模式识别（四） K-means聚类

• 问题描述

编程实现K均值算法对iris和sonar数据进行聚类。

• 基本原理

• 实验结果

• MATLAB核心代码展示

1、Kmeans函数

% Kmeans_.m

function [a,m] = Kmeans_(dataset,k)
color=['r.';'b.';'g.';'m.'];
for i=1:round(10/3)
    color=[color;color];
end
[n,p]=size(dataset);
p=p-1;
plotindex=unidrnd(p,1,2);  % 随机选两维特征画图
 
r=randperm(n);   %生成关于行数的随机排列行数序列
dataset=dataset(r, :);  %根据这个序列进行重新排序
data=dataset(:,1:end-1);
 
m=data(1:k,:);  % 初始化样本点中心
class=ones([1,n])*(-1);  % 分类结果
flag=1;
while flag
    % 按样本中心点分类
    for i=1:n
        d=zeros([1,k]);
        for j=1:k
            d(j)=Euclidean(data(i,:),m(j,:));
        end
        [value,index]=min(d);
        class(i)=index;
    end
    newdataset=[dataset,class'];
    newdataset=sort_label(newdataset);
    dataset=newdataset(:,1:end-1);  % 储存标签
    newdataset=[dataset(:,1:end-1),newdataset(:,end)];
 
    % 更新样本点中心
    old_m=m;
    classset=[];  % 同类集
    theclass=newdataset(1,end);  % 当前类
    for i=1:n
        classset=[classset;newdataset(i,1:end-1)];
        if i~=n && newdataset(i+1,end) ~= theclass
            m(theclass,:)=mean(classset);
            classset=[];
            theclass=newdataset(i+1,end);
        elseif i==n
            m(theclass,:)=mean(classset);
            classset=[];
        end
    end
    Euclidean(m,old_m)
    flag = Euclidean(m,old_m)>0.1;
    data=newdataset(:,1:end-1);
end
 
for i=1:n
    d=zeros([1,k]);
    for j=1:k
        d(j)=Euclidean(data(i,:),m(j,:));
    end
    [value,index]=min(d);
    class(i)=index;
end
newdataset=[dataset,class'];
newdataset=sort_label(newdataset);
dataset=newdataset(:,1:end-1);  % 储存标签
newdataset=[dataset(:,1:end-1),newdataset(:,end)];
data=newdataset(:,1:end-1);
acc=[];
for j=1:k
    d=zeros([1,n]);
    for i=1:n
       d(i)=Euclidean(data(i,:),m(j,:));
    end
    [value,index]=min(d);
    a=dataset(index,end);
    for i=1:n
       if newdataset(i,end)==j
           acc(end+1)=dataset(i,end)==a;
       end
    end    
end
a=mean(acc);
 
figure()
hold on
for i=1:n
    plot(m(:,1)',m(:,2)','ko')
    for j=1:k
        if newdataset(i,end)==j
            plot(dataset(i,plotindex(1)),dataset(i,plotindex(2)),color(j,:))
        end
    end 
end
hold off
 
figure()
hold on
for i=1:n
    for j=1:k
        if dataset(i,end)==j
            plot(dataset(i,plotindex(1)),dataset(i,plotindex(2)),color(j,:))
        end
    end 
end
hold off
end
           

2、run.m

% run.m

clc,clear
 
% 导入sonar数据
filename = 'sonar.csv';
dataset_sonar = csvread(filename);
dataset_sonar = sort_label(dataset_sonar);
 
% 导入iris数据
filename = 'iris.csv';
dataset_iris = csvread(filename);
dataset_iris = sort_label(dataset_iris);
 
[acc,m]=Kmeans_(dataset_iris,3);
[acc,m]=Kmeans_(dataset_sonar,2);
           

3、图像分割

clear all;
clc;
colors=[255,0,0;255,255,0;0,0,255;0,255,0;255,0,255;0,255,255;160,32,240;255,128,0;169,169,169];
nColors= 5; %分割的区域个数
I_rgb=imread('bus.jpg');
[nrows,ncols,col]= size(I_rgb);
 
%去噪
filter=ones(5,5);
filter=filter/sum(filter(:));
I_r=I_rgb(:,:,1);
I_g=I_rgb(:,:,2);
I_b=I_rgb(:,:,3);
denoised_r=conv2(I_r,filter,'same');
denoised_g=conv2(I_g,filter,'same');
denoised_b=conv2(I_b,filter,'same');
denoised_rgb=cat(3, denoised_r, denoised_g, denoised_b);
D_rgb=uint8(denoised_rgb);  % 强制为0~255
figure();imshow(D_rgb);title('去噪后图像');%去噪后的结果
 
imggray = rgb2gray(D_rgb);
figure();imshow(imggray);title('gray');
 
%将彩色图像从RGB转化到lab彩色空间
C = makecform('srgb2lab'); %设置转换格式
I_lab = applycform(I_rgb, C);
figure();imshow(I_lab);
 
ab = I_lab;
ab =double(ab);
ab =reshape(ab,nrows*ncols,3);
 
[cluster_idx,cluster_center] =kmeans(ab,nColors,'distance','sqEuclidean','Replicates',2); pixel_labels= reshape(cluster_idx,nrows,ncols);
 
result=I_rgb;
for i=1:nrows 
    for j=1:ncols 
        result(i,j,:)=colors(pixel_labels(i,j),:); 
    end
end
figure(),imshow(result)