[
https://issues.apache.org/jira/browse/FLINK-2030?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14705385#comment-14705385
]
ASF GitHub Bot commented on FLINK-2030:
---------------------------------------
Github user sachingoel0101 commented on a diff in the pull request:
https://github.com/apache/flink/pull/861#discussion_r37558122
--- Diff:
flink-staging/flink-ml/src/main/scala/org/apache/flink/ml/statistics/ContinuousHistogram.scala
---
@@ -0,0 +1,315 @@
+/*
+ * 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.flink.ml.statistics
+
+import scala.Double.MaxValue
+import scala.collection.mutable
+
+/** Implementation of a continuous valued online histogram
+ * Adapted from Ben-Haim and Yom-Tov's Streaming Decision Tree Algorithm
+ * Refer http://www.jmlr.org/papers/volume11/ben-haim10a/ben-haim10a.pdf
+ *
+ * =Parameters=
+ * -[[capacity]]:
+ * Number of bins to be used in the histogram
+ *
+ * -[[min]]:
+ * Lower limit on the elements
+ *
+ * -[[max]]:
+ * Upper limit on the elements
+ */
+class ContinuousHistogram(capacity: Int, min: Double, max: Double) extends
OnlineHistogram {
+
+ private val lower = min
+ private val upper = max
+
+ require(capacity > 0, "Capacity should be a positive integer")
+ require(lower < upper, "Lower must be less than upper")
+
+ val data = new mutable.ArrayBuffer[(Double, Int)]()
+
+ /** Adds a new item to the histogram
+ *
+ * @param p value to be added
+ */
+ override def add(p: Double): Unit = {
+ require(p > lower && p < upper, p + " not in (" + lower + "," + upper
+ ")")
+ // search for the index where the value is just higher than p
+ val search = find(p)
+ // add the new value there, shifting everything to the right
+ data.insert(search, (p, 1))
+ // If we're over capacity or any two elements are within 1e-9 of each
other, merge.
+ // This will take care of the case if p was actually equal to some
value in the histogram and
+ // just increment the value there
+ mergeElements()
+ }
+
+ /** Merges the histogram with h and returns a histogram with capacity B
+ *
+ * @param h histogram to be merged
+ * @param B capacity of the resultant histogram
+ * @return Merged histogram with capacity B
+ */
+ override def merge(h: OnlineHistogram, B: Int): ContinuousHistogram = {
+ h match {
+ case temp: ContinuousHistogram => {
+ val m: Int = bins
+ val n: Int = temp.bins
+ var i, j: Int = 0
+ val mergeList = new mutable.ArrayBuffer[(Double, Int)]()
+ while (i < m || j < n) {
+ if (i >= m) {
+ mergeList += ((temp.getValue(j), temp.getCounter(j)))
+ j = j + 1
+ } else if (j >= n || getValue(i) <= temp.getValue(j)) {
+ mergeList += data.apply(i)
+ i = i + 1
+ } else {
+ mergeList += ((temp.getValue(j), temp.getCounter(j)))
+ j = j + 1
+ }
+ }
+ // the size will be brought to capacity while constructing the new
histogram itself
+ val finalLower = Math.min(lower, temp.lower)
+ val finalUpper = Math.max(upper, temp.upper)
+ val ret = new ContinuousHistogram(B, finalLower, finalUpper)
+ ret.loadData(mergeList.toArray)
+ ret
+ }
+ case default =>
+ throw new RuntimeException("Only a continuous histogram is allowed
to be merged with a " +
+ "continuous histogram")
+
+ }
+ }
+
+ /** Returns the qth quantile of the histogram
+ *
+ * @param q Quantile value in (0,1)
+ * @return Value at quantile q
+ */
+ def quantile(q: Double): Double = {
+ require(bins > 0, "Histogram is empty")
+ require(q > 0 && q < 1, "Quantile must be between 0 and 1")
+ val wantedSum = (q * total).round.toInt
+ var currSum = count(getValue(0))
+
+ if (wantedSum < currSum) {
+ require(lower > -MaxValue, "Set a lower bound before proceeding")
+ return Math.sqrt(2 * wantedSum * Math.pow(getValue(0) - lower, 2) /
getCounter(0)) + lower
+ }
+
+ /** Walk the histogram to find sums at every bin value
+ * As soon as you hit the interval where you should be
+ * Walk along the trapezoidal line
+ * This leads to solving a quadratic equation.
+ */
+ for (i <- 1 to bins - 1) {
+ val tmpSum = count(getValue(i))
+ if (currSum <= wantedSum && wantedSum < tmpSum) {
+ val neededSum = wantedSum - currSum
+ val a: Double = getCounter(i) - getCounter(i - 1)
+ val b: Double = 2 * getCounter(i - 1)
+ val c: Double = -2 * neededSum
+ if (a == 0) {
+ return getValue(i - 1) + (getValue(i) - getValue(i - 1)) * (-c /
b)
+ } else {
+ return getValue(i - 1) +
+ (getValue(i) - getValue(i - 1)) * (-b + Math.sqrt(b * b - 4 *
a * c)) / (2 * a)
+ }
+ } else {
+ currSum = tmpSum
+ }
+ }
+ require(upper < MaxValue, "Set an upper bound before proceeding")
+ // this means wantedSum > sum(getValue(bins-1))
+ // this will likely fail to return a bounded value.
+ // Make sure you set some proper limits on min and max.
+ getValue(bins - 1) + Math.sqrt(
+ Math.pow(upper - getValue(bins - 1), 2) * 2 * (wantedSum - currSum)
/ getCounter(bins - 1))
+ }
+
+ /** Returns the probability (and by extension, the number of points) for
the value b
+ * Since this is a continuous histogram, return the cumulative
probability at b
+ *
+ * @return Cumulative number of points at b
+ */
+ def count(b: Double): Int = {
+ require(bins > 0, "Histogram is empty")
+ if (b < lower) {
+ return 0
+ }
+ if (b >= upper) {
+ return total
+ }
+ /** Suppose x is the index with value just less than or equal to b
+ * Then, sum everything up to x-1
+ * Add half the value at x
+ * Find area of the trapezoid for x and the value b
+ */
+
+ val index = find(b) - 1
+ var m_b, s: Double = 0
+ if (index == -1) {
+ m_b = getCounter(index + 1) * (b - lower) / (getValue(index + 1) -
lower)
+ s = m_b * (b - lower) / (2 * (getValue(index + 1) - lower))
+ return s.round.toInt
+ } else if (index == bins - 1) {
+ m_b = getCounter(index) +
+ (-getCounter(index)) * (b - getValue(index)) / (upper -
getValue(index))
+ s = (getCounter(index) + m_b) *
+ (b - getValue(index)) / (2 * (upper - getValue(index)))
+ } else {
+ m_b = getCounter(index) + (getCounter(index + 1) -
getCounter(index)) *
+ (b - getValue(index)) / (getValue(index + 1) - getValue(index))
+ s = (getCounter(index) + m_b) *
+ (b - getValue(index)) / (2 * (getValue(index + 1) -
getValue(index)))
--- End diff --
I meant mapping area as in, taking ratio of area to the number of elements.
The assumption is that elements are uniformly distributed between two different
bins. This is why the line connecting m_x and m_y is assumed to be linear.
> Implement an online histogram with Merging and equalization features
> --------------------------------------------------------------------
>
> Key: FLINK-2030
> URL: https://issues.apache.org/jira/browse/FLINK-2030
> Project: Flink
> Issue Type: Sub-task
> Components: Machine Learning Library
> Reporter: Sachin Goel
> Assignee: Sachin Goel
> Priority: Minor
> Labels: ML
>
> For the implementation of the decision tree in
> https://issues.apache.org/jira/browse/FLINK-1727, we need to implement an
> histogram with online updates, merging and equalization features. A reference
> implementation is provided in [1]
> [1].http://www.jmlr.org/papers/volume11/ben-haim10a/ben-haim10a.pdf
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