多維高斯分布講解

1、多維高斯分布講解 高斯分布 高 斯fl. CT2)A; (x S)一舟(X “)T£_i(x_p)對于1維的來說是期望，一一是方差；對于多維來說D表示X的維數(shù)，'-表示D*D的協(xié)方差矩陣，定義為劃一;芯哄 總：+A (/«.5). al X = 0,2. 13t為該協(xié)方差的行列式的值。Example 1.3.1, Compute the value of a Gaussian pdf. 2,2, l,3r? where冊=U s代碼如下:m=0 1' S=eye(2);x1=0.2 1.3' x2=2.2 -1.3'pg仁comp_gauss

2、_de ns_val(m,S,x1) pg2=comp_gauss_de ns_val(m,S,x2) 其中comp_gauss_dens_val函數(shù)文件的代碼如下： function z=comp_gauss_de ns_val(m,S,x) l,c=size(m);z=(1/( (2*pi)A(l/2)*det(S)A0.5) )*exp(-0.5*(x-m)'* in v(S)*(x-m);Example 1.3.2. (Consider t 2-class classitlcation task in lhe 2-tlimcnsional spacc< where I b

3、oth classes. a), an, are distributed according to the Gaussian di str i but i o ns A . 5 ) and j respectively. Let也=丨11|二加2 = 03= S =勿=AssumiJig that P(o) = 1/2. classifx x = 1.8, 1.8| jjiIo <i> or itn.題目大致意思就是判斷x是屬于w1還是w2 ?代碼如下：P仁 0.5;P2=0.5;m1=1 1'm2=3 3'S=eye(2);x=1.8 1.8'p1=pi*

4、comp_gauss_de ns_val(m1,S,x)p2=P2*comp_gauss_de ns_val(m2,S,x)Example 1.3.3. Generate N = 500 2-dimciisional data points that are distributed accorcGaussian distribution Awith mean /? = |0, 0|z and covariance matrix S °02 o following cases:erf = £ = |7 cr2 = 0= 5 = 02 a2 0erf = erf 二 2, tr

5、i2 = 021 21 21 acrcr252.o一一25a-2 2CF2一一5«o一一2a4-=a=oy = 0.3,巧2» crj2 0,5erf = 03. a 2t <7j2 *0.5Plot each data set and comment on the shape of the cluslers formed by the da題目大致意思就是給出正態(tài)分布的期望和方差構(gòu)造出一些服從這個分布的數(shù)據(jù)點代碼如下：% Generate the first dataset (case #1) randn('seed',0);m=0 0' S

6、=1 0;0 1;N=500;X = mvnrnd(m,S,N)'% Plot the first dataset figure(1), plot(X(1,:),X(2,:),'.');figure(1), axis equal figure(1), axis(-7 7 -7 7)% Generate and plot the second dataset (case #2) m=0 0'S=0.2 0;0 0.2;N=500;X = mvnrnd(m,S,N)' figure(2), plot(X(1,:),X(2,:),'.'); f

7、igure(2), axis equal figure(2), axis(-7 7 -7 7)% Generate and plot the third dataset (case #3) m=0 0'S=2 0;0 2;N=500;X = mvnrnd(m,S,N)' figure(3), plot(X(1,:),X(2,:),'.'); figure(3), axis equal figure(3), axis(-7 7 -7 7)% Generate and plot the fourth dataset (case #4) m=0 0'S=0.2

8、 0;0 2;N=500;X = mvnrnd(m,S,N)' figure(4), plot(X(1,:),X(2,:),'.'); figure(4), axis equal figure(4), axis(-7 7 -7 7)% Generate and plot the fifth dataset (case #5) m=0 0'S=2 0;0 0.2;N=500;X = mvnrnd(m,S,N)' figure(5), plot(X(1,:),X(2,:),'.');figure(5), axis equal figure(5

9、), axis(-7 7 -7 7)% Generate and plot the sixth dataset (case #6) m=0 0'S=1 0.5;0.5 1;N=500;X = mvnrnd(m,S,N)'figure(6), plot(X(1,:),X(2,:),'.');figure(6), axis equalfigure(6), axis(-7 7 -7 7)% Generate and plot the seventh dataset (case #7) m=0 0'S=.3 0.5;0.5 2;N=500;X = mvnrnd(m,S,N)'figure(7), plot(X(1,:),X(2,:),'.');figure(7), axis equal figure(7), axis(-7 7 -7 7)% Generate and plot the eighth dataset (case #8) m=0 0