基于粗糙集分类器的手写数字识别matlab实现
作者：互联网
1.计算等价集和下近似集
load ('template.mat');
patternNum=75;%每个类别取75个样品
bottom=zeros(patternNum*2,1);
bottom(1:patternNum,1)=0;
bottom(patternNum+1:patternNum*2,1)=1;
x=[pattern(1).feature(1:patternNum,:);
pattern(2).feature(1:patternNum,:)];%取75个第一类样品和75个第二类样品按列连接
x=[x bottom];%按行连接决策属性，构造出决策表
x=ceil(x);%特征二值化
ruleNum=patternNum*2;%决策表的行数，即样品总数
classX=zeros(ruleNum,ruleNum);%属性C的等价集矩阵（因为等价集最多为ruleNum个，且每个等价集最多有ruleNum个元素，定义一个ruleNum*ruleNum的全零矩阵用于存放等价集）
classNum=zeros(ruleNum,1);%定义一个ruleNum维的全零行向量用于存放各等价集中元素个数
%去重规则和不一致规则
for i=1:ruleNum-1
if(i>ruleNum-1)
break;
end
for j=i+1:ruleNum
if(j>ruleNum)
break;
end
while (x(i,1:25)==x(j,1:25))
x(j,:)=[];
ruleNum=ruleNum-1; %统计去重后的样品数量
if(j>ruleNum)
break;
end
end
end
end
x1=x;
%计算所有条件属性C的等价集（各条件属性值都相同的样品组成一个等价集，不考虑决策属性）
%%%%%%%%%%%%%%%%%%%% Begin %%%%%%%%%%%%%%%%%%%%
%去重后的决策表为x，行代表样品，列代表25维条件属性+1维决策属性
function[classX,m,classNum] = CalTiaoJian(num,classX,x,ruleNum,classNum);
if(num ~= 0)
x(1:ruleNum,num) = 0;
end
xNum = size(x,2);
x(:,xNum) = 0;
m=0;
for i = 1:ruleNum
if(x(i,xNum)~= 0)
continue;
else
m = m+1;
x(i,xNum) = m;
n = 1;
classX(m,n) = i;
end
for j = i+1:ruleNum
if(x(j,xNum)~= 0)
continue;
end
if(x(i,1:xNum-1)==x(j,1:xNum-1))
x(j,xNum) = m;
n = n+1;
classX(m,n) = j;
end
end
classNum(m) = n;
end
end
m=0;
n=1;
num=0;
[classX,m,classNum]=CalTiaoJian(num,classX,x,ruleNum,classNum);
fprintf('%s\n',num2str(m)) %输出等价集数量m（需在循环过程中将等价集的数量存入变量m）
%%%%%%%%%%%%%%%%%%%% End %%%%%%%%%%%%%%%%%%%%
%计算决策属性D的等价集
x=x1;
x=x(1:ruleNum,:);
ruleNumY1=0;
for m=1:ruleNum
if (x(m,26)==0)
ruleNumY1=ruleNumY1+1; %找到决策属性为0的样品的最大编号
end
end
ruleNumY2=ruleNum-ruleNumY1;
classY1=zeros(1,ruleNumY1);
classY2=zeros(1,ruleNumY2);
classY1=1:ruleNumY1; %决策属性等价集Y1，前ruleNumY1个样品
classY2=ruleNumY1+1:ruleNum; %决策属性等价集Y2，后ruleNum-ruleNumY1个样品
%计算决策属性等价集Y1、Y2关于所有条件属性C的下近似集C_Y1、C_Y2
%%%%%%%%%%%%%%%%%%%% Begin %%%%%%%%%%%%%%%%%%%%
C_Y1=[];
C_Y2=[];
%通过循环寻找属于U/C（U关于C的商集，也是C所有等价集的集合）的同时包含于classY1/2的样品集合，即为C_Y1/2
function[C_Y1,C_Y2] = CalXiaJinSi(classX,m,classNum,ruleNumY1);
C_Y1 = [];
C_Y2 = [];
for i = 1:m
Y1 = true;
Y2 = true;
for j = 1:classNum(i)
if(classX(i,j) > ruleNumY1)
Y1 = false;
else
Y2 = false;
end
if(~Y1&&~Y2)
break;
end
end
if(Y1)
C_Y1 = [C_Y1 classX(i,1:classNum(i))];
elseif(Y2)
C_Y2 = [C_Y2 classX(i,1:classNum(i))];
end
end
end
[C_Y1,C_Y2]=CalXiaJinSi(classX,m,classNum,ruleNumY1);
fprintf('%s\n',num2str(C_Y1(1))) %输出C_Y1的第一个元素
fprintf('%s\n',num2str(C_Y2(2))) %输出C_Y2的第一个元素
%%%%%%%%%%%%%%%%%%%% End %%%%%%%%%%%%%%%%%%%%
2.基于粗糙集分类器的手写数字识别
function Cucaoji()
%通过循环计算多个二分类器
for i=1:10
for j=1:i-1
ruleStruct(i,j).rule=CuCao2ClassTrain(i,j); %粗糙集两分类训练，见下方CuCao2ClassTrain()函数
end
end
save ruleStruct ruleStruct;%保存规则表
img=imread('Untitled.bmp');%读取测试图像
feature=Getfeature(img);
num=zeros(1,10);
for i=1:10
for j=1:i-1
%两类判别
G=CuCao2Class(i,j,feature,ruleStruct(i,j).rule);
if(G==0)
num(i)=num(i)+1;
elseif(G==1)
num(j)=num(j)+1;
end
end
end
[max_val,max_pos]=max(num);%取票数最高类别为识别结果
result=max_pos-1;
str = num2str(result);
str = ['应用粗糙集分类器的识别结果：' str];
fprintf('%s\n',str);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%函数名称：CuCao2ClassTrain()
%参数：class1:类别1；class2:类别2
%返回值：newRule:规则
%函数功能：粗糙集两类分类训练
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function newRule = CuCao2ClassTrain(class1,class2);
load ('template.mat');
patternNum=70;
bottom=zeros(patternNum*2,1);
bottom(1:patternNum,1)=0;
bottom(patternNum+1:patternNum*2,1)=1;
x=[pattern(class1).feature(1:patternNum,:);
pattern(class2).feature(1:patternNum,:)];
x=[x bottom];
x=ceil(x);
%一致性检测
ruleNum=patternNum*2;
%去重规则和不一致规则
for m=1:ruleNum-1
if(m>ruleNum-1)
break;
end
for n=m+1:ruleNum
if(n>ruleNum)
break;
end
while (x(m,1:25)==x(n,1:25))
x(n,:)=[];
ruleNum=ruleNum-1;
if(n>ruleNum)
break;
end
end
end
end
x=x(1:ruleNum,:);
ruleNumY1=0;
for m=1:ruleNum
if (x(m,26)==0)
ruleNumY1=ruleNumY1+1;
end
end
ruleNumY2=ruleNum-ruleNumY1;
classX=zeros(ruleNum,ruleNum);%X属性等价集矩阵
classNum=zeros(ruleNum,1);%等价集中元素个数
m=0;%等价集个数
n=1;
%计算条件X等价集
num=0;
[classX,m,classNum]=CalTiaoJian(num,classX,x,ruleNum,classNum); %利用CalTiaoJian()函数计算条件属性C的等价集，该函数与第一关计算等价集的代码一致
%决策D的等价集
classY1=zeros(1,ruleNumY1);
classY2=zeros(1,ruleNumY2);
classY1=1:ruleNumY1;
classY2=ruleNumY1+1:ruleNum;
%决策D的下近似集
C_Y1=zeros(1,ruleNumY1);
C_Y2=zeros(1,ruleNumY2);
[C_Y1,C_Y2]=CalXiaJinSi(classX,m,classNum,ruleNumY1);%利用CalXiaJinSi()函数计算决策D的下近似集，该函数与第一关计算下近似集的代码一致
%%%%%%%%%%%%%%%%%%%% Begin %%%%%%%%%%%%%%%%%%%%
%计算条件属性全集C的正域Pos(C,D)（C_Y1∪C_Y2）
PosXD=[C_Y1,C_Y2];
%依赖度r(C,D)（Pos(C,D)元素个数/论域中所有元素个数）
rXD=size(PosXD,2)/(ruleNum);
import=zeros(1,25);
%%%%%%%%%%%%%%%%%%%%% End %%%%%%%%%%%%%%%%%%%%%
xReserve=[]; %约简后的条件属性
%计算25个条件属性的重要度
for i=1:25;
%计算条件C-i的等价集
classX(:,:)=0;
[classX,m,classNum]=CalTiaoJian(i,classX,x,ruleNum,classNum);
%计算决策D的下近似集
[C_Y1,C_Y2]=CalXiaJinSi(classX,m,classNum,ruleNumY1);
%%%%%%%%%%%%%%%%%%%% Begin %%%%%%%%%%%%%%%%%%%%
%计算条件属性C-i的正域Pos(C-i,D)
%依赖度r(C-i,D)（Pos(C-i,D)元素个数/论域中所有元素个数）
PosXiD=[C_Y1,C_Y2];
%计算条件属性i的重要度import(i）（r(C,D)-r(C-i,D)）
import(i)=size(PosXiD,2)/(ruleNum);
%%%%%%%%%%%%%%%%%%%%% End %%%%%%%%%%%%%%%%%%%%%
if(import(i)==0)
if(Consistent(i,x,ruleNumY1,ruleNumY2)==1) %如果删除后一致
x(1:ruleNum,i)=0;
else
xReserve=[xReserve i];
end
else
xReserve=[xReserve i];
end
end
%得到简化后的决策表
xReserve=[xReserve 26];
xNum=size(xReserve,2);
xNew=zeros(ruleNum,xNum);
for i=1:ruleNum
for j=1:xNum
xNew(i,j)=x(i,xReserve(j)); %构造属性约简后的决策表
end
end
rule=[];
%计算条件X等价集
num=0;
classX(:,:)=0;
[classX,m,classNum]=CalTiaoJian(num,classX,xNew,ruleNum,classNum);
%获取规则
cf=[];
for i=1:m
temp=zeros(1,2);
for j=1:classNum(i)
if(size(find(classY1==classX(i,j)),2)~=0)
temp(1,1)=1;
end
if(size(find(classY2==classX(i,j)),2)~=0)
temp(1,2)=1;
end
if(temp(1,1)==1&&temp(1,2)==1)
cf=[cf i];%记录cf不为1的等价集
break;
end
end
end
temp=size(cf,2);
if(temp~=0)%舍去cf不为1的规则
for i=1:temp
for j=1:classNum(cf(i))
xNew(classX(cf(i),j),xNum)=2;
end
end
for i=1:ruleNum
while(xNew(i,xNum)==2)
xNew(i,:)=[];
ruleNum=ruleNum-1;
if(i>ruleNum)
break;
end
end
if(i>=ruleNum)
break;
end
end
end
%简化规则表，去掉重复规则
for m=1:ruleNum-1
if(m>ruleNum-1)
break;
end
for n=m+1:ruleNum
if(n>ruleNum)
break;
end
while(xNew(m,1:xNum)==xNew(n,1:xNum))
xNew(n,:)=[];
ruleNum=ruleNum-1;
if(n>ruleNum)
break;
end
end
end
end
ruleNumY1=0;
for m=1:ruleNum
if(xNew(m,xNum)==0)
ruleNumY1=ruleNumY1+1;
end
end
ruleNumY2=ruleNum-ruleNumY1;
for m=1:ruleNum
a=[];
for j=1:xNum
a=[a xNew(m,j)];
end
rule=[rule;a];
end
%规则化简
oldRule=rule;
newRule=[];
ruleJ=[];%统计可化简的规则
for i=1:size(xReserve,2)
rule=oldRule;
rule(:,i)=0;
flag=0;
for m=1:ruleNumY1-1
for n=m+1:ruleNumY1
if(rule(m,:)==rule(n,:))%可化简
rule(m,i)=inf;
newRule=[newRule;rule(m,:)];
flag=1;
ruleJ=[ruleJ m n];
break;
end
end
if(flag)
break;
end
end
flag=0;
for m=ruleNumY1+1:ruleNum-1
for n=m+1:ruleNum
if(rule(m,:)==rule(n,:))%可简化
rule(m,i)=inf;
newRule=[newRule;rule(m,:)];
flag=1;
ruleJ=[ruleJ m n];
break;
end
end
if(flag)
break;
end
end
end
for i=1:ruleNum
b=size(find(ruleJ==i),2);
if(b==0)%该规则不可约简
newRule=[newRule;oldRule(i,:)];
end
end
newRule=[newRule;xReserve];
标签：classNum,end,ruleNumY1,分类器,粗糙集,matlab,classX,Y1,ruleNum 来源： https://blog.csdn.net/m0_46384757/article/details/121265113