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package de.lmu.ifi.dbs.elki.index.tree.spatial.rstarvariants.strategies.split;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2013
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero 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 Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
import java.util.BitSet;
import java.util.Random;
import de.lmu.ifi.dbs.elki.data.ModifiableHyperBoundingBox;
import de.lmu.ifi.dbs.elki.data.spatial.SpatialComparable;
import de.lmu.ifi.dbs.elki.data.spatial.SpatialUtil;
import de.lmu.ifi.dbs.elki.logging.Logging;
import de.lmu.ifi.dbs.elki.utilities.Util;
import de.lmu.ifi.dbs.elki.utilities.datastructures.arraylike.ArrayAdapter;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.exceptions.AbortException;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
/**
* Line-time complexity split proposed by Ang and Tan.
*
* This split strategy tries to minimize overlap only, which can however
* degenerate to "slices".
*
* <p>
* C. H. Ang and T. C. Tan:<br />
* New linear node splitting algorithm for R-trees<br />
* In: Proceedings of the 5th International Symposium on Advances in Spatial
* Databases
* </p>
*
* @author Erich Schubert
*/
@Reference(authors = "C. H. Ang and T. C. Tan", title = "New linear node splitting algorithm for R-trees", booktitle = "Proceedings of the 5th International Symposium on Advances in Spatial Databases", url = "http://dx.doi.org/10.1007/3-540-63238-7_38")
public class AngTanLinearSplit implements SplitStrategy {
/**
* Logger class
*/
private static final Logging LOG = Logging.getLogger(AngTanLinearSplit.class);
/**
* Static instance.
*/
public static final AngTanLinearSplit STATIC = new AngTanLinearSplit();
@Override
public <E extends SpatialComparable, A> BitSet split(A entries, ArrayAdapter<E, A> getter, int minEntries) {
final int num = getter.size(entries);
// We need the overall MBR for computing edge preferences
ModifiableHyperBoundingBox total = new ModifiableHyperBoundingBox(getter.get(entries, 0));
{
for(int i = 1; i < num; i++) {
total.extend(getter.get(entries, i));
}
}
final int dim = total.getDimensionality();
// Prepare the axis lists (we use bitsets)
BitSet[] closer = new BitSet[dim];
{
for(int d = 0; d < dim; d++) {
closer[d] = new BitSet();
}
for(int i = 0; i < num; i++) {
E e = getter.get(entries, i);
for(int d = 0; d < dim; d++) {
double low = e.getMin(d) - total.getMin(d);
double hig = total.getMax(d) - e.getMax(d);
if(low >= hig) {
closer[d].set(i);
}
}
}
}
// Find the most even split
{
int axis = -1;
int bestcard = Integer.MAX_VALUE;
BitSet bestset = null;
double bestover = Double.NaN;
for(int d = 0; d < dim; d++) {
BitSet cand = closer[d];
int card = cand.cardinality();
card = Math.max(card, num - card);
if(card == num) {
continue;
}
if(card < bestcard) {
axis = d;
bestcard = card;
bestset = cand;
bestover = Double.NaN;
}
else if(card == bestcard) {
// Tie handling
if(Double.isNaN(bestover)) {
bestover = computeOverlap(entries, getter, bestset);
}
double overlap = computeOverlap(entries, getter, cand);
if(overlap < bestover) {
axis = d;
bestcard = card;
bestset = cand;
bestover = overlap;
}
else if(overlap == bestover) {
double bestlen = total.getMax(axis) - total.getMin(axis);
double candlen = total.getMax(d) - total.getMin(d);
if(candlen < bestlen) {
axis = d;
bestcard = card;
bestset = cand;
bestover = overlap;
}
}
}
}
if(bestset == null) {
LOG.warning("No Ang-Tan-Split found. Probably all points are the same? Returning random split.");
return Util.randomBitSet(num >> 1, num, new Random());
}
return bestset;
}
}
/**
* Compute overlap of assignment
*
* @param entries Entries
* @param getter Entry accessor
* @param assign Assignment
* @return Overlap amount
*/
protected <E extends SpatialComparable, A> double computeOverlap(A entries, ArrayAdapter<E, A> getter, BitSet assign) {
ModifiableHyperBoundingBox mbr1 = null, mbr2 = null;
for(int i = 0; i < getter.size(entries); i++) {
E e = getter.get(entries, i);
if(assign.get(i)) {
if(mbr1 == null) {
mbr1 = new ModifiableHyperBoundingBox(e);
}
else {
mbr1.extend(e);
}
}
else {
if(mbr2 == null) {
mbr2 = new ModifiableHyperBoundingBox(e);
}
else {
mbr2.extend(e);
}
}
}
if(mbr1 == null || mbr2 == null) {
throw new AbortException("Invalid state in split: one of the sets is empty.");
}
return SpatialUtil.overlap(mbr1, mbr2);
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
@Override
protected AngTanLinearSplit makeInstance() {
return AngTanLinearSplit.STATIC;
}
}
}
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