randomForest {randomForest}R Documentation

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 locating outliers or assessing proximities among data points.

Usage

randomForest(x, data=NULL, ..., subset, na.action=na.fail)
randomForest(x, y = NULL, xtest = NULL, ytest = NULL, addclass = 0, 
    ntree = 500, mtry = ifelse(!is.null(y) && !is.factor(y), 
        max(floor(ncol(x)/3), 1), floor(sqrt(ncol(x)))), classwt = NULL, cutoff,
    nodesize = ifelse(!is.null(y) && !is.factor(y), 5, 1), importance = FALSE, 
    proximity = FALSE, outscale = FALSE, norm.votes = TRUE, do.trace = FALSE, 
    keep.forest = is.null(xtest), corr.bias=FALSE, ...) 
NULL

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 a data frame or a matrix of predictors, or a formula describing the model to be fitted (for the print method, an randomForest object).
y 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).
xtest a data frame or matrix (like x) containing predictors for the test set.
ytest response for the test set.
addclass =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 is similar to =1, but the synthetic data are sampled from the uniform hyperrectangle that contain the input. Ignored for regression.
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 and regression
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 (positive) difference between proportion of votes and cutoff. Default is 1/k where k is the number of classes (i.e., majority vote wins).
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 and regression.
importance Should importance of predictors be assessed?
proximity Should proximity measure among the rows be calculated?
outscale Should outlyingness of rows be assessed? Ignored for regression.
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.
... 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:

call the original call to randomForest
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 two columns, each a different measure of importance of the predictors. If importance=FALSE, the last measure is still returned. This measure corresponds to average decrease in node impurity caused by splitting on the variables, and is always computed.
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 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.
proximity if 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).
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 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.

Note

The forest structure is slightly different between classification and regression.

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.

Here are the definitions of the variable importance measures. For classification, define the margin of a case as the proportion of votes for the correct class minus the maximum proportion of votes for the other classes. The first measure is the percent decrease in average margin when the out-of-bag portion of the data are permuted one variable at a time. The second measure is the total decrease in Gini index in nodes split by the variable, averaged over all trees. For regression, the first measure is the percent increase in mean squared residuals when the out-of-bag portion of the data are permuted one variable at a time. The second measure is the total decrease in sum of squares in nodes split by the variable, averaged over all trees.

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.

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

Examples

## Classification:
data(iris)
set.seed(71)
iris.rf <- randomForest(Species ~ ., data=iris, importance=TRUE,
                        proximity=TRUE)
print(iris.rf)
## Look at variable importance:
print(round(iris.rf$importance, 2))
## Do MDS on 1 - proximity:
require(mva)
iris.mds <- cmdscale(1 - iris.rf$proximity, eig=TRUE)
op <- par(pty="s")
pairs(cbind(iris[,1:4], iris.mds$points), cex=0.6, gap=0, 
      col=c("red", "green", "blue")[codes(iris$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], proximity=TRUE, outscale=TRUE)
## Look for Outliers:
plot(iris.urf$out, type="h", ylab="",
     main="Measure of Outlyingness for Iris Data")

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

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