数据挖掘：聚类分析

1、k-means:

目的：将n个对象分成k个簇，使得结果簇内的相似度高，而簇间的相似度低，且每个簇至少有一个对象，每个对象只属于一个簇。

思想：在所有对象中指定k个对象作为簇心（也可以自己设定不在对象中的点），计算各个对象到簇心的欧氏距离，并将对象划分到离自己最近的簇心所在的簇中，然后重新计算每个簇的簇心，通过迭代的方法再次计算各个对象到簇心的距离并重新划分，知道符合聚类结果的衡量标准（标准见下文）。

使用算法：迭代

聚类结果衡量标准：（1）各个簇中的点不在变化（2）设定一个准则函数：比如，所有对象到簇心的欧几里德距离；各个簇心的变化在某一个阈值之内

#include <iostream>#include <vector>#include <math.h>#define _NUM 3using namespace std;/**特征对象，表示一个点（对象），每个点有两个属性**/struct Dot{    int attrX;    int attrY;};/**计算两个点的欧氏距离**/double getDist(Dot dot1, Dot dot2){return sqrt((dot1.attrX - dot2.attrX) * (dot1.attrX - dot2.attrX) + (dot1.attrY - dot2.attrY) * (dot1.attrY - dot2.attrY));}/**计算簇的中心**/Dot getCenter(vector<Dot> c){int num = c.size();//注意：这里取得了vector的大小，后面就不要改变它的大小，因为vector是可以动态增加的int total_X = 0;int total_Y = 0;Dot dot_center;for (int i = 0; i < num; i++){total_X += c[i].attrX;total_Y += c[i].attrY;}dot_center.attrX = total_X / num;dot_center.attrY = total_Y / num;return dot_center;}/**准则函数**/double getE(vector<Dot> c[], Dot center[]){double sum = 0.0;for (int i = 0; i < _NUM; i++){vector<Dot> v = c[i];for (int j = 0; j < v.size(); j++){sum += (v[j].attrX - center[i].attrX) * (v[j].attrX - center[i].attrX) + (v[j].attrY - center[i].attrY) * (v[j].attrY - center[i].attrY);}}cout << "sum:" << sum << endl;return sum;}/**将点放到距离最近的簇（中心）**/int chooseClass(Dot d, Dot center[_NUM]){int dist = 0;int toC = 0;for (int i = 0; i < _NUM; i++){int temp = (d.attrX - center[i].attrX) * (d.attrX - center[i].attrX) + (d.attrY - center[i].attrY) * (d.attrY - center[i].attrY);if (i == 0){dist = temp;}else{if (temp < dist){dist = temp;toC = i;}}}return toC;}/**k-Means算法**/void k_Means(vector<Dot> init){vector<Dot> classes[_NUM];//簇数组Dot center[_NUM];//各个簇中心int c;double newE = -1, oldE = -1;for (int i = 0; i < _NUM; i++){cin >> c;classes[i].push_back(init[c - 1]);center[i] = getCenter(classes[i]);cout << "center[" << i << "]:" << center[i].attrX << "\t" << center[i].attrY << endl;}newE = getE(classes,center);cout << "oldE:" << oldE << "\tnewE:" << newE << endl;for (int i = 0; i < _NUM; i++)//清空每个簇{classes[i].clear();}double tmp = newE > oldE ? (newE - oldE) : (oldE - newE);while (tmp >= 1.0 ){for (int i = 0; i < init.size(); i++)//将各个点放在离它最近的簇中{int toC = chooseClass( init[i], center);classes[toC].push_back(init[i]);}cout << "------------------------------" << endl;for (int i = 0; i < _NUM; i++)//打印每个簇中所包含的点{cout << "簇" << i + 1 << ":" << endl;for (int j = 0; j < classes[i].size(); j++){cout << classes[i][j].attrX << "\t" << classes[i][j].attrY << endl;}}cout << "------------------------------" << endl;for (int i = 0; i < _NUM; i++)//更新每个簇的中心点{center[i] = getCenter(classes[i]);cout << "center[" << i << "]:" << center[i].attrX << "\t" << center[i].attrY << endl;}oldE = newE;newE = getE(classes, center);for (int i = 0; i < _NUM; i++)//清空每个簇{classes[i].clear();}tmp = newE > oldE ? (newE - oldE) : (oldE - newE);}}int main(int args, char* arg[]){    int n1,n2;    vector<Dot> init;//用于保存所有的点    while ((cin >> n1 >> n2) && n1 != -1 && n2 != -1)//输入每个点的属性值    {        Dot dot;dot.attrX = n1;  dot.attrY = n2;init.push_back(dot);    }k_Means(init);//调用k-Means算法进行聚类分析return 1;}