[14414] | 1 | #region License Information
|
---|
| 2 | /* HeuristicLab
|
---|
[15583] | 3 | * Copyright (C) 2002-2018 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
|
---|
[14414] | 4 | *
|
---|
| 5 | * This file is part of HeuristicLab.
|
---|
| 6 | *
|
---|
| 7 | * HeuristicLab is free software: you can redistribute it and/or modify
|
---|
| 8 | * it under the terms of the GNU General Public License as published by
|
---|
| 9 | * the Free Software Foundation, either version 3 of the License, or
|
---|
| 10 | * (at your option) any later version.
|
---|
| 11 | *
|
---|
| 12 | * HeuristicLab is distributed in the hope that it will be useful,
|
---|
| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
|
---|
| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
---|
| 15 | * GNU General Public License for more details.
|
---|
| 16 | *
|
---|
| 17 | * You should have received a copy of the GNU General Public License
|
---|
| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
|
---|
| 19 | */
|
---|
| 20 |
|
---|
| 21 | //Code is based on an implementation from Laurens van der Maaten
|
---|
| 22 |
|
---|
| 23 | /*
|
---|
| 24 | *
|
---|
| 25 | * Copyright (c) 2014, Laurens van der Maaten (Delft University of Technology)
|
---|
| 26 | * All rights reserved.
|
---|
| 27 | *
|
---|
| 28 | * Redistribution and use in source and binary forms, with or without
|
---|
| 29 | * modification, are permitted provided that the following conditions are met:
|
---|
| 30 | * 1. Redistributions of source code must retain the above copyright
|
---|
| 31 | * notice, this list of conditions and the following disclaimer.
|
---|
| 32 | * 2. Redistributions in binary form must reproduce the above copyright
|
---|
| 33 | * notice, this list of conditions and the following disclaimer in the
|
---|
| 34 | * documentation and/or other materials provided with the distribution.
|
---|
| 35 | * 3. All advertising materials mentioning features or use of this software
|
---|
| 36 | * must display the following acknowledgement:
|
---|
| 37 | * This product includes software developed by the Delft University of Technology.
|
---|
| 38 | * 4. Neither the name of the Delft University of Technology nor the names of
|
---|
| 39 | * its contributors may be used to endorse or promote products derived from
|
---|
| 40 | * this software without specific prior written permission.
|
---|
| 41 | *
|
---|
| 42 | * THIS SOFTWARE IS PROVIDED BY LAURENS VAN DER MAATEN ''AS IS'' AND ANY EXPRESS
|
---|
| 43 | * OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
|
---|
| 44 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
|
---|
| 45 | * EVENT SHALL LAURENS VAN DER MAATEN BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
---|
| 46 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
|
---|
| 47 | * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
|
---|
| 48 | * BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
---|
| 49 | * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
|
---|
| 50 | * IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
|
---|
| 51 | * OF SUCH DAMAGE.
|
---|
| 52 | *
|
---|
| 53 | */
|
---|
| 54 | #endregion
|
---|
| 55 |
|
---|
| 56 | using System.Collections.Generic;
|
---|
| 57 | using System.Linq;
|
---|
[14785] | 58 | using HeuristicLab.Collections;
|
---|
[14414] | 59 | using HeuristicLab.Random;
|
---|
| 60 |
|
---|
| 61 | namespace HeuristicLab.Algorithms.DataAnalysis {
|
---|
[14783] | 62 | /// <summary>
|
---|
| 63 | /// Vantage point tree (or VP tree) is a metric tree that segregates data in a metric space by choosing
|
---|
| 64 | /// a position in the space (the "vantage point") and partitioning the data points into two parts:
|
---|
| 65 | /// those points that are nearer to the vantage point than a threshold, and those points that are not.
|
---|
| 66 | /// By recursively applying this procedure to partition the data into smaller and smaller sets, a tree
|
---|
| 67 | /// data structure is created where neighbors in the tree are likely to be neighbors in the space.
|
---|
| 68 | /// </summary>
|
---|
| 69 | /// <typeparam name="T"></typeparam>
|
---|
[15207] | 70 | public class VantagePointTree<T> {
|
---|
[14785] | 71 | private readonly List<T> items;
|
---|
| 72 | private readonly Node root;
|
---|
| 73 | private readonly IDistance<T> distance;
|
---|
[14414] | 74 |
|
---|
[14785] | 75 | public VantagePointTree(IDistance<T> distance, IEnumerable<T> items) : base() {
|
---|
[14414] | 76 | root = null;
|
---|
| 77 | this.distance = distance;
|
---|
| 78 | this.items = items.Select(x => x).ToList();
|
---|
| 79 | root = BuildFromPoints(0, this.items.Count);
|
---|
| 80 | }
|
---|
| 81 |
|
---|
[15207] | 82 | /// <summary>
|
---|
| 83 | /// provides the k-nearest neighbours to a certain target element
|
---|
| 84 | /// </summary>
|
---|
| 85 | /// <param name="target">The target element</param>
|
---|
| 86 | /// <param name="k">How many neighbours</param>
|
---|
| 87 | /// <param name="results">The nearest neighbouring elements</param>
|
---|
| 88 | /// <param name="distances">The distances form the target corresponding to the neighbouring elements</param>
|
---|
[14785] | 89 | public void Search(T target, int k, out IList<T> results, out IList<double> distances) {
|
---|
| 90 | var heap = new PriorityQueue<double, IndexedItem<double>>(double.MaxValue, double.MinValue, k);
|
---|
[15207] | 91 | var tau = double.MaxValue;
|
---|
[14855] | 92 | Search(root, target, k, heap, ref tau);
|
---|
[14785] | 93 | var res = new List<T>();
|
---|
| 94 | var dist = new List<double>();
|
---|
[14414] | 95 | while (heap.Size > 0) {
|
---|
[15207] | 96 | res.Add(items[heap.PeekMinValue().Index]);// actually max distance
|
---|
[14785] | 97 | dist.Add(heap.PeekMinValue().Value);
|
---|
[14414] | 98 | heap.RemoveMin();
|
---|
| 99 | }
|
---|
[15207] | 100 | res.Reverse();
|
---|
[14785] | 101 | dist.Reverse();
|
---|
| 102 | results = res;
|
---|
| 103 | distances = dist;
|
---|
[14414] | 104 | }
|
---|
| 105 |
|
---|
[14855] | 106 | private void Search(Node node, T target, int k, PriorityQueue<double, IndexedItem<double>> heap, ref double tau) {
|
---|
[14785] | 107 | if (node == null) return;
|
---|
| 108 | var dist = distance.Get(items[node.index], target);
|
---|
| 109 | if (dist < tau) {
|
---|
[14855] | 110 | if (heap.Size == k) heap.RemoveMin(); // remove furthest node from result list (if we already have k results)
|
---|
[15207] | 111 | heap.Insert(-dist, new IndexedItem<double>(node.index, dist));
|
---|
[14785] | 112 | if (heap.Size == k) tau = heap.PeekMinValue().Value;
|
---|
| 113 | }
|
---|
| 114 | if (node.left == null && node.right == null) return;
|
---|
| 115 |
|
---|
| 116 | if (dist < node.threshold) {
|
---|
[14855] | 117 | if (dist - tau <= node.threshold) Search(node.left, target, k, heap, ref tau); // if there can still be neighbors inside the ball, recursively search left child first
|
---|
| 118 | if (dist + tau >= node.threshold) Search(node.right, target, k, heap, ref tau); // if there can still be neighbors outside the ball, recursively search right child
|
---|
[14785] | 119 | } else {
|
---|
[14855] | 120 | if (dist + tau >= node.threshold) Search(node.right, target, k, heap, ref tau); // if there can still be neighbors outside the ball, recursively search right child first
|
---|
| 121 | if (dist - tau <= node.threshold) Search(node.left, target, k, heap, ref tau); // if there can still be neighbors inside the ball, recursively search left child
|
---|
[14785] | 122 | }
|
---|
| 123 | }
|
---|
| 124 |
|
---|
[14414] | 125 | private Node BuildFromPoints(int lower, int upper) {
|
---|
| 126 | if (upper == lower) // indicates that we're done here!
|
---|
| 127 | return null;
|
---|
| 128 |
|
---|
| 129 | // Lower index is center of current node
|
---|
| 130 | var node = new Node { index = lower };
|
---|
| 131 | var r = new MersenneTwister(); //outer behaviour does not change with the random seed => no need to take the IRandom from the algorithm
|
---|
[14855] | 132 | if (upper - lower <= 1) return node;
|
---|
[14414] | 133 |
|
---|
[14855] | 134 | // if we did not arrive at leaf yet
|
---|
[14414] | 135 | // Choose an arbitrary point and move it to the start
|
---|
[14855] | 136 | var i = (int)(r.NextDouble() * (upper - lower - 1)) + lower;
|
---|
[14414] | 137 | items.Swap(lower, i);
|
---|
| 138 |
|
---|
| 139 | // Partition around the median distance
|
---|
| 140 | var median = (upper + lower) / 2;
|
---|
[15532] | 141 | items.PartialSort(lower + 1, upper - 1, median, distance.GetDistanceComparer(items[lower]));
|
---|
[14414] | 142 |
|
---|
| 143 | // Threshold of the new node will be the distance to the median
|
---|
| 144 | node.threshold = distance.Get(items[lower], items[median]);
|
---|
| 145 |
|
---|
| 146 | // Recursively build tree
|
---|
| 147 | node.index = lower;
|
---|
| 148 | node.left = BuildFromPoints(lower + 1, median);
|
---|
| 149 | node.right = BuildFromPoints(median, upper);
|
---|
| 150 |
|
---|
| 151 | // Return result
|
---|
| 152 | return node;
|
---|
| 153 | }
|
---|
| 154 |
|
---|
[14785] | 155 | private sealed class Node {
|
---|
[14414] | 156 | public int index;
|
---|
| 157 | public double threshold;
|
---|
| 158 | public Node left;
|
---|
| 159 | public Node right;
|
---|
| 160 |
|
---|
| 161 | internal Node() {
|
---|
| 162 | index = 0;
|
---|
| 163 | threshold = 0;
|
---|
| 164 | left = null;
|
---|
| 165 | right = null;
|
---|
| 166 | }
|
---|
| 167 | }
|
---|
| 168 | }
|
---|
| 169 | }
|
---|