Classification and Regression with Random Forest

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 locating outliers or assessing proximities among data points.

regression, classif, tree
## S3 method for class 'formula':
randomForest(x, data=NULL, ..., subset, na.action=na.fail)
## S3 method for class 'default':
randomForest(x, y = NULL, xtest = NULL, ytest = NULL, addclass = 0, 
    ntree = 500, mtry, classwt = NULL, cutoff, sampsize,
    nodesize, importance = FALSE, 
    proximity = FALSE, oob.prox = TRUE, outscale = FALSE, norm.votes = TRUE,
    do.trace = FALSE, keep.forest = is.null(xtest), corr.bias=FALSE, ...) 
## S3 method for class 'randomForest':
print(x, ...)
an optional data frame containing the variables in the model. By default the variables are taken from the environment which randomForest is called from.
an index vector indicating which rows should be used. (NOTE: If given, this argument must be named.)
A function to specify the action to be taken if NAs are found. (NOTE: If given, this argument must be named.)
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 with addclass=1 (unless explicitly set otherwise).
a data frame or matrix (like x) containing predictors for the test set.
response for the test set.
=0 (default) do not add a synthetic class to the data. =1 label the input data as class 1 and add a synthetic class by randomly sampling from the product of empirical marginal distributions of the input. =2
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.
Number of variables randomly sampled as candidates at each split. Note that the default values are different for classification and regression
Priors of the classes. Need not add up to one. Ignored for regression.
(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
(Classification only) Sizes of bootstrap sample to take from the classes. Use table(y) for simple stratified samples.
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 and regression.
Should importance of predictors be assessed?
Should proximity measure among the rows be calculated?
Should proximity be calculated only on ``out-of-bag'' data?
Should outlyingness of rows be assessed? Ignored for regression.
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.
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.
If set to FALSE, the forest will not be retained in the output object. If xtest is given, defaults to FALSE.
perform bias correction for regression? Note: Experimental. Use at your own risk.
optional parameters to be passed to the low level function randomForest.default.

  • 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.
  • 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).
  • outlier(classification only) if outscale=TRUE when randomForest is called, a vector indicating how outlying the data points are (based on the proximity measures).
  • 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.


The forest structure is slightly different between classification and regression. For details on how the trees are stored, see the help page for getTree.

If xtest is given, prediction of the test set is done ``in place'' as the trees are grown. If ytest is also given, and do.trace is set to some positive integer, then for every do.trace trees, the test set error is printed. Results for the test set is returned in the test component of the resulting randomForest object.

For large data sets, especially those with large number of variables, calling randomForest via the formula interface is not advised: There may be too much overhead in handling the formula. Here are the definitions of the variable importance measures. For each tree, the prediction accuracy on the out-of-bag portion of the data is recorded. Then the same is done after permuting each predictor variable. The difference between the two accuracies are then averaged over all trees, and normalized by the standard error. If the standard error is equal to 0 for a variable, the measure is set to -1000 + mean decrease in accuracy (which, most likely, is also 0). 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.


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.

See Also

predict.randomForest, var.imp.plot

  • randomForest
  • randomForest.formula
  • randomForest.default
  • print.randomForest
## Classification:
iris.rf <- randomForest(Species ~ ., data=iris, importance=TRUE,
## Look at variable importance:
print(round(iris.rf$importance, 2))
## Do MDS on 1 - proximity:
iris.mds <- cmdscale(1 - iris.rf$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")

## The `unsupervised' case:
iris.urf <- randomForest(iris[, -5], proximity=TRUE, outscale=TRUE)
## Look for Outliers:
plot(iris.urf$out, type="h", ylab="",
     main="Measure of Outlyingness for Iris Data")

## Regression:
ozone.rf <- randomForest(Ozone ~ ., data=airquality, mtry=3, importance=TRUE)
## Show "importance" of variables: higher value mean more important:
print(round(ozone.rf$importance, 2))
Documentation reproduced from package randomForest, version 4.0-7, License: GPL version 2 or later

Community examples

Looks like there are no examples yet.