matlab 3.向量的距离

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,4. 向量的数量积，矢量积与范数,的数量积,例如：,a=,1,2,3,b,=-1,5,6,c=1,0,1,则,Matlab,中数量积:,dot(,a,b,);,矢量积:,cross(,a,b,),dot,(,a,b,)=27,cross,(,a,c,)=(2,2,-2),a,b,c,的混合积为：,dot,(,a,cross,(,b,c,),练习：计算,a,b,c,的混合积,1,Matlab,中向量,a,的范数为：,norm,(,a,),例6,a=,1,2,3,b,=-1,5,6,c=1,0,1,求,a,b,的范数,解：,norm,(,a,)= 3.7417 , norm(,b,)=7.8740,练习：对例6计算：,a,b,夹角的余弦,dot(a/norm(a),b/norm(b),解法二：,dot(a,b)/norm(a)/norm(b),解法一：,=0.9164,思考：,a,b,c,三个向量那两个更接近？,2,二、向量的距离与计算,(1)欧氏距离,：,Matlab,中命令：,dist(A,B),计算,A,中,每个行向量,与,B,中,每个列向量,之间欧氏距离，,A,的行向量维数必须等于,B,的列向量维数,例7.,a=,1,2,3,b,=-1,5,6,c=1,0,1,求,a,b,c,欧氏距离,解：,dist(a,b),=,4.6904,dist(,a,c,)=,2.8284,dist(c,b,)=,7.3485,3,(2)绝对距离：,Matlab,中命令：,mandist(A,B),计算,A,中每个行向量与,B,中每个列向量之间绝对距离，,A,的行向量维数必须等于,B,的列向量维数.,例8. 求例6中向量之间的绝对值距离.,mandist(a,b)=8；mandist(a,c)=4；,mandist(c,b)=12,解,：,dist(,a,b,)=,4.6904,dist(,a,c,)=,2.8284,dist(c,b,)=,7.3485,由此，你发现了什么？,4,设样本,X,是,m,个,n,维行向量所组成的矩阵，则有：,pdist(,X,) ,样本,X,中各,n,维向量的欧氏距离,pdist(,X,cityblock,) ,各,n,维向量的绝对距离,pdist(,X,minkowski,，r,) ,闵可夫斯基距离,pdist(,X,mahal,) ,各,n,维向量的马氏距离,注意： 而,pdist(X),是个一行 列,矩阵。各列分别表示,X,中各行向量按如下顺序的距离 (1,2),(1,3),(1,m),(2,3),(2,4),(2,m),(m-1,m),5,例9.,现测得6只,Apf,和9只,Af,蠓虫的触长,翅长数据如下：,Apf：(1.14,1.78), (1.18,1.96), (1.20,1.86), (1.26,2.00), (1.28,2.00), (1.30,1.96) Af：(1.24,1.72), (1.36,1.74), (1.38,1.64), (1.38,1.82), (1.38,1.90), (1.40,1.70), (1.48,1.82),(1.54,1.82), (1.56,2.08),计算两类蠓虫的各自之间的欧氏、绝对、马氏距离,解:,Af=1.24,1.72;1.36,1.74;1.38,1.64;1.38,1.82; 1.38,1.90 ;,1.40,1.70;1.48,1.82;1.54,1.82;1.56,2.08；,d1=(pdist(Apf);,d2=(pdist(Apf,cityblock);,d3=pdist(Apf,mahal);,d=d1,d2,d3,Apf=1.14,1.78;1.18,1.96;1.2,1.86;1.26,2.;1.28,2;,1.30,1.96 ;,6,表一.,Apf,蠓虫之间的距离,Apf,蠓虫,欧氏距离,绝对距离,马氏距离,d12,0.1844,0.2200,2.5626,d13,0.1000,0.1400,0.9883,d14,0.2506,0.3400,2.4942,d15,0.2608,0.3600,2.5318,d16,0.2408,0.3400,2.5478,d23,0.1020,0.1200,2.2507,d24,0.0894,0.1200,1.5470,d25,0.1077,0.1400,2.0430,d26,0.1200,0.1200,3.0777,d34,0.1523,0.2000,1.6534,d35,0.1612,0.2200,1.5873,d36,0.1414,0.2000,1.6025,d45,0.0200,0.0200,0.5129,d46,0.0566,0.0800,1.6616,d56,0.0447,0.0600,1.1764,7,Af,蠓,欧氏距,绝对距,马氏距,Af,蠓,欧氏距,绝对距,马氏距,d12,0.1217,0.1400,1.4423,d37,0.2059,0.2800,1.3971,d13,0.1612,0.2200,2.3963,d38,0.2408,0.3400,1.6847,d14,0.1720,0.2400,1.4225,d39,0.4754,0.6200,3.4103,d15,0.2280,0.3200,1.5517,d45,0.0800,0.0800,0.7917,d16,0.1612,0.1800,2.2078,d46,0.1217,0.1400,1.3659,d17,0.2600,0.3400,2.6110,d47,0.1000,0.1000,1.2987,d18,0.3162,0.4000,3.3635,d48,0.1600,0.1600,2.0780,d19,0.4817,0.6800,3.3694,d49,0.3162,0.4400,2.1271,d23,0.1020,0.1200,1.1705,d56,0.2010,0.2200,2.1520,d24,0.0825,0.1000,0.6601,d57,0.1281,0.1800,1.8990,d25,0.1612,0.1800,1.4345,d58,0.1789,0.2400,2.6482,d26,0.0566,0.0800,0.8277,d59,0.2546,0.3600,1.8449,d27,0.1442,0.2000,1.2266,d67,0.1442,0.2000,0.9689,d28,0.1970,0.2600,1.9404,d68,0.1844,0.2600,1.4149,d29,0.3945,0.5400,2.6612,d69,0.4123,0.5400,2.9389,d34,0.1800,0.1800,1.7814,d78,0.0600,0.0600,0.7792,d35,0.2600,0.2600,2.5731,d79,0.2720,0.3400,2.0832,d36,0.0632,0.0800,0.4756,d89,0.2608,0.2800,2.4183,8,作业：,1.,（,1,）输入,A,B,并计算各行列式的值，逆矩阵；,（,2,）,A,的行向量的协方差矩阵，,B,的列向量 的相关系数矩阵,（,3,）计算,A,列向量间各种距离，夹角余弦，哪两个向量更接近？,（,4,）将矩阵,A,的各行向量标准化；并给出验证方法；,（,5,）求去掉,B,的第一行与第三列后的矩阵,C,，求,AC,C2,A.2,9,