QT+VS实现Kmeans++

1、Kmeans++的原理如下：

（1）首先选取样本中任一数据点作为第一个聚类中心；

（2）计算样本每一个数据点至现所有聚类中心的最近距离，并记录下来；

（3）逐一挑选所有数据点最近距离之中的最大值，即最远距离，最大值对应的数据点为待求聚类中心；

（4）剔除已选为聚类中心的样本点，重新计算（2）、（3）步骤，得到指定的最终的聚类中心点数。

2、实现结果如下：

注：当噪点太多时，初始K个聚类中心的计算会出现偏差，从而导致整个聚类结果出现偏差。

3、原始数据读入格式如下：

点号-X坐标-Y坐标（非此格式的数据无法正常读入，程序会报错）

4、根据Kmeans++选择k个初始聚类中心的Kmeans聚类算法整体代码如下：

//Kmeans.cpp文件
#include "Kmeans.h"

Kmeans::Kmeans(QWidget *parent)
    : QWidget(parent)
{
    start = false;
    //dd = blank;
    dd = to2K;
    ui.setupUi(this);
    connect(ui.pushButton, SIGNAL(clicked()), this, SLOT(onBtReadData()));
    connect(ui.pushButton_2, SIGNAL(clicked()), this, SLOT(onBtCalKmeans()));
    connect(ui.pushButton_3, SIGNAL(clicked()), this, SLOT(onBtReadK()));
}

void Kmeans::onBtReadData()
{
    K = ui.lineEdit->text().toInt();
    p.clear();

    //打开文件对话框
    QString fileName = QFileDialog::getOpenFileName(this, tr("打开"));
    QFile file(fileName);
    bool isOpen = 1;
    if (!file.open(QIODevice::ReadOnly | QIODevice::Text))
    {
        isOpen = 0;
        QMessageBox::StandardButton btnValue = QMessageBox::information(this, tr("提示"), tr("打开失败！"));
    }

    //逐行读取文本文件
    QTextStream stream(&file);
    while (!stream.atEnd())
    {
        Pointp pt;
        QString str = stream.readLine();
        QStringList list = str.split(",");
        pt.no = list.at(0);
        pt.x = list.at(1).toDouble();
        pt.y = list.at(2).toDouble();
        p.push_back(pt);
    }

    file.close();

    //判断是否读取完毕
    if (stream.atEnd()&&isOpen)
    {
        QMessageBox box;
        box.setText("数据读取完毕");
        box.exec();
    }
}

void Kmeans::onBtReadK()
{
    QString fileName = QFileDialog::getOpenFileName(this, tr("打开"));
    QFile file(fileName);
    bool isOpen = 1;
    if (!file.open(QIODevice::ReadOnly | QIODevice::Text))
    {
        isOpen = 0;
        QMessageBox::StandardButton btnValue = QMessageBox::information(this, tr("提示"), tr("打开失败！"));
    }
    QTextStream stream(&file);
    while (!stream.atEnd())
    {
        QString str = stream.readLine();
        QStringList list = str.split(",");
        Pointp k1;
        k1.no = list.at(0);
        k1.x = list.at(1).toDouble();
        k1.y = list.at(2).toDouble();
        k.push_back(k1);
    }

    //判断是否读取完毕
    if (stream.atEnd() && isOpen)
    {
        QMessageBox box;
        box.setText("数据读取完毕");
        box.exec();
    }
    dd = readK;
}

void Kmeans::toK()
{
    //随机选取k个初始聚类中心
    for (int i = 0; i < K; i++)
    {
        Pointp k1;
        k1.no = i + 1;
        k1.x = p.at(i).x;
        k1.y = p.at(i).y;
        k.push_back(k1);
    }
}

int Kmeans::onBtCalKmeans()
{
    K = ui.lineEdit->text().toInt();
    if (S.size()&&p.size()==S.size())
    {
        QMessageBox box;
        box.setText("已经计算完成");
        box.exec();
        return 0;
    }

    //if (dd == to2K)
    //{
    //    toK();
    //}

    CalK();

    CalDis();//S
    Calcentroid();//用到S,得dis
    //CKmeans();//用到dis，得new k.

    int iCount = 0;
    while (iCount < K)
    {
        if (dis.size())
        {
            for (int i = 0; i < k.size(); i++)
            {
                for (int j = 0; j < dis.size(); j++)
                {
                    if (k.at(i).no == dis.at(j).noK)
                    {
                        //qDebug() <<"k:" <<k.at(i).no<< k.at(i).x << k.at(i).y;
                        //qDebug() <<"dis:" <<dis.at(i).noK.toInt()<< dis.at(j).sx << dis.at(j).sy<<endl;
                        double detaX = k.at(i).x - dis.at(j).sx;
                        double detaY = k.at(i).y - dis.at(j).sy;
                        double sk = sqrt(detaX * detaX + detaY * detaY);
                        //qDebug() << sk;
                        if (sk == 0)
                        {
                            iCount++;
                        }
                        else
                        {
                            CKmeans();
                        }
                    }
                }
            }
        }

        dis.clear();
        S.clear();
        CalDis();
        Calcentroid();
    }

    start = true;
    qDebug() << "S" << S.size();
    drawPoint();
    //drawK();
    QMessageBox box;
    box.setText("计算完成");
    box.exec();
    qDebug() << "k" << k.size();
    //for (int i = 0; i < S.size(); i++)
    //{
    //    qDebug() << "S:" <<S.at(i).no<< S.at(i).noK;
    //}
    return 1;
}

Kmeans::~Kmeans()
{}

//计算质心
void Kmeans::Calcentroid()
{
    centroid s;
    for (int i = 0; i < k.size(); i++)
    {
        s.sx = 0; s.sy = 0; int iCt = 0;
        for (int j = 0; j < S.size(); j++)
        {
            if (k.at(i).no == S.at(j).noK)
            {
                s.sx = s.sx + S.at(j).x;
                s.sy = s.sy + S.at(j).y;
                iCt++;
            }
        }
        s.noK = k.at(i).no;
        s.sx = s.sx / iCt;
        s.sy = s.sy / iCt;
        dis.push_back(s);
    }
}

//计算每个对象至聚类中心的距离
void Kmeans::CalDis()
{
    for (int i = 0; i < p.size(); i++)
    {
        double s0 = 0; QString no; Dis ss; int t = 0;
        double x1 = p.at(i).x;
        double y1 = p.at(i).y;
        //double x = k.at(0).x;
        //double y = k.at(0).y;
        //s0 = sqrt((x1 - x) * (x1 - x) + (y1 - y) * (y1 - y));
        for (int j = 0; j < k.size(); j++)
        {
            double x2 = k.at(j).x;
            double y2 = k.at(j).y;
            double s1 = sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
            t++;
            if (t == 1)
            {
                s0 = s1;
                no = k.at(j).no;
            }
            if (s1 < s0)
            {
                s0 = s1;
                no = k.at(j).no;
            }
        }
        ss.s = s0;
        ss.no = p.at(i).no;
        ss.x = p.at(i).x;
        ss.y = p.at(i).y;
        ss.noK = no;
        S.push_back(ss);
    }


}

//将新的质心坐标赋值给k
void Kmeans::CKmeans()
{
    for (int i = 0; i < k.size(); i++)
    {
        for (int j = 0; j < dis.size(); j++)
        {
            if (k.at(i).no == dis.at(j).noK)
            {
                k.at(i).x = dis.at(j).sx;
                k.at(i).y = dis.at(j).sy;
            }
        }
    }
}

//绘图函数
void Kmeans::drawPoint()
{
    QPicture pp;
    pp.setBoundingRect(ui.label_2->rect());


    QPainter painterP(&pp);
    QPen pen;
    painterP.setRenderHint(QPainter::Antialiasing, true);

    Pointp p1;
    p1.no = p.at(0).no;
    p1.x = p.at(0).x;
    p1.y = p.at(0).y;
    for (int i = 1; i < p.size(); i++)
    {
        if (p1.x > p.at(i).x)
        {
            p1.x = p.at(i).x;
        }
        if (p1.y > p.at(i).y)
        {
            p1.y = p.at(i).y;
        }
    }
    double xmin = p1.x;
    double ymin = p1.y;

    for (int i = 1; i < p.size(); i++)
    {
        if (p1.x < p.at(i).x)
        {
            p1.x = p.at(i).x;
        }
        if (p1.y < p.at(i).y)
        {
            p1.y = p.at(i).y;
        }
    }
    double xmax = p1.x;
    double ymax = p1.y;

    int w=ui.label_2->width();
    int h=ui.label_2->height();

    double a = w/(xmax -xmin);
    double b1 = h/(ymax -ymin);

    for (int i = 0; i < k.size(); i++)
    {
        int r = qrand() % 256;
        int g = qrand() % 256;
        int b = qrand() % 256;
        QColor color = QColor(r, g, b);

        for (int j = 0; j < S.size(); j++)
        {
            if (k.at(i).no == S.at(j).noK)
            {
                pen.setColor(color);
                painterP.setPen(pen);
                int radius = 5;
                double x = S.at(j).x;
                double y = S.at(j).y;
                x = (x - xmin)*a;
                y = (y - ymin)*b1;
                painterP.drawEllipse(x - radius, y - radius, radius * 2, radius * 2);
            }
        }
    }

    ui.label_2->setPicture(pp);
}

void Kmeans::CalK()
{
    k.push_back(p.at(0));
    CalDistance();

    while (k.size() != K)
    {
        qDebug() << k.size() << k.at(k.size() - 1).no;
        S.clear();
        CalDistance();

        for (auto& val : k)
        {
            qDebug() << "CalK.k1" << val.no << val.x << val.y;
        }
        std::vector<Pointp> vk; int t3 = k.size();
        while (vk.size() != t3)
        {
            Pointp p9 = k.at(0); int t2 = 0;
            for (int i = 1; i < k.size(); i++)
            {
                Pointp p2 = k.at(i);
                if (p9.no.toInt() < k.at(i).no.toInt())
                {
                    p9 = k.at(i);
                    t2 = i;
                }
            }
            k.erase(k.begin() + t2);//删除下标为t2的元素;
            vk.push_back(p9);
        }

        for (int i = vk.size() - 1; i >= 0; i--)
        {
            k.push_back(vk.at(i));
        }

        for (auto& val : k)
        {
            qDebug() <<"CalK.k" << val.no << val.x << val.y;
        }


        int cv = 1;
        for (auto& val : k)
        {
            S.erase(S.begin() + (val.no.toInt() - cv));//删除下标为val.number的元素;
            cv++;
        }

        double s0 = 0;
        Pointp kk;
        kk = { 0,0,0 };
        for (auto& valS : S)
        {
            if (s0 <= valS.s)
            {
                s0 = valS.s;
                kk.no = valS.no;
                kk.x = valS.x;
                kk.y = valS.y;
            }
        }
        k.push_back(kk);
    }

    int count = 1;
    for (auto& val : k)
    {
        val.no = count;
        count++;
        //qDebug() << val.no << val.x << val.y;
    }
}

void Kmeans::drawK()
{
    QPicture pp;
    pp.setBoundingRect(ui.label_2->rect());


    QPainter painterP(&pp);
    QPen pen;
    painterP.setRenderHint(QPainter::Antialiasing, true);

    Pointp p1;
    p1.no = p.at(0).no;
    p1.x = p.at(0).x;
    p1.y = p.at(0).y;
    for (int i = 1; i < p.size(); i++)
    {
        if (p1.x > p.at(i).x)
        {
            p1.x = p.at(i).x;
        }
        if (p1.y > p.at(i).y)
        {
            p1.y = p.at(i).y;
        }
    }
    double xmin = p1.x;
    double ymin = p1.y;

    for (int i = 1; i < p.size(); i++)
    {
        if (p1.x < p.at(i).x)
        {
            p1.x = p.at(i).x;
        }
        if (p1.y < p.at(i).y)
        {
            p1.y = p.at(i).y;
        }
    }
    double xmax = p1.x;
    double ymax = p1.y;

    int w = ui.label_2->width();
    int h = ui.label_2->height();

    double a = w / (xmax - xmin);
    double b1 = h / (ymax - ymin);

    QColor color = QColor(123,223,46);

    for (int i = 0; i < k.size(); i++)
    {
        pen.setColor(color);
        pen.setWidth(3);
        painterP.setPen(pen);
        int radius = 10;
        double x = k.at(i).x;
        double y = k.at(i).y;
        x = (x - xmin) * a;
        y = (y - ymin) * b1;
        painterP.drawEllipse(x - radius, y - radius, radius * 2, radius * 2);
    }

    ui.label_2->setPicture(pp);
}

void Kmeans::CalDistance()
{
    Dis ss;
    for (auto& valP : p)
    {
        double s0 = 0; int c = 1;
        double x1 = valP.x;
        double y1 = valP.y;
        for (auto& valK : k)
        {
            double x2 = valK.x;
            double y2 = valK.y;

            x2 = x2 - x1;
            y2 = y2 - y1;

            double s = sqrt(x2 * x2 + y2 * y2);

            if (c == 1)
            {
                s0 = s;
                ss.no = valP.no;
                ss.noK = valK.no;
                ss.x = valP.x;
                ss.y = valP.y;
                ss.s = s;
                c++;
            }

            if (s0 == 0)
            {
                ss.no = valP.no;
                ss.noK = valK.no;
                ss.x = valP.x;
                ss.y = valP.y;
                ss.s = s;
                break;
            }

            if (s < s0)
            {
                s0 = s;
                ss.no = valP.no;
                ss.noK = valK.no;
                ss.x = valP.x;
                ss.y = valP.y;
                ss.s = s;
            }
        }
        S.push_back(ss);
    }
}

#pragma once

#include <QtWidgets/QWidget>
#include "ui_Kmeans.h"
#include<QFileDialog>
#include<QFile>
#include<QMessageBox>
#include<QTextStream>
#include<vector>
#pragma execution_character_set("UTF-8")
#include<qDebug>
#include<QPainter>
#include<QColor>
#include<QColorDialog>
#include<QPicture>
#include <algorithm>

struct Pointp
{
    double x;
    double y;
    QString no;
};

struct Dis
{
    double x;
    double y;
    QString no;
    QString noK;
    double s;
};

struct centroid
{
    QString noK;
    double sx;
    double sy;
};

enum Pd
{
    readK,
    to2K,
    blank
};

class Kmeans : public QWidget
{
    Q_OBJECT

public:
    Kmeans(QWidget *parent = nullptr);
    ~Kmeans();

public slots:
    void onBtReadData();
    int onBtCalKmeans();
    void onBtReadK();

public:
    std::vector<Pointp> p;//原始数据点
    std::vector<Pointp> k;//各簇质心坐标
    int K;
    std::vector<Dis> S;
    std::vector<centroid> dis;
    bool start;
    Pd dd;

public:
    void Calcentroid();
    void CKmeans();
    void CalDis();
    void drawPoint();
    void CalK();
    void drawK();
    void toK();
    void CalDistance();

private:
    Ui::KmeansClass ui;
};