支撑矢量机（SVM）分类

close all;clear all; %样本初始化x1(1,1)=5.1418; x1(1,2)=0.5950;x1(2,1)=5.5519; x1(2,2)=3.5091;x1(3,1)=5.3836; x1(3,2)=2.8033;x1(4,1)=3.2419; x1(4,2)=3.7278;x1(5,1)=4.4427; x1(5,2)=3.8981;x1(6,1)=4.9111; x1(6,2)=2.8710;x1(7,1)=2.9259; x1(7,2)=3.4879;x1(8,1)=4.2018; x1(8,2)=2.4973;x1(9,1)=4.7629; x1(9,2)=2.5163;x1(10,1)=2.7118; x1(10,2)=2.4264;x1(11,1)=3.0470; x1(11,2)=1.5699;x1(12,1)=4.7782; x1(12,2)=3.3504;x1(13,1)=3.9937; x1(13,2)=4.8529;x1(14,1)=4.5245; x1(14,2)=2.1322;x1(15,1)=5.3643; x1(15,2)=2.2477;x1(16,1)=4.4820; x1(16,2)=4.0843;x1(17,1)=3.2129; x1(17,2)=3.0592;x1(18,1)=4.7520; x1(18,2)=5.3119;x1(19,1)=3.8331; x1(19,2)=0.4484;x1(20,1)=3.1838; x1(20,2)=1.4494;x1(21,1)=6.0941; x1(21,2)=1.8544;x1(22,1)=4.0802; x1(22,2)=6.2646;x1(23,1)=3.0627; x1(23,2)=3.6474;x1(24,1)=4.6357; x1(24,2)=2.3344;x1(25,1)=5.6820; x1(25,2)=3.0450;x1(26,1)=4.5936; x1(26,2)=2.5265;x1(27,1)=4.7902; x1(27,2)=4.4668;x1(28,1)=4.1053; x1(28,2)=3.0274;x1(29,1)=3.8414; x1(29,2)=4.2269;x1(30,1)=4.8709; x1(30,2)=4.0535;x1(31,1)=3.8052; x1(31,2)=2.6531;x1(32,1)=4.0755; x1(32,2)=2.8295;x1(33,1)=3.4734; x1(33,2)=3.1919;x1(34,1)=3.3145; x1(34,2)=1.8009;x1(35,1)=3.7316; x1(35,2)=2.6421;x1(36,1)=2.8117; x1(36,2)=2.8658;x1(37,1)=4.2486; x1(37,2)=1.4651;x1(38,1)=4.1025; x1(38,2)=4.4063;x1(39,1)=3.9590; x1(39,2)=1.3024;x1(40,1)=1.7524; x1(40,2)=1.9339;x1(41,1)=3.4892; x1(41,2)=1.2457;x1(42,1)=4.2492; x1(42,2)=4.5982;x1(43,1)=4.3692; x1(43,2)=1.9794;x1(44,1)=4.1792; x1(44,2)=0.4113;x1(45,1)=3.9627; x1(45,2)=4.2198;  x2(1,1)=9.7302; x2(1,2)=5.5080;x2(2,1)=8.8067; x2(2,2)=5.1319;x2(3,1)=8.1664; x2(3,2)=5.2801;x2(4,1)=6.9686; x2(4,2)=4.0172;x2(5,1)=7.0973; x2(5,2)=4.0559;x2(6,1)=9.4755; x2(6,2)=4.9869;x2(7,1)=9.3809; x2(7,2)=5.3543;x2(8,1)=7.2704; x2(8,2)=4.1053;x2(9,1)=8.9674; x2(9,2)=5.8121;x2(10,1)=8.2606; x2(10,2)=5.1095;x2(11,1)=7.5518; x2(11,2)=7.7316;x2(12,1)=7.0016; x2(12,2)=5.4111;x2(13,1)=8.3442; x2(13,2)=3.6931;x2(14,1)=5.8173; x2(14,2)=5.3838;x2(15,1)=6.1123; x2(15,2)=5.4995;x2(16,1)=10.4188; x2(16,2)=4.4892;x2(17,1)=7.9136; x2(17,2)=5.2349;x2(18,1)=11.1547; x2(18,2)=4.4022;x2(19,1)=7.7080; x2(19,2)=5.0208;x2(20,1)=8.2079; x2(20,2)=5.4194;x2(21,1)=9.1078; x2(21,2)=6.1911;x2(22,1)=7.7857; x2(22,2)=5.7712;x2(23,1)=7.3740; x2(23,2)=2.3558;x2(24,1)=9.7184; x2(24,2)=5.2854;x2(25,1)=6.9559; x2(25,2)=5.8261;x2(26,1)=8.9691; x2(26,2)=4.9919;x2(27,1)=7.3872; x2(27,2)=5.8584;x2(28,1)=8.8922; x2(28,2)=5.7748;x2(29,1)=9.0175; x2(29,2)=6.3059;x2(30,1)=7.0041; x2(30,2)=6.2315;x2(31,1)=8.6396; x2(31,2)=5.9586;x2(32,1)=9.2394; x2(32,2)=3.3455;x2(33,1)=6.7376; x2(33,2)=4.0096;x2(34,1)=8.4345; x2(34,2)=5.6852;x2(35,1)=7.9559; x2(35,2)=4.0251;x2(36,1)=6.5268; x2(36,2)=4.3933;x2(37,1)=7.6699; x2(37,2)=5.6868;x2(38,1)=7.8075; x2(38,2)=5.0200;x2(39,1)=6.6997; x2(39,2)=6.0638;x2(40,1)=5.6549; x2(40,2)=3.6590;x2(41,1)=6.9086; x2(41,2)=5.4795;x2(42,1)=7.9933; x2(42,2)=3.3660;x2(43,1)=5.9318; x2(43,2)=3.5573;x2(44,1)=9.5157; x2(44,2)=5.2938;x2(45,1)=7.2795; x2(45,2)=4.8596;x2(46,1)=5.5233; x2(46,2)=3.8697;x2(47,1)=8.1331; x2(47,2)=4.7075;x2(48,1)=9.7851; x2(48,2)=4.4175;x2(49,1)=8.0636; x2(49,2)=4.1037;x2(50,1)=8.1944; x2(50,2)=5.2486;x2(51,1)=7.9677; x2(51,2)=3.5103;x2(52,1)=8.2083; x2(52,2)=5.3135;x2(53,1)=9.0586; x2(53,2)=2.9749;x2(54,1)=8.2188; x2(54,2)=5.5290;x2(55,1)=8.9064; x2(55,2)=5.3435;  for i=1:45 r1(i)=x1(i,1);end;for i=1:45 r2(i)=x1(i,2);end;for i=1:55 r3(i)=x2(i,1);end;for i=1:55 r4(i)=x2(i,2);end; figure(1);plot(r1,r2,'*',r3,r4,'o');hold on;  y1 = ones(45,1); %对于每一个xi，yi为相应的标识器，对于w1为1,对于w2为-1y2 =-ones(55,1);X = [x1;x2];     %x矩阵化Y = [y1;y2];     %y矩阵化l = zeros(100,1);% 对lambda进行初始化 A=[];b=[];       %不存在线性不等式约束，故为空Aeq=Y';beq=0;    %定义线性等式约束lb=zeros(100,1); %定义上下界约束，有lambda大于等于0lambda = fmincon('Optimization',l,A,b,Aeq,beq,lb);%用fmincon函数来求解非线性多变量约束问题，其中Optimization为等价最优任务w = X'*(lambda.*Y);% 求解支撑矢量 s = find(lambda > 0); %提取非0的元素位置下标构成新矩阵sum=0;                %初始化累计变量N = length(s) ;       %算出非0元素的个数for i=1:N;    j=s(i);    sum=sum+Y(j) - X(j,:)*w;% 由条件 w'x+w0=y 隐含得到,其中y为正负1endw0 = sum/N;% 计算w0的值，w0是通过所有条件的均值计算得出的 x = linspace(0,10,5000);% 取5000个x点画图y = (-w(1)/w(2))*x-w0/w(2); %x*w1+y*w2+w0=0,w=[w1;w2;w0]plot(x,y,'r');% 用红线标出分界面axis([1,12,0,8]);% 设定当前图中，x轴范围为1-12，为y轴范围为0-8display(w);% 显示出权向量display(w0);% 显示出w0endfunction fl = Optimization(lambda) %用此函数来描述最优化问题fl = (-1*ones(100,1))'*lambda+1/2*(lambda.*Y)'*X*X'*(lambda.*Y);%最优化问题的等价函数