原文来源：
MATLAB 距离计算_黑白_新浪博客
http://blog.sina.com.cn/s/blog_57235cc70100jjf8.html
判别分析时，通常涉及到计算两个样本之间的距离，多元统计学理论中有多种距离计算公式。MATLAB中已有对应函数，可方便直接调用计算。距离函数有：pdist, pdist2, mahal, squareform, mdscale, cmdscale
主要介绍pdist2 ,其它可参考matlab help
D = pdist2(X,Y)
D = pdist2(X,Y,distance)
D = pdist2(X,Y,'minkowski',P)
D = pdist2(X,Y,'mahalanobis',C)
D = pdist2(X,Y,distance,'Smallest',K)
D = pdist2(X,Y,distance,'Largest',K)
[D,I] = pdist2(X,Y,distance,'Smallest',K)
[D,I] = pdist2(X,Y,distance,'Largest',K)
练习：
2种计算方式，一种直接利用pdist计算，另一种按公式（见最后理论）直接计算。
% distance
clc;clear;
x = rand(4,3)
y = rand(1,3)
for i =1:size(x,1)
for j =1:size(y,1)
a = x(i,:); b=y(j,:);
% Euclidean distance
d1(i,j)=sqrt((a-b)*(a-b)');
% Standardized Euclidean distance
V = diag(1./std(x).^2);
d2(i,j)=sqrt((a-b)*V*(a-b)');
% Mahalanobis distance
C = cov(x);
d3(i,j)=sqrt((a-b)*pinv(C)*(a-b)');
% City block metric
d4(i,j)=sum(abs(a-b));
% Minkowski metric
p=3;
d5(i,j)=(sum(abs(a-b).^p))^(1/p);
% Chebychev distance
d6(i,j)=max(abs(a-b));
% Cosine distance
d7(i,j)=1-(a*b')/sqrt(a*a'*b*b');
% Correlation distance
ac = a-mean(a); bc = b-mean(b);
d8(i,j)=1- ac*bc'/(sqrt(sum(ac.^2))*sqrt(sum(bc.^2)));
end
end
md1 = pdist2(x,y,'Euclidean');
md2 = pdist2(x,y,'seuclidean');
md3 = pdist2(x,y,'mahalanobis');
md4 = pdist2(x,y,'cityblock');
md5 = pdist2(x,y,'minkowski',p);
md6 = pdist2(x,y,'chebychev');
md7 = pdist2(x,y,'cosine');
md8 = pdist2(x,y,'correlation');
md9 = pdist2(x,y,'hamming');
md10 = pdist2(x,y,'jaccard');
md11 = pdist2(x,y,'spearman');
D1=[d1,md1],D2=[d2,md2],D3=[d3,md3]
D4=[d4,md4],D5=[d5,md5],D6=[d6,md6]
D7=[d7,md7],D8=[d8,md8]
md9,md10,md11
运行结果如下：
x =
0.5225 0.6382 0.6837
0.3972 0.5454 0.2888
0.8135 0.0440 0.0690
0.6608 0.5943 0.8384
y =
0.5898 0.7848 0.4977
D1 =
0.2462 0.2462
0.3716 0.3716
0.8848 0.8848
0.3967 0.3967
D2 =
0.8355 0.8355
1.5003 1.5003
3.1915 3.1915
1.2483 1.2483
D3 =
439.5074 439.5074
437.5606 437.5606
438.3339 438.3339
437.2702 437.2702
D4 =
0.3999 0.3999
0.6410 0.6410
1.3934 1.3934
0.6021 0.6021
D5 =
0.2147 0.2147
0.3107 0.3107
0.7919 0.7919
0.3603 0.3603
D6 =
0.1860 0.1860
0.2395 0.2395
0.7409 0.7409
0.3406 0.3406
D7 =
0.0253 0.0253
0.0022 0.0022
0.3904 0.3904
0.0531 0.0531
D8 =
1.0731 1.0731
0.0066 0.0066
1.2308 1.2308
1.8954 1.8954
md9 =
1
1
1
1
md10 =
1
1
1
1
md11 =
1.5000
0.0000
1.5000
2.0000
基本理论公式如下：
