Title: Breiman Example

#Breiman Example

#### Introduction

This page describes how to run the Breiman example, which implements the test procedure described in [Leo Breiman's paper](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.23.3999&rep=rep1&type=pdf). The basic algorithm is as follows :

 * repeat *I* iterations
 * in each iteration do
  * keep 10% of the dataset apart as a testing set 
  * build two forests using the training set, one with *m = int(log2(M) + 1)* (called Random-Input) and one with *m = 1* (called Single-Input)
  * choose the forest that gave the lowest oob error estimation to compute
the test set error
  * compute the test set error using the Single Input Forest (test error),
this demonstrates that even with *m = 1*, Decision Forests give comparable
results to greater values of *m*
  * compute the mean testset error using every tree of the chosen forest
(tree error). This should indicate how well a single Decision Tree performs
 * compute the mean test error for all iterations
 * compute the mean tree error for all iterations


#### Running the Example

The current implementation is compatible with the [UCI repository](http://archive.ics.uci.edu/ml/) file format. We'll show how to run this example on two datasets:

First, we deal with [Glass Identification](http://archive.ics.uci.edu/ml/datasets/Glass+Identification): download the [dataset](http://archive.ics.uci.edu/ml/machine-learning-databases/glass/glass.data) file called **glass.data** and store it onto your local machine. Next, we must generate the descriptor file **glass.info** for this dataset with the following command:

    bin/mahout org.apache.mahout.classifier.df.tools.Describe -p /path/to/glass.data -f /path/to/glass.info -d I 9 N L

Substitute */path/to/* with the folder where you downloaded the dataset, the argument "I 9 N L" indicates the nature of the variables. Here it means 1
ignored (I) attribute, followed by 9 numerical(N) attributes, followed by
the label (L).

Finally, we build and evaluate our random forest classifier as follows:

    bin/mahout org.apache.mahout.classifier.df.BreimanExample -d /path/to/glass.data -ds /path/to/glass.info -i 10 -t 100
which builds 100 trees (-t argument) and repeats the test 10 iterations (-i
argument) 

The example outputs the following results:

 * Selection error: mean test error for the selected forest on all iterations
 * Single Input error: mean test error for the single input forest on all
iterations
 * One Tree error: mean single tree error on all iterations
 * Mean Random Input Time: mean build time for random input forests on all
iterations
 * Mean Single Input Time: mean build time for single input forests on all
iterations

We can repeat this for a [Sonar](http://archive.ics.uci.edu/ml/datasets/Connectionist+Bench+%28Sonar,+Mines+vs.+Rocks%29) usecase: download the [dataset](http://archive.ics.uci.edu/ml/machine-learning-databases/undocumented/connectionist-bench/sonar/sonar.all-data) file called **sonar.all-data** and store it onto your local machine. Generate the descriptor file **sonar.info** for this dataset with the following command:

    bin/mahout org.apache.mahout.classifier.df.tools.Describe -p /path/to/sonar.all-data -f /path/to/sonar.info -d 60 N L

The argument "60 N L" means 60 numerical(N) attributes, followed by the label (L). Analogous to the previous case, we run the evaluation as follows:

    bin/mahout org.apache.mahout.classifier.df.BreimanExample -d /path/to/sonar.all-data -ds /path/to/sonar.info -i 10 -t 100