Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/216#discussion_r11168529
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/discretization/EntropyMinimizationDiscretizer.scala
---
@@ -0,0 +1,317 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.spark.mllib.discretization
+
+import scala.collection.mutable
+import org.apache.spark.SparkContext._
+import org.apache.spark.rdd.RDD
+import org.apache.spark.storage.StorageLevel
+import org.apache.spark.mllib.regression.LabeledPoint
+
+/**
+ * This class contains methods to calculate thresholds to discretize
continuous values with the
+ * method proposed by Fayyad and Irani in Multi-Interval Discretization of
Continuous-Valued
+ * Attributes (1993).
+ *
+ * @param continuousFeaturesIndexes Indexes of features to be discretized.
+ * @param elementsPerPartition Maximum number of thresholds to treat in
each RDD partition.
+ * @param maxBins Maximum number of bins for each discretized feature.
+ */
+class EntropyMinimizationDiscretizer private (
+ val continuousFeaturesIndexes: Seq[Int],
+ val elementsPerPartition: Int,
+ val maxBins: Int)
+ extends Serializable {
+
+ private val partitions = { x: Long => math.ceil(x.toDouble /
elementsPerPartition).toInt }
+ private val log2 = { x: Double => math.log(x) / math.log(2) }
+
+ /**
+ * Run the algorithm with the configured parameters on an input.
+ * @param data RDD of LabeledPoint's.
+ * @return A EntropyMinimizationDiscretizerModel with the thresholds to
discretize.
+ */
+ def run(data: RDD[LabeledPoint]) = {
+ val labels2Int =
data.context.broadcast(data.map(_.label).distinct.collect.zipWithIndex.toMap)
+ val nLabels = labels2Int.value.size
+
+ var thresholds = Map.empty[Int, Seq[Double]]
+ for (i <- continuousFeaturesIndexes) {
+ val featureValues = data.map({
+ case LabeledPoint(label, values) => (values(i),
labels2Int.value(label))
+ })
+ val sortedValues = featureValues.sortByKey()
+ val initialCandidates = initialThresholds(sortedValues, nLabels)
+ val thresholdsForFeature = this.getThresholds(initialCandidates,
nLabels)
+ thresholds += ((i, thresholdsForFeature))
+ }
+
+ new EntropyMinimizationDiscretizerModel(thresholds)
+
+ }
+
+ /**
+ * Calculates the initial candidate treholds for a feature
+ * @param data RDD of (value, label) pairs.
+ * @param nLabels Number of distinct labels in the dataset.
+ * @return RDD of (candidate, class frequencies between last and current
candidate) pairs.
+ */
+ private def initialThresholds(data: RDD[(Double, Int)], nLabels: Int) = {
+ data.mapPartitions({ it =>
+ var lastX = Double.NegativeInfinity
+ var lastY = Int.MinValue
+ var result = Seq.empty[(Double, Array[Long])]
+ var freqs = Array.fill[Long](nLabels)(0L)
+
+ for ((x, y) <- it) {
+ if (x != lastX && y != lastY && lastX != Double.NegativeInfinity) {
+ // new candidate and interval
+ result = ((x + lastX) / 2, freqs) +: result
+ freqs = Array.fill[Long](nLabels)(0L)
+ freqs(y) = 1L
+ } else {
+ // we continue on the same interval
+ freqs(y) += 1
+ }
+ lastX = x
+ lastY = y
+ }
+
+ // we add last element as a candidate threshold for convenience
+ result = (lastX, freqs) +: result
+
+ result.reverse.toIterator
+ }).persist(StorageLevel.MEMORY_AND_DISK)
+ }
+
+ /**
+ * Returns a sequence of doubles that define the intervals to make the
discretization.
+ *
+ * @param candidates RDD of (value, label) pairs
+ */
+ private def getThresholds(candidates: RDD[(Double, Array[Long])],
nLabels: Int): Seq[Double] = {
+
+ // Create queue
+ val stack = new mutable.Queue[((Double, Double), Option[Double])]
+
+ // Insert first in the stack
+ stack.enqueue(((Double.NegativeInfinity, Double.PositiveInfinity),
None))
+ var result = Seq(Double.NegativeInfinity)
+
+ // While more elements to eval, continue
+ while(stack.length > 0 && result.size < this.maxBins){
+
+ val (bounds, lastThresh) = stack.dequeue
+
+ var cands = candidates.filter({ case (th, _) => th > bounds._1 && th
<= bounds._2 })
+ val nCands = cands.count
+ if (nCands > 0) {
+ cands = cands.coalesce(partitions(nCands))
+
+ evalThresholds(cands, lastThresh, nLabels) match {
+ case Some(th) =>
+ result = th +: result
+ stack.enqueue(((bounds._1, th), Some(th)))
+ stack.enqueue(((th, bounds._2), Some(th)))
+ case None => /* criteria not fulfilled, finish */
+ }
+ }
+ }
+ (Double.PositiveInfinity +: result).sorted
+ }
+
+ /**
+ * Selects one final thresholds among the candidates and returns two
partitions to recurse
+ *
+ * @param candidates RDD of (candidate, class frequencies between last
and current candidate)
+ * @param lastSelected last selected threshold to avoid selecting it
again
+ */
+ private def evalThresholds(
+ candidates: RDD[(Double, Array[Long])],
+ lastSelected : Option[Double],
+ nLabels: Int) = {
+
+ var result = candidates.map({
+ case (cand, freqs) =>
+ (cand, freqs, Array.empty[Long], Array.empty[Long])
+ }).cache
+
+ val numPartitions = candidates.partitions.size
+ val bcNumPartitions = candidates.context.broadcast(numPartitions)
+
+ // stores accumulated freqs from left to right
+ val bcLeftTotal =
candidates.context.accumulator(Array.fill(nLabels)(0L))(ArrayAccumulator)
+ // stores accumulated freqs from right to left
+ val bcRightTotal =
candidates.context.accumulator(Array.fill(nLabels)(0L))(ArrayAccumulator)
+
+ // calculates accumulated frequencies for each candidate
+ (0 until numPartitions) foreach { l2rIndex =>
--- End diff --
This block is still quite complicated. Let's say you have partitioned
frequency sequence
~~~
1 2 1 3 || 1 1 1 1 || 1 2 3 2
~~~
From left to right, you want
~~~
1 3 4 7 || 8 9 10 11 || 12 14 17 19
~~~
From right to left, you want
~~~
19 18 16 15 || 12 11 10 9 || 8 7 5 2
~~~
This can be done by first computing partition-wise sums:
~~~
7 || 4 || 8
~~~
Then compute cumsums from left to right
~~~
0 || 7 || 11 || 19
~~~
and from right to left
~~~
19 || 12 || 8 || 0
~~~
The global cumsum becomes, from left to right
~~~
0 + cumsum(1, 2, 1, 3) || 7 + cumsum(1, 1, 1, 1) || 11 + cumsum(1, 2, 3, 2)
~~~
from right to left
~~~
19 - cumsum(0, 1, 2, 1) || 12 - cumsum(0, 1, 1, 1) || 8 - cumsum(0, 1, 2, 3)
~~~
There are some details I may miss. But two jobs should be sufficient for
this computation.
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