聚类算法-DBSCAN-C++实现

程序流程图：

DBSCAN核心功能函数，计算每个point的eps范围内的point数量pts；

对于所有pts >Minpts的point，记为Core point；

对于所有的corepoint，将其eps范围内的core point下标添加到vector<int>::corepts中；

对于所有的corepoint，采用深度优先的方式遍历core point的所有cluster，使得相互连接的core point具有相同的cluster编号；

计算所有pts < Minpts且在Core point范围内的，记为Borderpoint；

将所有Borderpoint加入到任意一个关联的core point；

剩余的point的为Noise point，文件写写入时忽略；

将point信息写入clustering文件，程序结束。

/*
	DBSCAN Algorithm
	15S103182
	Ethan
*/
#include <iostream>
#include <sstream>
#include <fstream>
#include <vector>
#include <ctime>
#include <cstdlib>
#include <limits>
#include <cmath>
#include <stack>
using namespace std;
class point{
public:
	float x;
	float y;
	int cluster=0;
	int pointType=1;//1 noise 2 border 3 core
	int pts=0;//points in MinPts
	vector<int> corepts;
	int visited = 0;
	point (){}
	point (float a,float b,int c){
		x = a;
		y = b;
		cluster = c;
	}
};
float stringToFloat(string i){
	stringstream sf;
	float score=0;
	sf<<i;
	sf>>score;
	return score;
}
vector<point> openFile(const char* dataset){
	fstream file;
	file.open(dataset,ios::in);
	if(!file)
    {
        cout <<"Open File Failed!" <<endl;
        vector<point> a;
        return a;
    }
	vector<point> data;
	int i=1;
	while(!file.eof()){
		string temp;
		file>>temp;
		int split = temp.find(',',0);
		point p(stringToFloat(temp.substr(0,split)),stringToFloat(temp.substr(split+1,temp.length()-1)),i++);
		data.push_back(p);
	}
	file.close();
	cout<<"successful!"<<endl;
	return data;
}
float squareDistance(point a,point b){
	return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
void DBSCAN(vector<point> dataset,float Eps,int MinPts){
	int len = dataset.size();
	//calculate pts
	cout<<"calculate pts"<<endl;
	for(int i=0;i<len;i++){
		for(int j=i+1;j<len;j++){
			if(squareDistance(dataset[i],dataset[j])<Eps)
				dataset[i].pts++;
				dataset[j].pts++;
		}
	}
	//core point
	cout<<"core point "<<endl;
	vector<point> corePoint;
	for(int i=0;i<len;i++){
		if(dataset[i].pts>=MinPts) {
			dataset[i].pointType = 3;
			corePoint.push_back(dataset[i]);
		}
	}
	cout<<"joint core point"<<endl;
	//joint core point
	for(int i=0;i<corePoint.size();i++){
		for(int j=i+1;j<corePoint.size();j++){
			if(squareDistance(corePoint[i],corePoint[j])<Eps){
				corePoint[i].corepts.push_back(j);
				corePoint[j].corepts.push_back(i);
			}
		}
	}
	for(int i=0;i<corePoint.size();i++){
		stack<point*> ps;
		if(corePoint[i].visited == 1) continue;
		ps.push(&corePoint[i]);
		point *v;
		while(!ps.empty()){
			v = ps.top();
			v->visited = 1;
			ps.pop();
			for(int j=0;j<v->corepts.size();j++){
				if(corePoint[v->corepts[j]].visited==1) continue;
				corePoint[v->corepts[j]].cluster = corePoint[i].cluster;
				corePoint[v->corepts[j]].visited = 1;
				ps.push(&corePoint[v->corepts[j]]);
			}
		}
	}
	cout<<"border point,joint border point to core point"<<endl;
	//border point,joint border point to core point
	for(int i=0;i<len;i++){
		if(dataset[i].pointType==3) continue;
		for(int j=0;j<corePoint.size();j++){
			if(squareDistance(dataset[i],corePoint[j])<Eps) {
				dataset[i].pointType = 2;
				dataset[i].cluster = corePoint[j].cluster;
				break;
			}
		}
	}
	cout<<"output"<<endl;
	//output
	fstream clustering;
	clustering.open("clustering.txt",ios::out);
	for(int i=0;i<len;i++){
		if(dataset[i].pointType == 2)
			clustering<<dataset[i].x<<","<<dataset[i].y<<","<<dataset[i].cluster<<"\n";
	}
	for(int i=0;i<corePoint.size();i++){
			clustering<<corePoint[i].x<<","<<corePoint[i].y<<","<<corePoint[i].cluster<<"\n";
	}
	clustering.close();
}
int main(int argc, char** argv) {
	vector<point> dataset = openFile("dataset3.txt");
	DBSCAN(dataset,1.5,2);
	return 0;
}

数据文件格式：（x，y）

运行结果格式：（x，y，cluster）

图形化展现：

特殊形状：

桥梁：

变化密度：

总结：

DBSCAN算法能够很好处理不同形状与大小的数据，并且抗噪音数据。但对于变化的密度，DBSCAN算法具有局限性。在实现Core point连接时，遇到了一点小小的麻烦，很难将相互连接的core point的cluster编号统一，后来通过给每个core point增加一个数组用于记录相连core point的下标信息，并采用深度优先进行遍历的方式，不仅提高了计算速度，同时也保证了准确性。对于实验数据结果，如果不对其进行图形化展现，很难看出聚类的效果，采用WPF(C#)技术对数据点进行处理，对不同cluster编号的点，赋予不同的颜色，进行图形展现。