具体描述见《统计学习方法》第三章。
1 //
2 // main.cpp
3 // kNN
4 //
5 // Created by feng on 15/10/24.
6 // Copyright © 2015年 ttcn. All rights reserved.
7 //
8
9 #include <iostream>
10 #include <vector>
11 #include <algorithm>
12 #include <cmath>
13 using namespace std;
14
15 template<typename T>
16 struct KdTree {
17 // ctor
18 KdTree():parent(nullptr), leftChild(nullptr), rightChild(nullptr) {}
19
20 // KdTree是否为空
21 bool isEmpty() { return root.empty(); }
22
23 // KdTree是否为叶子节点
24 bool isLeaf() { return !root.empty() && !leftChild && !rightChild;}
25
26 // KdTree是否为根节点
27 bool isRoot() { return !isEmpty() && !parent;}
28
29 // 判断KdTree是否为根节点的左儿子
30 bool isLeft() { return parent->leftChild->root == root; }
31
32 // 判断KdTree是否为根节点的右儿子
33 bool isRight() { return parent->rightChild->root == root; }
34
35 // 存放根节点的数据
36 vector<T> root;
37
38 // 父节点
39 KdTree<T> *parent;
40
41 // 左儿子
42 KdTree<T> *leftChild;
43
44 // 右儿子
45 KdTree<T> *rightChild;
46 };
47
48
49 /**
50 * 矩阵转置
51 *
52 * @param matrix 原矩阵
53 *
54 * @return 原矩阵的转置矩阵
55 */
56 template<typename T>
57 vector<vector<T>> transpose(const vector<vector<T>> &matrix) {
58 size_t rows = matrix.size();
59 size_t cols = matrix[0].size();
60 vector<vector<T>> trans(cols, vector<T>(rows, 0));
61 for (size_t i = 0; i < cols; ++i) {
62 for (size_t j = 0; j < rows; ++j) {
63 trans[i][j] = matrix[j][i];
64 }
65 }
66
67 return trans;
68 }
69
70 /**
71 * 找中位数
72 *
73 * @param vec 数组
74 *
75 * @return 数组中的中位数
76 */
77 template<typename T>
78 T findMiddleValue(vector<T> vec) {
79 sort(vec.begin(), vec.end());
80 size_t pos = vec.size() / 2;
81 return vec[pos];
82 }
83
84 /**
85 * 递归构造KdTree
86 *
87 * @param tree KdTree根节点
88 * @param data 数据矩阵
89 * @param depth 当前节点深度
90 *
91 * @return void
92 */
93 template<typename T>
94 void buildKdTree(KdTree<T> *tree, vector<vector<T>> &data, size_t depth) {
95 // 输入数据个数
96 size_t samplesNum = data.size();
97
98 if (samplesNum == 0) {
99 return;
100 }
101
102 if (samplesNum == 1) {
103 tree->root = data[0];
104 return;
105 }
106
107 // 每一个输入数据的维度，属性个数
108 size_t k = data[0].size();
109 vector<vector<T>> transData = transpose(data);
110
111 // 找到当前切分点
112 size_t splitAttributeIndex = depth % k;
113 vector<T> splitAttributes = transData[splitAttributeIndex];
114 T splitValue = findMiddleValue(splitAttributes);
115
116 vector<vector<T>> leftSubSet;
117 vector<vector<T>> rightSubset;
118
119 for (size_t i = 0; i < samplesNum; ++i) {
120 if (splitAttributes[i] == splitValue && tree->isEmpty()) {
121 tree->root = data[i];
122 } else if (splitAttributes[i] < splitValue) {
123 leftSubSet.push_back(data[i]);
124 } else {
125 rightSubset.push_back(data[i]);
126 }
127 }
128
129 tree->leftChild = new KdTree<T>;
130 tree->leftChild->parent = tree;
131 tree->rightChild = new KdTree<T>;
132 tree->rightChild->parent = tree;
133 buildKdTree(tree->leftChild, leftSubSet, depth + 1);
134 buildKdTree(tree->rightChild, rightSubset, depth + 1);
135 }
136
137 /**
138 * 递归打印KdTree
139 *
140 * @param tree KdTree
141 * @param depth 当前深度
142 *
143 * @return void
144 */
145 template<typename T>
146 void printKdTree(const KdTree<T> *tree, size_t depth) {
147 for (size_t i = 0; i < depth; ++i) {
148 cout << "\t";
149 }
150
151 for (size_t i = 0; i < tree->root.size(); ++i) {
152 cout << tree->root[i] << " ";
153 }
154 cout << endl;
155
156 if (tree->leftChild == nullptr && tree->rightChild == nullptr) {
157 return;
158 } else {
159 if (tree->leftChild) {
160 for (int i = 0; i < depth + 1; ++i) {
161 cout << "\t";
162 }
163 cout << "left : ";
164 printKdTree(tree->leftChild, depth + 1);
165 }
166
167 cout << endl;
168
169 if (tree->rightChild) {
170 for (size_t i = 0; i < depth + 1; ++i) {
171 cout << "\t";
172 }
173 cout << "right : ";
174 printKdTree(tree->rightChild, depth + 1);
175 }
176 cout << endl;
177 }
178 }
179
180 /**
181 * 节点之间的欧氏距离
182 *
183 * @param p1 节点1
184 * @param p2 节点2
185 *
186 * @return 节点之间的欧式距离
187 */
188 template<typename T>
189 T calDistance(const vector<T> &p1, const vector<T> &p2) {
190 T res = 0;
191 for (size_t i = 0; i < p1.size(); ++i) {
192 res += pow(p1[i] - p2[i], 2);
193 }
194
195 return res;
196 }
197
198 /**
199 * 搜索目标节点的最近邻
200 *
201 * @param tree KdTree
202 * @param goal 待分类的节点
203 *
204 * @return 最近邻节点
205 */
206 template <typename T>
207 vector<T> searchNearestNeighbor(KdTree<T> *tree, const vector<T> &goal ) {
208 // 节点数属性个数
209 size_t k = tree->root.size();
210 // 划分的索引
211 size_t d = 0;
212 KdTree<T> *currentTree = tree;
213 vector<T> currentNearest = currentTree->root;
214 // 找到目标节点的最叶节点
215 while (!currentTree->isLeaf()) {
216 size_t index = d % k;
217 if (currentTree->rightChild->isEmpty() || goal[index] < currentNearest[index]) {
218 currentTree = currentTree->leftChild;
219 } else {
220 currentTree = currentTree->rightChild;
221 }
222
223 ++d;
224 }
225 currentNearest = currentTree->root;
226 T currentDistance = calDistance(goal, currentTree->root);
227
228 KdTree<T> *searchDistrict;
229 if (currentTree->isLeft()) {
230 if (!(currentTree->parent->rightChild)) {
231 searchDistrict = currentTree;
232 } else {
233 searchDistrict = currentTree->parent->rightChild;
234 }
235 } else {
236 searchDistrict = currentTree->parent->leftChild;
237 }
238
239 while (!(searchDistrict->parent)) {
240 T districtDistance = abs(goal[(d + 1) % k] - searchDistrict->parent->root[(d + 1) % k]);
241
242 if (districtDistance < currentDistance) {
243 T parentDistance = calDistance(goal, searchDistrict->parent->root);
244
245 if (parentDistance < currentDistance) {
246 currentDistance = parentDistance;
247 currentTree = searchDistrict->parent;
248 currentNearest = currentTree->root;
249 }
250
251 if (!searchDistrict->isEmpty()) {
252 T rootDistance = calDistance(goal, searchDistrict->root);
253 if (rootDistance < currentDistance) {
254 currentDistance = rootDistance;
255 currentTree = searchDistrict;
256 currentNearest = currentTree->root;
257 }
258 }
259
260 if (!(searchDistrict->leftChild)) {
261 T leftDistance = calDistance(goal, searchDistrict->leftChild->root);
262 if (leftDistance < currentDistance) {
263 currentDistance = leftDistance;
264 currentTree = searchDistrict;
265 currentNearest = currentTree->root;
266 }
267 }
268
269 if (!(searchDistrict->rightChild)) {
270 T rightDistance = calDistance(goal, searchDistrict->rightChild->root);
271 if (rightDistance < currentDistance) {
272 currentDistance = rightDistance;
273 currentTree = searchDistrict;
274 currentNearest = currentTree->root;
275 }
276 }
277
278 }
279
280 if (!(searchDistrict->parent->parent)) {
281 searchDistrict = searchDistrict->parent->isLeft()? searchDistrict->parent->parent->rightChild : searchDistrict->parent->parent->leftChild;
282 } else {
283 searchDistrict = searchDistrict->parent;
284 }
285 ++d;
286 }
287
288 return currentNearest;
289 }
290
291 int main(int argc, const char * argv[]) {
292 vector<vector<double>> trainDataSet{{2,3},{5,4},{9,6},{4,7},{8,1},{7,2}};
293 KdTree<double> *kdTree = new KdTree<double>;
294 buildKdTree(kdTree, trainDataSet, 0);
295 printKdTree(kdTree, 0);
296
297 vector<double> goal{3, 4.5};
298 vector<double> nearestNeighbor = searchNearestNeighbor(kdTree, goal);
299
300 for (auto i : nearestNeighbor) {
301 cout << i << " ";
302 }
303 cout << endl;
304
305 return 0;
306 }
时间： 2024-11-10 03:06:55