/*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/*
* MedianOfWidestDimension.java
* Copyright (C) 2007-2012 University of Waikato, Hamilton, New Zealand
*/
package weka.core.neighboursearch.kdtrees;
import weka.core.RevisionUtils;
import weka.core.TechnicalInformation;
import weka.core.TechnicalInformation.Field;
import weka.core.TechnicalInformation.Type;
import weka.core.TechnicalInformationHandler;
/**
<!-- globalinfo-start -->
* The class that splits a KDTree node based on the median value of a dimension in which the node's points have the widest spread.<br/>
* <br/>
* For more information see also:<br/>
* <br/>
* Jerome H. Friedman, Jon Luis Bentley, Raphael Ari Finkel (1977). An Algorithm for Finding Best Matches in Logarithmic Expected Time. ACM Transactions on Mathematics Software. 3(3):209-226.
* <p/>
<!-- globalinfo-end -->
*
<!-- technical-bibtex-start -->
* BibTeX:
* <pre>
* @article{Friedman1977,
* author = {Jerome H. Friedman and Jon Luis Bentley and Raphael Ari Finkel},
* journal = {ACM Transactions on Mathematics Software},
* month = {September},
* number = {3},
* pages = {209-226},
* title = {An Algorithm for Finding Best Matches in Logarithmic Expected Time},
* volume = {3},
* year = {1977}
* }
* </pre>
* <p/>
<!-- technical-bibtex-end -->
*
<!-- options-start -->
<!-- options-end -->
*
* @author Ashraf M. Kibriya (amk14[at-the-rate]cs[dot]waikato[dot]ac[dot]nz)
* @version $Revision: 8034 $
*/
public class MedianOfWidestDimension
extends KDTreeNodeSplitter
implements TechnicalInformationHandler {
/** for serialization. */
private static final long serialVersionUID = 1383443320160540663L;
/**
* Returns a string describing this nearest neighbour search algorithm.
*
* @return a description of the algorithm for displaying in the
* explorer/experimenter gui
*/
public String globalInfo() {
return
"The class that splits a KDTree node based on the median value of "
+ "a dimension in which the node's points have the widest spread.\n\n"
+ "For more information see also:\n\n"
+ getTechnicalInformation().toString();
}
/**
* Returns an instance of a TechnicalInformation object, containing detailed
* information about the technical background of this class, e.g., paper
* reference or book this class is based on.
*
* @return the technical information about this class
*/
public TechnicalInformation getTechnicalInformation() {
TechnicalInformation result;
result = new TechnicalInformation(Type.ARTICLE);
result.setValue(Field.AUTHOR, "Jerome H. Friedman and Jon Luis Bentley and Raphael Ari Finkel");
result.setValue(Field.YEAR, "1977");
result.setValue(Field.TITLE, "An Algorithm for Finding Best Matches in Logarithmic Expected Time");
result.setValue(Field.JOURNAL, "ACM Transactions on Mathematics Software");
result.setValue(Field.PAGES, "209-226");
result.setValue(Field.MONTH, "September");
result.setValue(Field.VOLUME, "3");
result.setValue(Field.NUMBER, "3");
return result;
}
/**
* Splits a node into two based on the median value of the dimension
* in which the points have the widest spread. After splitting two
* new nodes are created and correctly initialised. And, node.left
* and node.right are set appropriately.
*
* @param node The node to split.
* @param numNodesCreated The number of nodes that so far have been
* created for the tree, so that the newly created nodes are
* assigned correct/meaningful node numbers/ids.
* @param nodeRanges The attributes' range for the points inside
* the node that is to be split.
* @param universe The attributes' range for the whole
* point-space.
* @throws Exception If there is some problem in splitting the
* given node.
*/
public void splitNode(KDTreeNode node, int numNodesCreated,
double[][] nodeRanges, double[][] universe) throws Exception {
correctlyInitialized();
int splitDim = widestDim(nodeRanges, universe);
//In this case median is defined to be either the middle value (in case of
//odd number of values) or the left of the two middle values (in case of
//even number of values).
int medianIdxIdx = node.m_Start + (node.m_End-node.m_Start)/2;
//the following finds the median and also re-arranges the array so all
//elements to the left are < median and those to the right are > median.
int medianIdx = select(splitDim, m_InstList, node.m_Start, node.m_End, (node.m_End-node.m_Start)/2+1);
node.m_SplitDim = splitDim;
node.m_SplitValue = m_Instances.instance(m_InstList[medianIdx]).value(splitDim);
node.m_Left = new KDTreeNode(numNodesCreated+1, node.m_Start, medianIdxIdx,
m_EuclideanDistance.initializeRanges(m_InstList, node.m_Start, medianIdxIdx));
node.m_Right = new KDTreeNode(numNodesCreated+2, medianIdxIdx+1, node.m_End,
m_EuclideanDistance.initializeRanges(m_InstList, medianIdxIdx+1, node.m_End));
}
/**
* Partitions the instances around a pivot. Used by quicksort and
* kthSmallestValue.
*
* @param attIdx The attribution/dimension based on which the
* instances should be partitioned.
* @param index The master index array containing indices of the
* instances.
* @param l The begining index of the portion of master index
* array that should be partitioned.
* @param r The end index of the portion of master index array
* that should be partitioned.
* @return the index of the middle element
*/
protected int partition(int attIdx, int[] index, int l, int r) {
double pivot = m_Instances.instance(index[(l + r) / 2]).value(attIdx);
int help;
while (l < r) {
while ((m_Instances.instance(index[l]).value(attIdx) < pivot) && (l < r)) {
l++;
}
while ((m_Instances.instance(index[r]).value(attIdx) > pivot) && (l < r)) {
r--;
}
if (l < r) {
help = index[l];
index[l] = index[r];
index[r] = help;
l++;
r--;
}
}
if ((l == r) && (m_Instances.instance(index[r]).value(attIdx) > pivot)) {
r--;
}
return r;
}
/**
* Implements computation of the kth-smallest element according
* to Manber's "Introduction to Algorithms".
*
* @param attIdx The dimension/attribute of the instances in
* which to find the kth-smallest element.
* @param indices The master index array containing indices of
* the instances.
* @param left The begining index of the portion of the master
* index array in which to find the kth-smallest element.
* @param right The end index of the portion of the master index
* array in which to find the kth-smallest element.
* @param k The value of k
* @return The index of the kth-smallest element
*/
public int select(int attIdx, int[] indices, int left, int right, int k) {
if (left == right) {
return left;
} else {
int middle = partition(attIdx, indices, left, right);
if ((middle - left + 1) >= k) {
return select(attIdx, indices, left, middle, k);
} else {
return select(attIdx, indices, middle + 1, right, k - (middle - left + 1));
}
}
}
/**
* Returns the revision string.
*
* @return the revision
*/
public String getRevision() {
return RevisionUtils.extract("$Revision: 8034 $");
}
}