【matlab】距离函数

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：

原文地址

http://blog.sina.com.cn/s/blog_57235cc70100jjf8.html