KNN算法即k-Nearest Neighbor algorithm，是一个理论上比较成熟的方法，也是最简单的机器学习算法之一,可应用于基于智能终端传感器的活动识别。KNN算法思路如下：
1、假设一个样本空间里的样本可分成几个类型
2、给定一个未知类型的待分类样本
3、基本思路：
a人以类聚、物以群归
b待分类样本与哪一类的样本比较相近，就归属于哪一类
c具体的相近比较基于最近的K个样本
d归属于K个样本中的多数样本所属的类
维基百科上的KNN词条中有一个比较经典的图如右：
从右图中可以看到
-图中的有两个类型的样本数据 
-一类是蓝色的正方形
-一类是红色的三角形。
-绿色的圆形是待分类的数据。
如果K=3，那么离绿色点最近的有2个红色三角形和1个蓝色的正方形，这3个点投票，于是绿色的这个待分类点属于红色的三角形。
如果K=5，那么离绿色点最近的有2个红色三角形和3个蓝色的正方形，这5个点投票，于是绿色的这个待分类点属于蓝色的正方形。
KNN算法实现：
Knn.h
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#pragma once class Knn { private: double** trainingDataset; double* arithmeticMean; double* standardDeviation; int m, n; void RescaleDistance(double* row); void RescaleTrainingDataset(); void ComputeArithmeticMean(); void ComputeStandardDeviation(); double Distance(double* x, double* y); public: Knn(double** trainingDataset, int m, int n); ~Knn(); double Vote(double* test, int k); }; |
Knn.cpp
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#include "Knn.h" #include <cmath> #include <map> using namespace std; Knn::Knn(double** trainingDataset, int m, int n) { this->trainingDataset = trainingDataset; this->m = m; this->n = n; ComputeArithmeticMean(); ComputeStandardDeviation(); RescaleTrainingDataset(); } void Knn::ComputeArithmeticMean() { arithmeticMean = new double[n - 1]; double sum; for(int i = 0; i < n - 1; i++) { sum = 0; for(int j = 0; j < m; j++) { sum += trainingDataset[j][i]; } arithmeticMean[i] = sum / n; } } void Knn::ComputeStandardDeviation() { standardDeviation = new double[n - 1]; double sum, temp; for(int i = 0; i < n - 1; i++) { sum = 0; for(int j = 0; j < m; j++) { temp = trainingDataset[j][i] - arithmeticMean[i]; sum += temp * temp; } standardDeviation[i] = sqrt(sum / n); } } void Knn::RescaleDistance(double* row) { for(int i = 0; i < n - 1; i++) { row[i] = (row[i] - arithmeticMean[i]) / standardDeviation[i]; } } void Knn::RescaleTrainingDataset() { for(int i = 0; i < m; i++) { RescaleDistance(trainingDataset[i]); } } Knn::~Knn() { delete[] arithmeticMean; delete[] standardDeviation; } double Knn::Distance(double* x, double* y) { double sum = 0, temp; for(int i = 0; i < n - 1; i++) { temp = (x[i] - y[i]); sum += temp * temp; } return sqrt(sum); } double Knn::Vote(double* test, int k) { RescaleDistance(test); double distance; map<int, double>::iterator max; map<int, double> mins; for(int i = 0; i < m; i++) { distance = Distance(test, trainingDataset[i]); if(mins.size() < k) mins.insert(map<int, double>::value_type(i, distance)); else { max = mins.begin(); for(map<int, double>::iterator it = mins.begin(); it != mins.end(); it++) { if(it->second > max->second) max = it; } if(distance < max->second) { mins.erase(max); mins.insert(map<int, double>::value_type(i, distance)); } } } map<double, int> votes; double temp; for(map<int, double>::iterator it = mins.begin(); it != mins.end(); it++) { temp = trainingDataset[it->first][n-1]; map<double, int>::iterator voteIt = votes.find(temp); if(voteIt != votes.end()) voteIt->second ++; else votes.insert(map<double, int>::value_type(temp, 1)); } map<double, int>::iterator maxVote = votes.begin(); for(map<double, int>::iterator it = votes.begin(); it != votes.end(); it++) { if(it->second > maxVote->second) maxVote = it; } test[n-1] = maxVote->first; return maxVote->first; } |
main.cpp
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#include <iostream> #include "Knn.h" using namespace std; int main(const int& argc, const char* argv[]) { double** train = new double* [14]; for(int i = 0; i < 14; i ++) train[i] = new double[5]; double trainArray[14][5] = { {0, 0, 0, 0, 0}, {0, 0, 0, 1, 0}, {1, 0, 0, 0, 1}, {2, 1, 0, 0, 1}, {2, 2, 1, 0, 1}, {2, 2, 1, 1, 0}, {1, 2, 1, 1, 1}, {0, 1, 0, 0, 0}, {0, 2, 1, 0, 1}, {2, 1, 1, 0, 1}, {0, 1, 1, 1, 1}, {1, 1, 0, 1, 1}, {1, 0, 1, 0, 1}, {2, 1, 0, 1, 0} }; for(int i = 0; i < 14; i ++) for(int j = 0; j < 5; j ++) train[i][j] = trainArray[i][j]; Knn knn(train, 14, 5); double test[5] = {2, 2, 0, 1, 0}; cout<<knn.Vote(test, 3)<<endl; for(int i = 0; i < 14; i ++) delete[] train[i]; delete[] train; return 0; } |
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