《模式识别》课程实验线性分类器设计实验

1、模式识别课程实验线性分类器设计实验一、实验目的：1、掌握Fisher线性分类器设计方法；2、掌握感知准则函数分类器设计方法。二、实验内容：1、对下列两种情况，求采用Fisher判决准则时的投影向量和分类界面，并做图。，(2,0,(2,2)t,(2,4)t,(3,3)t1，(0,3)T，(-2,2)t，(-1,-1)T,(1,-2)t,(3,1)t2，(1,1)t,(2,0)t,(2,1)t,(0,2)t,(1,3)t1，(-1,2)t,(0,0)t,(-1,0),(-1,-1)t,(0,-2)t22、对下面的两类分类问题，采用感知准则函数，利用迭代修正求权向量的方法求两类的线性判决函数及线性识

2、别界面，并画出识别界面将训练样本区分的结果图。，(1,1)T,(2,0)t,(2,1)T,(0,2)t,(1,3)T1，(-1,2)t,(0,0)t,(-1,0),(-1,-1)t,(0,-2)t2三、实验原理：Fisher判决准则投影方向：w*，S-i(卩一卩)w12感知准则函数：J(v)，工(-VTZ)z，Zk当Zk为空时，即J(v)0,v*即为所求p四、解题思路：1、fisher线性判决器:用mean函数求两类样本的均值求两类样本的均值的类内离散矩阵Si利用类内离散矩阵求总类内离散矩阵Sw求最佳投影方向Wo定义阈值，并求得分界面2、感知准则函数分类器：获得增广样本向量和初始增广权向量对样

3、本进行规范化处理获得解区，并用权向量迭代修正错分样本集，得到最终解区五、实验结果：1、fisher线性判决分类器：条件：取pw1=pw2=0.5，阈值系数为0.5厂赁訪巳谡性判决A.第一种情况B.第二种情况2、感知准则函数判决:条件：取步长row为1感知准则判决感知谁则判决结果:六、结果分析：1、fisher线性判决器中，调整阈值系数时，分界面会随之平行上下移动，通过调整阈值系数的大小，就能比较合理的得到分界面。而投影方向不会随阈值系数的变化而变化。2、fisher线性判决器中，由于题目中样本数目少，所以其先验概率统一取为0.5。而改变其先验概率对结果的影响不是很大。3、感知准则函数分类判决中

4、，调整步长row的大小可使分界面的方向和位置发生变动，但是变动范围不大，仅限于小范围的调整。七、源程序functionvarargout=fisherganzhi(varargin)gui_Singleton=1;gui_State=struct(gui_Name,mfilename,.gui_Singleton,gui_Singleton,.gui_OpeningFcn,fisherganzhi_OpeningFcn,.gui_OutputFcn,fisherganzhi_OutputFcn,.gui_LayoutFcn,.gui_Callback,);ifnargin&ischar(var

5、argin1)gui_State.gui_Callback=str2func(varargin1);endifnargoutvarargout1:nargout=gui_mainfcn(gui_State,varargin:);elsegui_mainfcn(gui_State,varargin:);end%-Executesjustbeforefisherganzhiismadevisible.functionfisherganzhi_OpeningFcn(hObject,eventdata,handles,varargin)handles.output=hObject;%Updatehan

6、dlesstructureguidata(hObject,handles);%-Outputsfromthisfunctionarereturnedtothecommandline.functionvarargout=fisherganzhi_OutputFcn(hObject,eventdata,handles)varargout1=handles.output;%-Executesonbuttonpressinpushbutton2.functionpushbutton2_Callback(hObject,eventdata,handles)pw1=str2num(get(handles.

7、edit1,String);pw2=str2num(get(handles.edit2,String);k=str2num(get(handles.edit3,String);w1=11;20;21;02;13;w2=-12;00;-10;-1-1;0-2;u1=mean(w1);u2=mean(w2);s1=zeros(2,2);s2=zeros(2,2);forn=1:length(w1)s1=s1+(w1(n,:)-u1)*(w1(n,:)-u1);end;form=1:length(w2)s2=s2+(w2(m,:)-u2)*(w2(m,:)-u2);end;sw=pw1*s1+pw2

8、*s2;wo=inv(sw)*(u1-u2);y0=k*(wo*u1+wo*u2);x1=-4:0.3:6;x2=(y0-wo(1)*x1)/wo(2);x3=wo(2)*x1/wo(1);cla(handles.axes1);axes(handles.axes1);holdon;plot(x1,x2,b,x1,x3,k);plot(w1(:,2),w1(:,1),*r);plot(w2(:,2),w2(:,1),og);title(Fisher线性分类器(2);12);handles)text(3.5,13,*表示第1类,FontSize,10,Color,rtext(3.5,11,o表示第

9、2类,FontSize,10,Color,gtext(wo(1),wo(2),leftarrow投影方向,FontSizeholdoff;%-Executesonbuttonpressinpushbutton1.functionpushbutton1_Callback(hObject,eventdata,pw1=str2num(get(handles.edit1,String);pw2=str2num(get(handles.edit2,String);k=str2num(get(handles.edit3,String);w1=20;22;24;33;w2=03;-22;-1-1;1-2;3

10、-1;u1=mean(w1);u2=mean(w2);s1=zeros(2,2);s2=zeros(2,2);forn=1:length(w1)s1=s1+(w1(n,:)-u1)*(w1(n,:)-u1);end;form=1:length(w2)s2=s2+(w2(m,:)-u2)*(w2(m,:)-u2);end;sw=pw1*s1+pw2*s2;wo=inv(sw)*(u1-u2);y0=k*(wo*u1+wo*u2);x1=-4:0.3:6;x2=(y0-wo(1)*x1)/wo(2);x3=wo(2)*x1/wo(1);cla(handles.axes1);axes(handles

11、.axes1);holdon;plot(x1,x2,b,x1,x3,k);plot(w1(:,2),w1(:,1),*r);plot(w2(:,2),w2(:,1),og);title(Fisher线性分类器(2);text(3.5,9,*表示第1类,FontSize,10,Color,r);text(3.5,8,o表示第2类,FontSize,10,Color,g);text(wo(1),wo(2),leftarrow投影方向,FontSize,12);holdoff;functionedit3_Callback(hObject,eventdata,handles)%-Executesdur

12、ingobjectcreation,aftersettingallproperties.functionedit3_CreateFcn(hObject,eventdata,handles)ifispc&isequal(get(hObject,BackgroundColor),get(0,defaultUicontrolBackgroundColor)set(hObject,BackgroundColor,white);endfunctionedit2_Callback(hObject,eventdata,handles)%-Executesduringobjectcreation,afters

13、ettingallproperties.functionedit2_CreateFcn(hObject,eventdata,handles)ifispc&isequal(get(hObject,BackgroundColor),get(0,defaultUicontrolBackgroundColor)set(hObject,BackgroundColor,white);endfunctionedit1_Callback(hObject,eventdata,handles)functionedit1_CreateFcn(hObject,eventdata,handles)ifispc&iseq

14、ual(get(hObject,BackgroundColor),get(0,defaultUicontrolBackgroundColor)set(hObject,BackgroundColor,white);end%-Executesonbuttonpressinpushbutton3.functionpushbutton3_Callback(hObject,eventdata,handles)row=str2num(get(handles.edit4,String);w1=11;20;21;02;13;w2=-12;00;-10;-1-1;0-2;y1=ones(1,5);w1;y2=-

15、ones(1,5);w2;w=y1y2;v=y1(:,1);sumz=zeros(3,1);z=ones(1,10);whilesum(z)0v=v+row*sumz;h=v*w;z=(abs(h)h);Z=w.*z;z;z;sumz=sum(Z);endx1=-2:0.5:2.5;x2=(-v(1)-v(2)*x1)/v(3);cla(handles.axes1);axes(handles.axes1);holdon;plot(x1,x2);plot(w1(1,:),w1(2,:),*r)plot(w2(1,:),w2(2,:),og)title(感知准则函数分类器);text(1.5,5,

16、*表示第1类,FontSize,10,Color,r);text(1.5,4,o表示第2类,FontSize,10,Color,g)holdoff;functionedit4_Callback(hObject,eventdata,handles)%hObjecthandletoedit4(seeGCBO)%eventdatareservedtobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,String)returnscontentsofedit4astext%str2double(get(hObject,String)returnscontentsofedit4asadouble%-Executesduringobjectcreation,aftersettingallproperties.functionedit4_CreateFcn(hObject,eventdata,handles)%hObjecthandletoedit4(seeGCBO)%eventdatareserved-tobedefinedinafutureversi