prediction for the node; 0 if the node is not terminal
Author(s)
Andy Liaw <andy\_liaw@merck.com>
See Also
RRF
Examples
data(iris)
## Look at the third trees in the forest.
getTree(RRF(iris[,-5], iris[,5], ntree=10), 3, labelVar=TRUE)
grow 5
grow Add trees to an ensemble
Description
Add additional trees to an existing ensemble of trees.
Usage
## S3 method for class 'RRF'
grow(x, how.many, ...)
Arguments
xan object of class RRF, which contains a forest component.
how.many number of trees to add to the RRF object.
... currently ignored.
Value
An object of class RRF, containing how.many additional trees.
Note
The confusion,err.rate,mse and rsq components (as well as the corresponding components in
the test compnent, if exist) of the combined object will be NULL.
Author(s)
Andy Liaw <andy\_liaw@merck.com>
See Also
combine,RRF
Examples
data(iris)
iris.rf <- RRF(Species ~ ., iris, ntree=50, norm.votes=FALSE)
iris.rf <- grow(iris.rf, 50)
print(iris.rf)
6importance
importance Extract variable importance measure
Description
This is the extractor function for variable importance measures as produced by RRF.
Usage
## S3 method for class 'RRF'
importance(x, type=NULL, class=NULL, scale=TRUE, ...)
Arguments
xan object of class RRF.
type either 1 or 2, specifying the type of importance measure (1=mean decrease in
accuracy, 2=mean decrease in node impurity).
class for classification problem, which class-specific measure to return.
scale For permutation based measures, should the measures be divided their “standard
errors”?
... not used.
Details
Here are the definitions of the variable importance measures. The first measure is computed from
permuting OOB data: For each tree, the prediction error on the out-of-bag portion of the data is
recorded (error rate for classification, MSE for regression). Then the same is done after permuting
each predictor variable. The difference between the two are then averaged over all trees, and nor-
malized by the standard deviation of the differences. If the standard deviation of the differences is
equal to 0 for a variable, the division is not done (but the average is almost always equal to 0 in that
case).
The second measure is the total decrease in node impurities from splitting on the variable, averaged
over all trees. For classification, the node impurity is measured by the Gini index. For regression, it
is measured by residual sum of squares.
Value
A matrix of importance measure, one row for each predictor variable. The column(s) are different
importance measures.
See Also
RRF,varImpPlot
Examples
set.seed(4543)
data(mtcars)
mtcars.rf <- RRF(mpg ~ ., data=mtcars, ntree=1000,
keep.forest=FALSE, importance=TRUE)
importance(mtcars.rf)
importance(mtcars.rf, type=1)
imports85 7
imports85 The Automobile Data
Description
This is the ‘Automobile’ data from the UCI Machine Learning Repository.
Usage
data(imports85)
Format
imports85 is a data frame with 205 cases (rows) and 26 variables (columns). This data set consists
of three types of entities: (a) the specification of an auto in terms of various characteristics, (b)
its assigned insurance risk rating, (c) its normalized losses in use as compared to other cars. The
second rating corresponds to the degree to which the auto is more risky than its price indicates.
Cars are initially assigned a risk factor symbol associated with its price. Then, if it is more risky
(or less), this symbol is adjusted by moving it up (or down) the scale. Actuarians call this process
‘symboling’. A value of +3 indicates that the auto is risky, -3 that it is probably pretty safe.
The third factor is the relative average loss payment per insured vehicle year. This value is normal-
ized for all autos within a particular size classification (two-door small, station wagons, sports/speciality,
etc...), and represents the average loss per car per year.
Author(s)
Andy Liaw
Source
Originally created by Jeffrey C. Schlimmer, from 1985 Model Import Car and Truck Specifica-
tions, 1985 Ward’s Automotive Yearbook, Personal Auto Manuals, Insurance Services Office, and
Insurance Collision Report, Insurance Institute for Highway Safety.
The original data is at http://www.ics.uci.edu/~mlearn/MLSummary.html.
References
1985 Model Import Car and Truck Specifications, 1985 Ward’s Automotive Yearbook.
Personal Auto Manuals, Insurance Services Office, 160 Water Street, New York, NY 10038
Insurance Collision Report, Insurance Institute for Highway Safety, Watergate 600, Washington,
DC 20037
See Also
RRF
8margin
Examples
data(imports85)
imp85 <- imports85[,-2] # Too many NAs in normalizedLosses.
imp85 <- imp85[complete.cases(imp85), ]
## Drop empty levels for factors.
imp85[] <- lapply(imp85, function(x) if (is.factor(x)) x[, drop=TRUE] else x)
stopifnot(require(RRF))
price.rf <- RRF(price ~ ., imp85, do.trace=10, ntree=100)
print(price.rf)
numDoors.rf <- RRF(numOfDoors ~ ., imp85, do.trace=10, ntree=100)
print(numDoors.rf)
margin Margins of RRF Classifier
Description
Compute or plot the margin of predictions from a RRF classifier.
Usage
## S3 method for class 'RRF'
margin(x, ...)
## Default S3 method:
margin(x, observed, ...)
## S3 method for class 'margin'
plot(x, sort=TRUE, ...)
Arguments
xan object of class RRF, whose type is not regression, or a matrix of predicted
probabilities, one column per class and one row per observation. For the plot
method, xshould be an object returned by margin.
observed the true response corresponding to the data in x.
sort Should the data be sorted by their class labels?
... other graphical parameters to be passed to plot.default.
Value
For margin, the margin of observations from the RRF classifier (or whatever classifier that produced
the predicted probability matrix given to margin). The margin of a data point is defined as the
proportion of votes for the correct class minus maximum proportion of votes for the other classes.
Thus under majority votes, positive margin means correct classification, and vice versa.
Author(s)
Robert Gentlemen, with slight modifications by Andy Liaw
See Also
RRF
MDSplot 9
Examples
set.seed(1)
data(iris)
iris.rf <- RRF(Species ~ ., iris, keep.forest=FALSE)
plot(margin(iris.rf))
MDSplot Multi-dimensional Scaling Plot of Proximity matrix from RRF
Description
Plot the scaling coordinates of the proximity matrix from RRF.
Usage
MDSplot(rf, fac, k=2, palette=NULL, pch=20, ...)
Arguments
rf an object of class RRF that contains the proximity component.
fac a factor that was used as response to train rf.
knumber of dimensions for the scaling coordinates.
palette colors to use to distinguish the classes; length must be the equal to the number
of levels.
pch plotting symbols to use.
... other graphical parameters.
Value
The output of cmdscale on 1 - rf$proximity is returned invisibly.
Note
If k>2,pairs is used to produce the scatterplot matrix of the coordinates.
Author(s)
Robert Gentleman, with slight modifications by Andy Liaw
See Also
RRF
Examples
set.seed(1)
data(iris)
iris.rf <- RRF(Species ~ ., iris, proximity=TRUE,
keep.forest=FALSE)
MDSplot(iris.rf, iris$Species)
## Using different symbols for the classes:
MDSplot(iris.rf, iris$Species, palette=rep(1, 3), pch=as.numeric(iris$Species))
10 na.roughfix
na.roughfix Rough Imputation of Missing Values
Description
Impute Missing Values by median/mode.
Usage
na.roughfix(object, ...)
Arguments
object a data frame or numeric matrix.
... further arguments special methods could require.
Value
A completed data matrix or data frame. For numeric variables, NAs are replaced with column medi-
ans. For factor variables, NAs are replaced with the most frequent levels (breaking ties at random).
If object contains no NAs, it is returned unaltered.
Note
This is used as a starting point for imputing missing values by random forest.
Author(s)
Andy Liaw
See Also
rrfImpute,RRF.
Examples
data(iris)
iris.na <- iris
set.seed(111)
## artificially drop some data values.
for (i in 1:4) iris.na[sample(150, sample(20)), i] <- NA
iris.roughfix <- na.roughfix(iris.na)
iris.narf <- RRF(Species ~ ., iris.na, na.action=na.roughfix)
print(iris.narf)
outlier 11
outlier Compute outlying measures
Description
Compute outlying measures based on a proximity matrix.
Usage
## Default S3 method:
outlier(x, cls=NULL, ...)
## S3 method for class 'RRF'
outlier(x, ...)
Arguments
xa proximity matrix (a square matrix with 1 on the diagonal and values between
0 and 1 in the off-diagonal positions); or an object of class RRF, whose type is
not regression.
cls the classes the rows in the proximity matrix belong to. If not given, all data are
assumed to come from the same class.
... arguments for other methods.
Value
A numeric vector containing the outlying measures. The outlying measure of a case is computed as
n / sum(squared proximity), normalized by subtracting the median and divided by the MAD, within
each class.
See Also
RRF
Examples
set.seed(1)
iris.rf <- RRF(iris[,-5], iris[,5], proximity=TRUE)
plot(outlier(iris.rf), type="h",
col=c("red", "green", "blue")[as.numeric(iris$Species)])
partialPlot Partial dependence plot
Description
Partial dependence plot gives a graphical depiction of the marginal effect of a variable on the class
probability (classification) or response (regression).
12 partialPlot
Usage
## S3 method for class 'RRF'
partialPlot(x, pred.data, x.var, which.class,
w, plot = TRUE, add = FALSE,
n.pt = min(length(unique(pred.data[, xname])), 51),
rug = TRUE, xlab=deparse(substitute(x.var)), ylab="",
main=paste("Partial Dependence on", deparse(substitute(x.var))),
...)
Arguments
xan object of class RRF, which contains a forest component.
pred.data a data frame used for contructing the plot, usually the training data used to con-
truct the random forest.
x.var name of the variable for which partial dependence is to be examined.
which.class For classification data, the class to focus on (default the first class).
wweights to be used in averaging; if not supplied, mean is not weighted
plot whether the plot should be shown on the graphic device.
add whether to add to existing plot (TRUE).
n.pt if x.var is continuous, the number of points on the grid for evaluating partial
dependence.
rug whether to draw hash marks at the bottom of the plot indicating the deciles of
x.var.
xlab label for the x-axis.
ylab label for the y-axis.
main main title for the plot.
... other graphical parameters to be passed on to plot or lines.
Details
The function being plotted is defined as:
˜
f(x) = 1
n
n
X
i=1
f(x, xiC ),
where xis the variable for which partial dependence is sought, and xiC is the other variables in
the data. The summand is the predicted regression function for regression, and logits (i.e., log of
fraction of votes) for which.class for classification:
f(x) = log pk(x)−1
K
K
X
j=1
log pj(x),
where Kis the number of classes, kis which.class, and pjis the proportion of votes for class j.
Value
A list with two components: xand y, which are the values used in the plot.
plot.RRF 13
Note
The RRF object must contain the forest component; i.e., created with RRF(..., keep.forest=TRUE).
This function runs quite slow for large data sets.
Author(s)
Andy Liaw <andy\_liaw@merck.com>
References
Friedman, J. (2001). Greedy function approximation: the gradient boosting machine, Ann. of Stat.
See Also
RRF
Examples
data(airquality)
airquality <- na.omit(airquality)
set.seed(131)
ozone.rf <- RRF(Ozone ~ ., airquality)
partialPlot(ozone.rf, airquality, Temp)
data(iris)
set.seed(543)
iris.rf <- RRF(Species~., iris)
partialPlot(iris.rf, iris, Petal.Width, "versicolor")
plot.RRF Plot method for RRF objects
Description
Plot the error rates or MSE of a RRF object
Usage
## S3 method for class 'RRF'
plot(x, type="l", main=deparse(substitute(x)), ...)
Arguments
xan object of class RRF.
type type of plot.
main main title of the plot.
... other graphical parameters.
14 predict.RRF
Value
Invisibly, the error rates or MSE of the RRF object. If the object has a non-null test component,
then the returned object is a matrix where the first column is the out-of-bag estimate of error, and
the second column is for the test set.
Note
This function does not work for RRF objects that have type=unsupervised.
If the xhas a non-null test component, then the test set errors are also plotted.
Author(s)
Andy Liaw
See Also
RRF
Examples
data(mtcars)
plot(RRF(mpg ~ ., mtcars, keep.forest=FALSE, ntree=100), log="y")
predict.RRF predict method for random forest objects
Description
Prediction of test data using random forest.
Usage
## S3 method for class 'RRF'
predict(object, newdata, type="response",
norm.votes=TRUE, predict.all=FALSE, proximity=FALSE, nodes=FALSE,
cutoff, ...)
Arguments
object an object of class RRF, as that created by the function RRF.
newdata a data frame or matrix containing new data. (Note: If not given, the out-of-bag
prediction in object is returned.
type one of response,prob. or votes, indicating the type of output: predicted val-
ues, matrix of class probabilities, or matrix of vote counts. class is allowed,
but automatically converted to "response", for backward compatibility.
norm.votes Should the vote counts be normalized (i.e., expressed as fractions)? Ignored if
object$type is regression.
predict.all Should the predictions of all trees be kept?
proximity Should proximity measures be computed? An error is issued if object$type is
regression.
predict.RRF 15
nodes Should the terminal node indicators (an n by ntree matrix) be return? If so, it is
in the “nodes” attribute of the returned object.
cutoff (Classification only) A vector of length equal to number of classes. The ‘win-
ning’ class for an observation is the one with the maximum ratio of proportion of
votes to cutoff. Default is taken from the forest$cutoff component of object
(i.e., the setting used when running RRF).
... not used currently.
Value
If object$type is regression, a vector of predicted values is returned. If predict.all=TRUE,
then the returned object is a list of two components: aggregate, which is the vector of predicted
values by the forest, and individual, which is a matrix where each column contains prediction by
a tree in the forest.
If object$type is classification, the object returned depends on the argument type:
response predicted classes (the classes with majority vote).
prob matrix of class probabilities (one column for each class and one row for each
input).
vote matrix of vote counts (one column for each class and one row for each new
input); either in raw counts or in fractions (if norm.votes=TRUE).
If predict.all=TRUE, then the individual component of the returned object is a character matrix
where each column contains the predicted class by a tree in the forest.
If proximity=TRUE, the returned object is a list with two components: pred is the prediction (as
described above) and proximity is the proximitry matrix. An error is issued if object$type is
regression.
If nodes=TRUE, the returned object has a “nodes” attribute, which is an n by ntree matrix, each
column containing the node number that the cases fall in for that tree.
NOTE: If the object inherits from RRF.formula, then any data with NA are silently omitted from
the prediction. The returned value will contain NA correspondingly in the aggregated and individual
tree predictions (if requested), but not in the proximity or node matrices.
NOTE2: Any ties are broken at random, so if this is undesirable, avoid it by using odd number
ntree in RRF().
Author(s)
Andy Liaw <andy\_liaw@merck.com> and Matthew Wiener <matthew\_wiener@merck.com>,
based on original Fortran code by Leo Breiman and Adele Cutler.
References
Breiman, L. (2001), Random Forests, Machine Learning 45(1), 5-32.
See Also
RRF
16 RRF
Examples
data(iris)
set.seed(111)
ind <- sample(2, nrow(iris), replace = TRUE, prob=c(0.8, 0.2))
iris.rf <- RRF(Species ~ ., data=iris[ind == 1,])
iris.pred <- predict(iris.rf, iris[ind == 2,])
table(observed = iris[ind==2, "Species"], predicted = iris.pred)
## Get prediction for all trees.
predict(iris.rf, iris[ind == 2,], predict.all=TRUE)
## Proximities.
predict(iris.rf, iris[ind == 2,], proximity=TRUE)
## Nodes matrix.
str(attr(predict(iris.rf, iris[ind == 2,], nodes=TRUE), "nodes"))
RRF Feature Selection with Regularized Random Forest
Description
RRF implements the regularized random forest algorithm. It is based on the randomForest R package
by Andy Liaw, Matthew Wiener, Leo Breiman and Adele Cutler.
Usage
## S3 method for class 'formula'
RRF(formula, data=NULL, ..., subset, na.action=na.fail)
## Default S3 method:
RRF(x, y=NULL, xtest=NULL, ytest=NULL, ntree=500,
mtry=if (!is.null(y) && !is.factor(y))
max(floor(ncol(x)/3), 1) else floor(sqrt(ncol(x))),
replace=TRUE, classwt=NULL, cutoff, strata,
sampsize = if (replace) nrow(x) else ceiling(.632*nrow(x)),
nodesize = if (!is.null(y) && !is.factor(y)) 5 else 1,
maxnodes = NULL,
importance=FALSE, localImp=FALSE, nPerm=1,
proximity, oob.prox=proximity,
norm.votes=TRUE, do.trace=FALSE,
keep.forest=!is.null(y) && is.null(xtest), corr.bias=FALSE,
keep.inbag=FALSE, coefReg=NULL, flagReg=1, feaIni=NULL,...)
## S3 method for class 'RRF'
print(x, ...)
Arguments
data an optional data frame containing the variables in the model. By default the
variables are taken from the environment which RRF is called from.
subset an index vector indicating which rows should be used. (NOTE: If given, this
argument must be named.)
na.action A function to specify the action to be taken if NAs are found. (NOTE: If given,
this argument must be named.)
RRF 17
x, formula a data frame or a matrix of predictors, or a formula describing the model to be
fitted (for the print method, an RRF object).
yA response vector. If a factor, classification is assumed, otherwise regression is
assumed. If omitted, RRF will run in unsupervised mode.
xtest a data frame or matrix (like x) containing predictors for the test set.
ytest response for the test set.
ntree Number of trees to grow. This should not be set to too small a number, to ensure
that every input row gets predicted at least a few times.
mtry Number of variables randomly sampled as candidates at each split. Note that
the default values are different for classification (sqrt(p) where p is number of
variables in x) and regression (p/3)
replace Should sampling of cases be done with or without replacement?
classwt Priors of the classes. Need not add up to one. Ignored for regression.
cutoff (Classification only) A vector of length equal to number of classes. The ‘win-
ning’ class for an observation is the one with the maximum ratio of proportion
of votes to cutoff. Default is 1/k where k is the number of classes (i.e., majority
vote wins).
strata A (factor) variable that is used for stratified sampling.
sampsize Size(s) of sample to draw. For classification, if sampsize is a vector of the length
the number of strata, then sampling is stratified by strata, and the elements of
sampsize indicate the numbers to be drawn from the strata.
nodesize Minimum size of terminal nodes. Setting this number larger causes smaller trees
to be grown (and thus take less time). Note that the default values are different
for classification (1) and regression (5).
maxnodes Maximum number of terminal nodes trees in the forest can have. If not given,
trees are grown to the maximum possible (subject to limits by nodesize). If set
larger than maximum possible, a warning is issued.
importance Should importance of predictors be assessed?
localImp Should casewise importance measure be computed? (Setting this to TRUE will
override importance.)
nPerm Number of times the OOB data are permuted per tree for assessing variable
importance. Number larger than 1 gives slightly more stable estimate, but not
very effective. Currently only implemented for regression.
proximity Should proximity measure among the rows be calculated?
oob.prox Should proximity be calculated only on “out-of-bag” data?
norm.votes If TRUE (default), the final result of votes are expressed as fractions. If FALSE,
raw vote counts are returned (useful for combining results from different runs).
Ignored for regression.
do.trace If set to TRUE, give a more verbose output as RRF is run. If set to some integer,
then running output is printed for every do.trace trees.
keep.forest If set to FALSE, the forest will not be retained in the output object. If xtest is
given, defaults to FALSE.
corr.bias perform bias correction for regression? Note: Experimental. Use at your own
risk.
keep.inbag Should an nby ntree matrix be returned that keeps track of which samples are
“in-bag” in which trees (but not how many times, if sampling with replacement)
18 RRF
coefReg the coefficient(s) of regularization. A smaller coefficient may lead to a smaller
feature subset, i.e. there are fewer variables with non-zero importance scores.
coefReg must be either a single value (all variables have the same coefficient) or
a numeric vector of length equal to the number of predictor variables. default:
0.8
flagReg 1: with regularization; 0: without regularization. default: 1
feaIni initial feature subset, useful only when flagReg = 1
... optional parameters to be passed to the low level function RRF.default.
Value
An object of class RRF, which is a list with the following components:
call the original call to RRF
type one of regression,classification, or unsupervised.
predicted the predicted values of the input data based on out-of-bag samples.
importance a matrix with nclass + 2 (for classification) or two (for regression) columns.
For classification, the first nclass columns are the class-specific measures com-
puted as mean descrease in accuracy. The nclass + 1st column is the mean
descrease in accuracy over all classes. The last column is the mean decrease
in Gini index. For Regression, the first column is the mean decrease in accu-
racy and the second the mean decrease in MSE. If importance=FALSE, the last
measure is still returned as a vector.
importanceSD The “standard errors” of the permutation-based importance measure. For classi-
fication, a pby nclass + 1 matrix corresponding to the first nclass + 1
columns of the importance matrix. For regression, a length pvector.
localImp a p by n matrix containing the casewise importance measures, the [i,j] ele-
ment of which is the importance of i-th variable on the j-th case. NULL if
localImp=FALSE.
ntree number of trees grown.
mtry number of predictors sampled for spliting at each node.
forest (a list that contains the entire forest; NULL if RRF is run in unsupervised mode or
if keep.forest=FALSE.
err.rate (classification only) vector error rates of the prediction on the input data, the i-th
element being the (OOB) error rate for all trees up to the i-th.
confusion (classification only) the confusion matrix of the prediction (based on OOB data).
votes (classification only) a matrix with one row for each input data point and one
column for each class, giving the fraction or number of (OOB) ‘votes’ from the
random forest.
oob.times number of times cases are ‘out-of-bag’ (and thus used in computing OOB error
estimate)
proximity if proximity=TRUE when RRF is called, a matrix of proximity measures among
the input (based on the frequency that pairs of data points are in the same termi-
nal nodes).
feaSet features selected
mse (regression only) vector of mean square errors: sum of squared residuals divided
by n.
RRF 19
rsq (regression only) “pseudo R-squared”: 1 - mse / Var(y).
test if test set is given (through the xtest or additionally ytest arguments), this
component is a list which contains the corresponding predicted,err.rate,
confusion,votes (for classification) or predicted,mse and rsq (for regres-
sion) for the test set. If proximity=TRUE, there is also a component, proximity,
which contains the proximity among the test set as well as proximity between
test and training data.
Note
For large data sets, especially those with large number of variables, calling RRF via the formula
interface is not advised: There may be too much overhead in handling the formula.
Author(s)
Houtao Deng <softwaredeng@gmail.com>, based on the randomForest R package by Andy Liaw,
Matthew Wiener, Leo Breiman and Adele Cutler.
References
Houtao Deng and George C. Runger (2013), Gene Selection with Guided Regularized Random
Forest, Pattern Recognition 46(12): 3483-3489.
Houtao Deng and George C. Runger (2012), Feature Selection via Regularized Trees, the 2012
International Joint Conference on Neural Networks (IJCNN).
Houtao Deng (2013), Guided Random Forest in the RRF Package, arXiv:1306.0237.
Examples
#-----Example 1 -----
library(RRF);set.seed(1)
#only the first feature and last feature are truly useful
X <- matrix(runif(50*50), ncol=50)
class <- (X[,1])^2 + (X[,50])^2
class[class>median(class)] <- 1;
class[class<=median(class)] <- 0
#ordinary random forest.
rf <- RRF(X,as.factor(class), flagReg = 0)
impRF <- rf$importance
impRF <- impRF[,"MeanDecreaseGini"]
rf$feaSet
#regularized random forest
rrf <- RRF(X,as.factor(class), flagReg = 1)
rrf$feaSet
#guided regularized random forest
imp <- impRF/(max(impRF))#normalize the importance score
gamma <- 0.5
coefReg <- (1-gamma)+gamma*imp #weighted average
grrf <- RRF(X,as.factor(class),coefReg=coefReg, flagReg=1)
grrf$feaSet
#guided random forest
20 rrfcv
gamma <- 1
coefReg <- (1-gamma)+gamma*imp
grf <- RRF(X,as.factor(class),coefReg=coefReg, flagReg=0)
grf$feaSet
#-----Example 2 XOR learning-----
#only the first 3 features are needed
#and each individual feature is not useful
#bSample <- sample(0:1,20000,replace=TRUE)
#X <- matrix(bSample,ncol=40)
#class <- xor(xor(X[,1],X[,2]),X[,3])
rrfcv Random Forest Cross-Valdidation for feature selection
Description
This function shows the cross-validated prediction performance of models with sequentially re-
duced number of predictors (ranked by variable importance) via a nested cross-validation proce-
dure.
Usage
rrfcv(trainx, trainy, cv.fold=5, scale="log", step=0.5,
mtry=function(p) max(1, floor(sqrt(p))), recursive=FALSE, ...)
Arguments
trainx matrix or data frame containing columns of predictor variables
trainy vector of response, must have length equal to the number of rows in trainx
cv.fold number of folds in the cross-validation
scale if "log", reduce a fixed proportion (step) of variables at each step, otherwise
reduce step variables at a time
step if log=TRUE, the fraction of variables to remove at each step, else remove this
many variables at a time
mtry a function of number of remaining predictor variables to use as the mtry param-
eter in the RRF call
recursive whether variable importance is (re-)assessed at each step of variable reduction
... other arguments passed on to RRF
Value
A list with the following components:
list(n.var=n.var, error.cv=error.cv, predicted=cv.pred)
n.var vector of number of variables used at each step
error.cv corresponding vector of error rates or MSEs at each step
predicted list of n.var components, each containing the predicted values from the cross-
validation
rrfImpute 21
Author(s)
Andy Liaw
References
Svetnik, V., Liaw, A., Tong, C. and Wang, T., “Application of Breiman’s Random Forest to Mod-
eling Structure-Activity Relationships of Pharmaceutical Molecules”, MCS 2004, Roli, F. and
Windeatt, T. (Eds.) pp. 334-343.
See Also
RRF,importance
Examples
## The following can take a while to run, so if you really want to try
## it, copy and paste the code into R.
## Not run:
set.seed(647)
myiris <- cbind(iris[1:4], matrix(runif(508 * nrow(iris)), nrow(iris), 508))
result <- rrfcv(myiris, iris$Species)
with(result, plot(n.var, error.cv, log="x", type="o", lwd=2))
result <- replicate(5, rrfcv(myiris, iris$Species), simplify=FALSE)
error.cv <- sapply(result, "[[", "error.cv")
matplot(result[[1]]$n.var, cbind(rowMeans(error.cv), error.cv), type="l",
lwd=c(2, rep(1, ncol(error.cv))), col=1, lty=1, log="x",
xlab="Number of variables", ylab="CV Error")
## End(Not run)
rrfImpute Missing Value Imputations by RRF
Description
Impute missing values in predictor data using proximity from RRF.
Usage
## Default S3 method:
rrfImpute(x, y, iter=5, ntree=300, ...)
## S3 method for class 'formula'
rrfImpute(x, data, ..., subset)
22 rrfImpute
Arguments
xA data frame or matrix of predictors, some containing NAs, or a formula.
yResponse vector (NA’s not allowed).
data A data frame containing the predictors and response.
iter Number of iterations to run the imputation.
ntree Number of trees to grow in each iteration of RRF.
... Other arguments to be passed to RRF.
subset A logical vector indicating which observations to use.
Details
The algorithm starts by imputing NAs using na.roughfix. Then RRF is called with the completed
data. The proximity matrix from the RRF is used to update the imputation of the NAs. For continuous
predictors, the imputed value is the weighted average of the non-missing obervations, where the
weights are the proximities. For categorical predictors, the imputed value is the category with the
largest average proximity. This process is iterated iter times.
Note: Imputation has not (yet) been implemented for the unsupervised case. Also, Breiman (2003)
notes that the OOB estimate of error from RRF tend to be optimistic when run on the data matrix
with imputed values.
Value
A data frame or matrix containing the completed data matrix, where NAs are imputed using proxim-
ity from RRF. The first column contains the response.
Author(s)
Andy Liaw
References
Leo Breiman (2003). Manual for Setting Up, Using, and Understanding Random Forest V4.0.
https://www.stat.berkeley.edu/~breiman/Using_random_forests_v4.0.pdf
See Also
na.roughfix.
Examples
data(iris)
iris.na <- iris
set.seed(111)
## artificially drop some data values.
for (i in 1:4) iris.na[sample(150, sample(20)), i] <- NA
set.seed(222)
iris.imputed <- rrfImpute(Species ~ ., iris.na)
set.seed(333)
iris.rf <- RRF(Species ~ ., iris.imputed)
print(iris.rf)
rrfNews 23
rrfNews Show the NEWS file
Description
Show the NEWS file of the RRF package.
Usage
rrfNews()
Value
None.
treesize Size of trees in an ensemble
Description
Size of trees (number of nodes) in and ensemble.
Usage
treesize(x, terminal=TRUE)
Arguments
xan object of class RRF, which contains a forest component.
terminal count terminal nodes only (TRUE) or all nodes (FALSE
Value
A vector containing number of nodes for the trees in the RRF object.
Note
The RRF object must contain the forest component; i.e., created with RRF(..., keep.forest=TRUE).
Author(s)
Andy Liaw <andy\_liaw@merck.com>
See Also
RRF
Examples
data(iris)
iris.rf <- RRF(Species ~ ., iris)
hist(treesize(iris.rf))
24 tuneRRF
tuneRRF Tune RRF for the optimal mtry parameter
Description
Starting with the default value of mtry, search for the optimal value (with respect to Out-of-Bag
error estimate) of mtry for RRF.
Usage
tuneRRF(x, y, mtryStart, ntreeTry=50, stepFactor=2, improve=0.05,
trace=TRUE, plot=TRUE, doBest=FALSE, ...)
Arguments
xmatrix or data frame of predictor variables
yresponse vector (factor for classification, numeric for regression)
mtryStart starting value of mtry; default is the same as in RRF
ntreeTry number of trees used at the tuning step
stepFactor at each iteration, mtry is inflated (or deflated) by this value
improve the (relative) improvement in OOB error must be by this much for the search to
continue
trace whether to print the progress of the search
plot whether to plot the OOB error as function of mtry
doBest whether to run a forest using the optimal mtry found
... options to be given to RRF
Value
If doBest=FALSE (default), it returns a matrix whose first column contains the mtry values searched,
and the second column the corresponding OOB error.
If doBest=TRUE, it returns the RRF object produced with the optimal mtry.
See Also
RRF
Examples
data(fgl, package="MASS")
fgl.res <- tuneRRF(fgl[,-10], fgl[,10], stepFactor=1.5)
varImpPlot 25
varImpPlot Variable Importance Plot
Description
Dotchart of variable importance as measured by a Random Forest
Usage
varImpPlot(x, sort=TRUE, n.var=min(30, nrow(x$importance)),
type=NULL, class=NULL, scale=TRUE,
main=deparse(substitute(x)), ...)
Arguments
xAn object of class RRF.
sort Should the variables be sorted in decreasing order of importance?
n.var How many variables to show? (Ignored if sort=FALSE.)
type, class, scale
arguments to be passed on to importance
main plot title.
... Other graphical parameters to be passed on to dotchart.
Value
Invisibly, the importance of the variables that were plotted.
Author(s)
Andy Liaw <andy\_liaw@merck.com>
See Also
RRF,importance
Examples
set.seed(4543)
data(mtcars)
mtcars.rf <- RRF(mpg ~ ., data=mtcars, ntree=1000, keep.forest=FALSE,
importance=TRUE)
varImpPlot(mtcars.rf)
26 varUsed
varUsed Variables used in a random forest
Description
Find out which predictor variables are actually used in the random forest.
Usage
varUsed(x, by.tree=FALSE, count=TRUE)
Arguments
xAn object of class RRF.
by.tree Should the list of variables used be broken down by trees in the forest?
count Should the frequencies that variables appear in trees be returned?
Value
If count=TRUE and by.tree=FALSE, a integer vector containing frequencies that variables are used
in the forest. If by.tree=TRUE, a matrix is returned, breaking down the counts by tree (each column
corresponding to one tree and each row to a variable).
If count=FALSE and by.tree=TRUE, a list of integer indices is returned giving the variables used in
the trees, else if by.tree=FALSE, a vector of integer indices giving the variables used in the entire
forest.
Author(s)
Andy Liaw
See Also
RRF
Examples
data(iris)
set.seed(17)
varUsed(RRF(Species~., iris, ntree=100))
Index
∗Topic NA
na.roughfix,10
∗Topic classif
classCenter,2
combine,3
grow,5
importance,6
margin,8
MDSplot,9
outlier,11
partialPlot,11
plot.RRF,13
predict.RRF,14
rrfcv,20
rrfImpute,21
rrfNews,23
treesize,23
tuneRRF,24
varImpPlot,25
∗Topic datasets
imports85,7
∗Topic regression
combine,3
grow,5
importance,6
partialPlot,11
plot.RRF,13
predict.RRF,14
rrfcv,20
rrfImpute,21
treesize,23
varImpPlot,25
∗Topic tree
getTree,4
importance,6
MDSplot,9
partialPlot,11
plot.RRF,13
rrfImpute,21
tuneRRF,24
varImpPlot,25
varUsed,26
classCenter,2
cmdscale,9
combine,3,5
dotchart,25
getTree,4
grow,3,5
importance,6,21,25
imports85,7
margin,8
MDSplot,3,9
na.roughfix,10,22
outlier,11
pairs,9
partialPlot,11
plot.margin (margin),8
plot.RRF,13
predict.RRF,14
print.RRF (RRF),16
RRF,3–11,13–15,16,21–26
rrfcv,20
rrfImpute,10,21
rrfNews,23
treesize,23
tuneRRF,24
varImpPlot,6,25
varUsed,26
27
