多维高斯分布讲解

1、多维高斯分布讲解 高斯分布 高 斯fl. CT2)A; (x S)一舟(X “)T£_i(x_p)对于1维的来说是期望，一一是方差；对于多维来说D表示X的维数，'-表示D*D的协方差矩阵，定义为划一;芯哄 总：+A (/«.5). al X = 0,2. 13t为该协方差的行列式的值。Example 1.3.1, Compute the value of a Gaussian pdf. 2,2, l,3r? where册=U s代码如下: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函数文件的代码如下： 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.题目大致意思就是判断x是属于w1还是w2 ?代码如下：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题目大致意思就是给出正态分布的期望和方差构造出一些服从这个分布的数据点代码如下：% 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