randomForest: Classification and Regression with Random Forest

Description

randomForest implements Breiman's random forest algorithm (based on Breiman and Cutler's original Fortran code) for classification and regression. It can also be used in unsupervised mode for assessing proximities among data points.

Usage

## S3 method for class 'formula':
randomForest(formula, data=NULL, ..., subset, na.action=na.fail)
## S3 method for class 'default':
randomForest(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, 
             importance=FALSE, localImp=FALSE, nPerm=1,
             proximity=FALSE, oob.prox=proximity,
             norm.votes=TRUE, do.trace=FALSE,
             keep.forest=!is.null(y) && is.null(xtest), corr.bias=FALSE,
             keep.inbag=FALSE, ...)
## S3 method for class 'randomForest':
print(x, ...)

Arguments

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment which randomForest 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.)

x, formula

a data frame or a matrix of predictors, or a formula describing the model to be fitted (for the print method, an randomForest object).

A response vector. If a factor, classification is assumed, otherwise regression is assumed. If omitted, randomForest 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 `winning' 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 v

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).

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 randomForest 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 n by 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)

...

optional parameters to be passed to the low level function randomForest.default.

Value

An object of class randomForest, which is a list with the following components:
callthe original call to randomForest
typeone of regression, classification, or {unsupervised}.
predictedthe predicted values of the input data based on out-of-bag samples.
importancea matrix with nclass + 2 (for classification) or two (for regression) columns. For classification, the first nclass columns are the class-specific measures computed 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 accuracy and the second the mean decrease in MSE. If importance=FALSE, the last measure is still returned as a vector.
importanceSDThe ``standard errors'' of the permutation-based importance measure. For classification, a p by nclass + 1 matrix corresponding to the first nclass + 1 columns of the importance matrix. For regression, a length p vector.
localImpa p by n matrix containing the casewise importance measures, the [i,j] element of which is the importance of i-th variable on the j-th case. NULL if localImp=FALSE.
ntreenumber of trees grown.
mtrynumber of predictors sampled for spliting at each node.
forest(a list that contains the entire forest; NULL if randomForest 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 error rate for all trees up to the i-th.
confusion(classification only) the confusion matrix of the prediction.
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 `votes' from the random forest.
oob.timesnumber of times cases are `out-of-bag' (and thus used in computing OOB error estimate)
proximityif proximity=TRUE when randomForest is called, a matrix of proximity measures among the input (based on the frequency that pairs of data points are in the same terminal nodes).
mse(regression only) vector of mean square errors: sum of squared residuals divided by n.
rsq(regression only) ``pseudo R-squared'': 1 - mse / Var(y).
testif 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 regression) 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.

References

Breiman, L. (2001), Random Forests, Machine Learning 45(1), 5-32.

Breiman, L (2002), ``Manual On Setting Up, Using, And Understanding Random Forests V3.1'', http://oz.berkeley.edu/users/breiman/Using_random_forests_V3.1.pdf.

Examples

Run this code

## Classification:
##data(iris)
set.seed(71)
iris.rf <- randomForest(Species ~ ., data=iris, importance=TRUE,
                        proximity=TRUE)
print(iris.rf)
## Look at variable importance:
round(importance(iris.rf), 2)
## Do MDS on 1 - proximity:
iris.mds <- cmdscale(1 - iris.rf$proximity, eig=TRUE)
op <- par(pty="s")
pairs(cbind(iris[,1:4], iris.mds$points), cex=0.6, gap=0, 
      col=c("red", "green", "blue")[as.numeric(iris$Species)],
      main="Iris Data: Predictors and MDS of Proximity Based on RandomForest")
par(op)
print(iris.mds$GOF)

## The `unsupervised' case:
set.seed(17)
iris.urf <- randomForest(iris[, -5])
MDSplot(iris.urf, iris$Species)

## Regression:
## data(airquality)
set.seed(131)
ozone.rf <- randomForest(Ozone ~ ., data=airquality, mtry=3,
                         importance=TRUE, na.action=na.omit)
print(ozone.rf)
## Show "importance" of variables: higher value mean more important:
round(importance(ozone.rf), 2)