【异常检测】Isolation forest 的spark 分布式实现

1.算法简介

　　算法的原始论文 http://cs.nju.edu.cn/zhouzh/zhouzh.files/publication/icdm08b.pdf 。python的sklearn中已经实现了相关的api，对于单机的数据已经足够使用了，链接如下 http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.IsolationForest.html 。如果你想探究分布式下该算法怎么实现，下面细看。

　　按照惯例先讲一下算法的思想，对于已经了解的小伙伴来说，这段跳过。它的思路有点类似随机森林，并发训练N棵树，每棵树是没有关联的，且每棵树用到的样本和属性也是随机的，所不同的是，isolation forest (下面简称IF)是非监督的算法，通过构建二叉树，然后在构建好的树上，来预测样本的深度，如果深度太浅，则是疑似异常的样本。更加详细的论断和细节请查看论文，或者参考国内各大博客主写的个人感悟，我们把重点放在分布式实现上面。

2.分布式实现

在实现之前重点关注一点，IF算法并不需要所有的样本，甚至不能使用太多的样本，使用小样本的情况，算法效果更优。这一点在论文中有论断:

如上图所示，如果使用全部的样本作为训练集，则异常的样本，未必能识别出来，而在小样本下可以轻松识别。论文中比较了这两种方式，前者AUC达到0.67，而后者能达到0.91。

基于上面的论断，每棵树的样本大小不能太大，当然下面实现的方式既支持小样本又支持大样本，这个依赖于用户自己喜欢了

import java.util.concurrent.Executors
import org.apache.spark.SparkContext
import org.apache.spark.rdd.RDD

import org.apache.spark.storage.StorageLevel
import scala.concurrent.duration.Duration
import scala.concurrent.{Await, ExecutionContext, Future}
import scala.util.Random
import org.apache.hadoop.fs._

sealed trait ITree

case class ITreeBranch(left: ITree, right: ITree, split_column: Int, split_value: Double) extends ITree

case class ITreeLeaf(size: Long) extends ITree

/** @param trees      trained trees
  * @param maxSamples The number of samples to train each base tree
  */
case class IForest(trees: Array[ITree], maxSamples: Int) {

  def predict(x: Array[Double]) = {
    if (trees.forall(_ == null)) {
      throw new Exception("Please train before predict!!")
    } else {
      val predictions = trees.map(s => pathLength(x, s, 0)).toList
      math.pow(2, -(predictions.sum / predictions.size) / cost(maxSamples))
    }
  }

  @scala.annotation.tailrec
  final def pathLength(x: Array[Double], tree: ITree, path_length: Int): Double = {
    tree match {
      case ITreeLeaf(size) =>
        path_length + cost(size)

      case ITreeBranch(left, right, split_column, split_value) =>
        val sample_value = x(split_column)
        if (sample_value < split_value)
          pathLength(x, left, path_length + 1)
        else
          pathLength(x, right, path_length + 1)
    }
  }

  private def cost(num_items: Long): Double =
    if (num_items <= 1) 1.0 else 2.0 * (math.log(num_items - 1.0) + 0.577215664901532860606512090082402431) - (2.0 * (num_items - 1.0) / num_items)

}

object IForest {

  /**
    * @param numTrees    The number of base tree in the ensemble
    * @param maxSamples  The number of samples to train each base tree ,should be small!! should be small!! should be small!!
    *                    should be small!! should be small!! should be small!!
    * @param maxFeatures The fraction of features to train each base tree value in (0.0,1.0]
    *                    //    * @param withReplacement whether sampling is done with replacement, do something in future
    * @param nJobs       The number of jobs to run in parallel for fit ,do something in future
    */
  def buildForest(data: RDD[Array[Double]], numTrees: Int = 100, maxSamples: Int = 256, maxFeatures: Double = 1.0, nJobs: Int = 10, distribute: Boolean = false) = {
    val sc = data.sparkContext
    val cacheData = if (sc.getRDDStorageInfo.filter(_.id == data.id).nonEmpty) data else data.persist(StorageLevel.MEMORY_AND_DISK)
    val dataCnt = data.count()
    println(s"AllSmaples =>${dataCnt}")

    val numFeatures = cacheData.take(1)(0).size
    checkData(cacheData, numFeatures)
    val sampleNumSamples = Math.min(maxSamples, dataCnt).toInt
    val sampleNumFeatures = (maxFeatures * numFeatures).toInt
    val maxDepth = Math.ceil((math.log(math.max(sampleNumSamples, 2)) / math.log(2))).toInt

    val sampleRatio = Math.min(sampleNumSamples * 1.0 / dataCnt * 2, 1.0)
    val trees =
      if (distribute) {
        implicit val xc = ExecutionContext.fromExecutorService(Executors.newFixedThreadPool(nJobs))
        val tasks = (0 until numTrees).map {
          i =>
            val sampleData = cacheData.sample(false, sampleRatio, System.currentTimeMillis()).zipWithIndex().filter(_._2 <= sampleNumSamples).map(_._1)
            parallizeGrow(sampleData, maxDepth, numFeatures, sampleNumFeatures)
        }
        val results = Await.result(Future.sequence(tasks), Duration.Inf)
        results.toArray
      }
      else
        (0 until numTrees).sliding(nJobs, nJobs).map {
          arr =>
            sc.union(
              arr.map {
                i =>
                  cacheData.sample(false, sampleRatio, System.currentTimeMillis()).zipWithIndex().filter(_._2 <= sampleNumSamples)
                    .map(_._1).repartition(1).mapPartitions {
                    iter =>
                      val delta = iter.toArray
                      val sampleFeatures = if (sampleNumFeatures < numFeatures) Random.shuffle((0 until numFeatures).toList).take(sampleNumFeatures) else (0 until numFeatures).toList
                      Iterator(growTree(delta, maxDepth, sampleFeatures, 0))
                  }
              }
            ).collect()
        }.reduce(_ ++ _)

    new IForest(trees, maxSamples)
  }

  def saveModel(sc: SparkContext, iforest: IForest, path: String) = {
    val hdfs=FileSystem.get(sc.hadoopConfiguration)
    hdfs.delete(new Path(path), true)
    sc.parallelize(Seq(iforest), 1).saveAsObjectFile(path)
  }

  def loadModel(sc: SparkContext, path: String) = {
    sc.objectFile[IForest](path).collect()(0)
  }

  private def growTree(data: Array[Array[Double]], maxDepth: Int, sampleFeatures: Seq[Int], currentDepth: Int): ITree = {
    val numSamples = data.length
    if (currentDepth >= maxDepth || numSamples <= 1 || data.distinct.length == 1) {
      new ITreeLeaf(numSamples)
    } else {
      val splitColumn = sampleFeatures(Random.nextInt(sampleFeatures.length))
      val columnValue = data.map(_.apply(splitColumn))
      val colMin = columnValue.min
      val colMax = columnValue.max
      val splitValue = colMin + Random.nextDouble() * (colMax - colMin)
      val dataLeft = data.filter(_ (splitColumn) < splitValue)
      val dataRight = data.filter(_ (splitColumn) >= splitValue)
      new ITreeBranch(growTree(dataLeft, maxDepth, sampleFeatures, currentDepth + 1),
        growTree(dataRight, maxDepth, sampleFeatures, currentDepth + 1),
        splitColumn, splitValue)
    }
  }

  private def parallizeGrow(data: RDD[Array[Double]], maxDepth: Int, numFeatures: Int, sampleNumFeatures: Int)(implicit xc: ExecutionContext) = Future {
    val sampleFeatures = if (sampleNumFeatures < numFeatures) Random.shuffle((0 until numFeatures).toList).take(sampleNumFeatures) else (0 until numFeatures)
    growTree(data, maxDepth, sampleFeatures, 0)
  }

  private def growTree(data: RDD[Array[Double]], maxDepth: Int, sampleFeatures: Seq[Int], currentDepth: Int): ITree = {
    val sc = data.sparkContext
    val cacheData = if (sc.getRDDStorageInfo.filter(_.id == data.id).length > 0) data else data.persist(StorageLevel.MEMORY_AND_DISK)
    val numSamples = cacheData.count()
    val ret = if (currentDepth >= maxDepth || numSamples <= 1 || cacheData.distinct.count() == 1) {
      new ITreeLeaf(numSamples)
    } else {
      val splitColumn = sampleFeatures(Random.nextInt(sampleFeatures.length))
      val columnValue = cacheData.map(_ (splitColumn))
      val colMin = columnValue.min()
      val colMax = columnValue.max()
      val splitValue = colMin + Random.nextDouble() * (colMax - colMin)
      val dataLeft = cacheData.filter(_ (splitColumn) < splitValue)
      val dataRight = cacheData.filter(_ (splitColumn) >= splitValue)
      new ITreeBranch(growTree(dataLeft, maxDepth, sampleFeatures, currentDepth + 1),
        growTree(dataRight, maxDepth, sampleFeatures, currentDepth + 1),
        splitColumn, splitValue)
    }

    cacheData.unpersist()
    ret
  }

  private def checkData(data: RDD[Array[Double]], numFeatures: Int) = {
    assert(data.filter(arr => !(arr.length == numFeatures)).isEmpty(), "data must in equal column size")
  }

}

　　代码说明:

1. 代码主要参考https://github.com/hsperr/first_steps_in_scala
2. 原始代码中有错误，具体在predict 函数中num_samples 参数应该是每棵树的样本数量，而不是所有的样本数量。
3. 原始代码中，不是并行的，关键在于trees.map(s=>growTree(getRandomSubsample(data, subSampleSize/numSamples.toDouble, seed), maxHeight, numColumns)) 这一行，在spark的driver端进行解析中，是一个个action串行执行的。
4. 原始代码中其实漏掉了一个树的停止分裂的条件，那就是如果剩余的样本都相同的话，也停止生长。另外两个的停止生长的条件是达到树的最大深度和只剩下小于等于1个样本。
5. buildForest函数，参数的具体含义参照注释，基本是仿照python的参数来实现的，唯一值得解释的是distribute，默认值是false。当该参数为true时，代码会在driver端起njobs个线程，然后每个线程监控执行一个action算子去生成一棵树，具体调用的是 growTree(data: RDD[Array[Double]]...)这个函数；参数为false时，实际上每个partition里面的样本是对原始样本上的小采样，然后在小采样的样本上进行构建一个棵树，你会发现里面的实现和单机是一样的，唯一区别是在分布式的大数据上进行的采样，以及生成大批量的一堆树，具体实现参照 growTree(data: Array[Array[Double]]...) 函数。
6. 每颗树的深度是样本数目取log2之后算出来的，这个和python的api保持一致。
7. 至于什么样的样本才是异常的，这个根据打出来的分数，降序排列。然后可以根据百分比进行设置阈值，或者根据具体的分数进行设置阈值。唯一抓住的核心是，要看一下分数在总体样本上的一个分布，然后根据分布做决策。

3.总结

1.代码已经测试通过，直接mvn编译打包，运行环境为hadoop3.1.0和spark2.3，大家放心使用。

2.如有疑问欢迎指正，大家相互学习交流。