模式识别——C均值算法的实现

中国矿业大学 计算机科学与技术学院 模式识别实验报告课程名称 模式识别 实验名称 C均值算法的实现 姓名 褚钰博 学号 手机 QQ Email: 班级 信科11-1 班 教师 陈伟 手机 QQ Email: cumt_ 实验日期 2014. 06 .09 实验报告要求：1.实验目的 2.实验内容 3.实验原理或步骤 4.运行结果和分析 5.实验体会与总结一、实验目的1.掌握监督学习方法与非监督学习方法的区别，2.对动态聚类方法有深入的理解，了解其步骤，3.掌握C均值算法的基本思想、步骤，4.会熟练运用C均值算法进行聚类，5、通过c均值算法具体实现，熟练掌握其思想。二、实验内容写程序实现c均值算法，并用下表中的三维数据进行测试，下面给出了每种测试的类别数目和初始值。不要求编程环境，可以使用C，MATLAB等语言来实现。（1）c=2, m1(0)=(1,1,1)T, m2(0)=(-1,1,-1)T。 （2）c=2, m1(0)=(0,0,0)T, m2(0)=(1,1,-1)T。将（2）得到的结果与（1）中的结果进行比较，并解释差别，包括迭代次数的差别。（3）c=3, m1(0)=(0,0,0)T, m2(0)=(1,1,1)T, m3(0)=(-1,0,2)T。（4）c=3, m1(0)=(-0.1,0,0.1)T, m2(0)=(0,-0.1,0.1)T, m3(0)=(-0.1,-0.1,0.1)T。将（4）得到的结果与（3）中的结果进行比较，并解释差别，包括迭代次数的差别。数据如下表所示： 样本编号样本编号1-7.82-4.58-3.97116.182.815.822-6.683.162.71126.72-0.93-4.0434.36-2.192.0913-6.25-0.260.5646.720.882.8014-6.94-1.221.135-8.643.063.50158.090.202.256-6.870.57-5.45166.180.17-4.1574.47-2.625.7617-486.73-2.014.1818-6.38-1.741.439-7.712.34-6.33194.081.305.3310-6.91-0.49-5.68206.270.93-2.78三、实验原理或步骤 C均值算法的基本思想即是通过迭代寻找c个聚类的一种划分方案，使得用这c个聚类的均值来代表相应各类样本时所得到的总体误差最小。 C均值算法的基础是最小误差平方和准则。若是第i聚类中的样本数目，是这些样本的均值，即 把中的各样本y与均值间的误差平方和对所有类相加后为是误差平方和聚类准则，它是样本集和类别集的函数。 C均值算法的步骤：1.选择初始划分，并计算每个聚类的均值以及误差平方和；2.选择一个备选样本y，设y； 3.若样本数目为1，则转2，否则继续； 4.计算：ji时，； j=i时， ；5. 考查中的最小者，若，则把y从移到中； 6.重新计算聚类i和k的均值，并修改误差平方和；7.若多次迭代后误差平方和不变，则停止，否则转到步骤2。四、运行结果和分析当c=2时,m1(0)=(1,1,1),m2(0)=(-1,1,-1)currentis:409.49777afterrecalculatemeanby25stepsclass0:(4.36,-2.19,2.09)(6.72,0.88,2.80)(4.47,-2.62,5.76)(6.73,-2.01,4.18)(6.18,2.81,5.82)(6.72,-0.93,-4.04)(8.09,0.20,2.25)(6.18,0.17,-4.15)(4.08,1.30,5.33)(6.27,0.93,-2.78)class1:(-8.64,3.06,3.50)(-6.87,0.57,-5.45)(-7.71,2.34,-6.33)(-6.91,-0.49,-5.68)(-6.25,-0.26,0.56)(-6.94,-1.22,1.13)(-5.19,4.24,4.04)(-6.38,-1.74,1.43)(-7.82，-4.58，-3,.97)(-6.68，3.16，2.71)m1(0)=(0,0,0),m2(0)=(1,1,-1)currentis:409.49777afterrecalculatemeanby18steps(2)的结果与(1)的结果相同，虽然初始设置的聚类均值不同，但它只影响迭代次数，对最后结果没影响。当c=3时,m1(0)=(0,0,0), m2(0)=(1,1,1), m3(0)=(-1,0,2)currentis:263.06184afterrecalculatemeanby35stepsclass0:(-6.87,0.57,-5.45)(-7.71,2.34,-6.33)(-6.91,-0.49,-5.68)(-7.82，-4.58，-3,.97)class1:(6.72,0.88,2.80)(4.47,-2.62,5.76)(6.73,-2.01,4.18)(6.18,2.81,5.82)(6.72,-0.93,-4.04)(8.09,0.20,2.25)(6.18,0.17,-4.15)(4.08,1.30,5.33)(6.27,0.93,-2.78)(4.36，-2.19，2.09)class2:(-8.64,3.06,3.50)(-6.25,-0.26,0.56)(-6.94,-1.22,1.13)(-5.19,4.24,4.04)(-6.38,-1.74,1.43)(-6.68，3.16，2.71)m1(0)=(-0.1,0,0.1),m2(0)=(0,-0.1,0.1),m3(0)=(-0.1,-0.1,0.1)currentis:295.afterrecalculatemeanby22stepsclass0:(-8.64,3.06,3.50)(-6.25,-0.26,0.56)(-7.82，-4.58，-3,.97)(-6.94,-1.22,1.13)(-5.19,4.24,4.04)(-6.38,-1.74,1.43)(4.36，-2.19，2.09)class1:(6.72,0.88,2.80)(4.47,-2.62,5.76)(6.73,-2.01,4.18)(6.18,2.81,5.82)(6.72,-0.93,-4.04)(8.09,0.20,2.25)(6.18,0.17,-4.15)(4.08,1.30,5.33)(6.27,0.93,-2.78)class2:(-6.91,-0.49,-5.68)(-6.87,0.57,-5.45)(-7.71,2.34,-6.33)(-6.68，3.16，2.71)( 3 )和( 4 )的聚类结果也基本接近，初始均值设置的不同会影响迭代的次数以及各次迭代所产生的聚类中心，但它不会影响最后的分类结果。程序如下：clear all dataset=-7.82,-4.58,-3.97;-6.68,3.16,2.71;4.36,-2.19,2.09;6.72,0.88,2.80;-8.64,3.06,3.50; -6.87,0.57,-5.45;4.47,-2.62,5.76;6.73,-2.01,4.18;-7.71,2.34,-6.33;-6.91,-0.49,-5.68; 6.18,2.81,5.82;6.72,-0.93,-4.04;-6.25,-0.26,0.56;-6.94,-1.22,1.13;8.09,0.20,2.25; 6.18,0.17,-4.15;-5.19,4.24,4.04;-6.38,-1.74,1.43;4.08,1.30,5.33;6.27,0.93,-2.78; center1=1 1 1;-1 1 -1; center2=0 0 0;1 1 -1; center3=0 0 0;1 1 1;-1 0 2; center4=-0.1 0 0.1;0 -0.1 0.1;-0.1 -0.1 0.1; %kmeans k_class1,C1,sumd1,D1=kmean(dataset.data,2,start,center1); one1=dataset.data(find(k_class1=1),:); second1=dataset.data(find(k_class1=2),:); scatter3(one1(:,1),one1(:,2),one1(:,3),*,r) hold on scatter3(second1(:,1),second1(:,2),second1(:,3),o,g) hold off xlabel(X1,Fontsize,15);ylabel(X2,Fontsize,15);zlabel(X3,Fontsize,15);title(the first results of kmeans,Fontsize,15) % k_class2,C2,sumd2,D2=kmeans(dataset.data,2,start,center2); one2=dataset.data(find(k_class2=1),:); second2=dataset.data(find(k_class2=2),:); figure,scatter3(one2(:,1),one2(:,2),one2(:,3),*,r) hold on scatter3(second2(:,1),second2(:,2),second2(:,3),o,g) hold off xlabel(X1,Fontsize,15);ylabel(X2,Fontsize,15);zlabel(X3,Fontsize,15);title(the second results of kmeans,Fontsize,15) % k_class3,C3,sumd3,D3=kmeans(dataset.data,3,start,center3); one3=dataset.data(find(k_class3=1),:); second3=dataset.data(find(k_class3=2),:); third3=dataset.data(find(k_class3=3),:); figure,scatter3(one3(:,1),one3(:,2),one3(:,3),*,r) hold on scatter3(second3(:,1),second3(:,2),second3(:,3),o,g) hold on scatter3(third3(:,1),third3(:,2),third3(:,3),x,b) hold off xlabel(X1,Fontsize,15);ylabel(X2,Fontsize,15);zlabel(X3,Fontsize,15);title(the third results of kmeans,Fontsize,15) % k_class4,C4,sumd4,D4=kmeans(dataset.data,3,start,center4); one4=dataset.data(find(k_class4=1),:); second4=dataset.data(find(k_class4=2),:); third4=dataset.data(find(k_class4=3),:); figure,scatter3(one4(:,1),one4(:,2),one4(:,3),*,r) hold on scatter3(second4(:,1),second4(:,2),second4(:,3),o,g) hold on scatter3(third4(:,1),third4(:,2),third4(:,3),x,b) hold off xlabel(X1,Fontsize,15);ylabel(X2,Fontsize,15);zlabel(X3,Fontsize,15);title(the fourth results of kmeans,Fontsize,15) %fcm class_jwei1,fuzzy_jwei1=fcm_jwei(dataset.sample,2,center1,2); class_jwei2,fuzzy_jwei2=fcm_jwei(dataset.sample,2,center2,2); class_jwei3,fuzzy_jwei3=fcm_jwei(dataset.sample,2,center3,3); class_jwei4,fuzzy_jwei4=fcm_jwei(dataset.sample,2,center4,3); %子函数fcm_jwei部分 function class_center,fuzzy,time=fcm_jwei(sample,b,initial_center,class_num) % close all % clear all % clc % dataset=load(F:?e2010experience1.mat); % initial_center=0 0 0;1 1 1;-1 0 2; % b=2; % class_num=3; % sample=dataset.sample; %sample is a two demention matrix,each row is a feature feature_num,sample_num=size(sample); fuzzy=zeros(class_num,sample_num); class_center=initial_center; class_cen=initial_center; time=0; while(1) for i=1:sample_num for j=1:class_num fuzzy(j,i)=(sample(:,i)-class_center(:,j)*. (sample(:,i)-class_center(:,j)+eps; fuzzy(j,i)=fuzzy(j,i).(-(1/(b-1); end end normal_