pdist

文档
调用格式:
- D = pdist(X)returns the Euclidean distance between pairs of observations in X.
  - 一个矩阵A的大小为MN，那么B=pdist(A)得到的矩阵B的大小为1行M(M-1)/2列，表示的意义是M行数据，每两行计算一下欧式距离pdist(x,distance),distance也可以用来表示其他距离，默认的是欧式距离。
  - 返回函数中的观测对之间的欧几里得距离
- D = pdist(X,Distance) returns the distance by using the method specified by Distance.
- D = pdist(X,Distance,DistParameter) returns the distance by using the method specified by Distance and DistParameter. You can specify DistParameter only when Distance is ‘seuclidean’, ‘minkowski’, or ‘mahalanobis’.
Distance — Distance metric
- Distance metric, specified as a character vector, string scalar, or function handle, as described in the following table.
- metric’取值如下： ‘euclidean’：欧氏距离（默认）；

栗子:Compute the Euclidean distance between pairs of observations, and convert the distance vector to a matrix using squareform.

计算观测对之间的欧氏距离，并用squareform将距离矢量转换为矩阵。

rng('default') % For reproducibility
X = rand(3,2);
%生成矩阵坐标，第一列为横坐标，第二列为纵坐标
D = pdist(X)
%answer
D = 1×3

    0.2954    1.0670    0.9448
%**The pairwise distances are arranged in the order (2,1), (3,1), (3,2)**. **You can easily locate the distance between observations i and j by using squareform.**
%**如果a是3*2矩阵，那么pdist函数计算欧几里德距离的顺序是第二行与第一行计算欧几里得距离，然后是第3行于第一行计算欧几里得距离，最后是第3行与第2行的欧几里德距离**
% 如果`b = squareform(pdist(a))`，那么`b(i,j)`就是矩阵a第i行与第j行之间的欧几里得距离
Z = squareform(D)
Z = 3×3

         0    0.2954    1.0670
    0.2954         0    0.9448
    1.0670    0.9448         0
%squareform returns a symmetric matrix **where Z(i,j) corresponds to the pairwise distance between observations i and j**. For example,** you can find the distance between observations 2 and 3.**
%squareform返回一个对称矩阵，**其中Z(i,j)对应于观察i和j之间的成对距离。**
Z(2,3)
ans = 0.9448


%验证pdist函数计算行顺序
clc,clear;
a = [0 0
    3 4
    5 6];
b = pdist(a);
d = sqrt(3^2+4^2)
e = sqrt(5^2+6^2)
g = sqrt(2^2+2^2)
b