Mahout的BreimanExample例子分析，mahoutexample

Mahout的BreimanExample例子分析，mahoutexample

Mahout的BreimanExample例子执行了
Leo Breiman: Random Forests. Machine Learning 45(1): 5-32 (2001)这篇论文的测试。
对它的分析我分为3个部分
- 森林生成的Iteration部分
- BreimanExample的测试执行部分
- 命令行执行部分

Iteration部分

迭代函数如下，对于训练数据集data，根据随机生成器rng随机将data分成训练集与测试集两部分，之后生成随机森林，并进行准确率检测。

/**
   * runs one iteration of the procedure.
   * 
   * @param rng
   *          random numbers generator
   * @param data
   *          training data
   * @param m
   *          number of random variables to select at each tree-node
   *          take m to be the first integer less than log2(M) + 1, where M is the number of attributes
   * @param nbtrees
   *          number of trees to grow
   */
  private void runIteration(Random rng, Data data, int m, int nbtrees)

1.数据集的构造

data是输入的数据集，不过并不会将data的全部都用来做训练，而是将它分为两部分：
第一部分train是训练集，用data克隆一下，咦，好奇怪啊，那不就和data一样了么？
第二部分test为测试集，它是从train中随机取出10%左右的数据构成，同时将这些数据从train中删除，具体是使用Data类的rsplit函数实现的。

Data train = data.clone();
Data test = train.rsplit(rng, (int) (data.size() * 0.1));

1.1Data类的rsplit函数

Data类位于org.apache.mahout.classifier.df.data.Data。
它的成员变量有两个，相关说明是
Holds a list of vectors and their corresponding Dataset

  private final List<Instance> instances;

  private final Dataset dataset;

rpslit函数如下，它从Data对象的instances变量存储的数据随机取出了subsize个放到新构造的subset集合中去，这subsize个数据也就从instances中给去掉了。
因为数据同出一源，所以最后返回的Data对象它的dataset和调用rsplit的Data对象的dataset是相同的。

/**
   * Splits the data in two, returns one part, and this gets the rest of the data. <b>VERY SLOW!</b>
   */
  public Data rsplit(Random rng, int subsize) {
    List<Instance> subset = Lists.newArrayListWithCapacity(subsize);

    for (int i = 0; i < subsize; i++) {
      subset.add(instances.remove(rng.nextInt(instances.size())));
    }

    return new Data(dataset, subset);
  }

1.2TreeBuilder

接着定义了决策树的构造器以及森林的构造器。
两个类分别位于
org.apache.mahout.classifier.df.builder.DefaultTreeBuilder;
org.apache.mahout.classifier.df.ref.SequentialBuilder;

/**
 * Builds a Decision Tree <br>
 * Based on the algorithm described in the "Decision Trees" tutorials by Andrew W. Moore, available at:<br>
 * <br>
 * http://www.cs.cmu.edu/~awm/tutorials
 * <br><br>
 * This class can be used when the criterion variable is the categorical attribute.
 */
    DefaultTreeBuilder treeBuilder = new DefaultTreeBuilder();
 /**
 * Builds a Random Decision Forest using a given TreeBuilder to grow the trees
 */
    SequentialBuilder forestBuilder = new SequentialBuilder(rng, treeBuilder, train);

接着用forestBuilder来构造一个随机森林。

  /* grow a forest with m = log2(M)+1*/
    treeBuilder.setM(m);
    DecisionForest forestM = forestBuilder.build(nbtrees);

SequentialBuilder中的build函数如下，它循环使用bagging生成了nbTrees颗树。用trees记录各棵树的根节点。

public class SequentialBuilder {

private final Bagging bagging;

public DecisionForest build(int nbTrees) {
    List<Node> trees = Lists.newArrayList();

    for (int treeId = 0; treeId < nbTrees; treeId++) {
      trees.add(bagging.build(rng));
      logProgress(((float) treeId + 1) / nbTrees);
    }

    return new DecisionForest(trees);
  }
}

1.3Bagging

bagging是如何建树的呢？
如下所示，先是用Data的bagging方法从数据中采样出一个训练集bag，之后用这个bag按照决策树的方法建树就好了。

  /**
   * Builds one tree
   */
  public Node build(Random rng) {
    log.debug("Bagging...");
    Arrays.fill(sampled, false);
    Data bag = data.bagging(rng, sampled);

    log.debug("Building...");
    return treeBuilder.build(rng, bag);
  }

那么如何bagging采样呢？
如下所示，也即有放回从N个样本的数据集中随机采样N次，同一个数据可以多次采样，挺奇怪的这个sampled有什么用呢？

  /**
   * if data has N cases, sample N cases at random -but with replacement.
   * 
   * @param sampled
   *          indicating which instance has been sampled
   * 
   * @return sampled data
   */
  public Data bagging(Random rng, boolean[] sampled) {
    int datasize = size();
    List<Instance> bag = Lists.newArrayListWithCapacity(datasize);

    for (int i = 0; i < datasize; i++) {
      int index = rng.nextInt(datasize);
      bag.add(instances.get(index));
      sampled[index] = true;
    }

    return new Data(dataset, bag);
  }

接下来又按照m=1的