spxy.m

SPXY 一个用于化学计量学分析中样本选择的方法

function m = spxy(X,y,Ncal)
dminmax = zeros(1,Ncal); % Inicializes the vector of minimum distances.
M = size(X,1); % Number of objects
samples = 1:M;
Dx = zeros(M,M); % Inicializes the matrix of X-distances.
Dy = zeros(M,M); % Inicializes the matriz de y-distances.
for i = 1:M-1
 xa = X(i,:);
 ya = y(i,:);
 for j = i + 1:M
  xb = X(j,:);
  yb = y(j,:);
  Dx(i, j) = norm(xa-xb);
  Dy(i, j) = norm(ya-yb);
 end
end
Dxmax = max(max(Dx));
Dymax = max(max(Dy));
D = Dx/Dxmax + Dy/Dymax; % Combines the X and y distances.
% D is an upper triangular matrix.
% D(i,j) is the distance between objects i and j (j > i).
[maxD,index_row] = max(D);
% maxD is a row vector containing the largest element for each column of D.
% index_row is the row in which the largest element of the column if found.
[dummy,index_column] = max(maxD);
% index_column is the column containing the largest element of matrix D.
m(1) = index_row(index_column);
m(2) = index_column;
for i = 3:Ncal
 pool = setdiff(samples,m);
 % Pool is the index set of the samples that have not been selected yet.
 dmin = zeros(1,M - i + 1);
 % dmin will store the minimum distance of each sample in “pool” with respect to the previously selected samples.
 for j = 1:(M -i + 1)
   indexa = pool(j);
   d = zeros(1,i-1);
   for k = 1:(i - 1)
    indexb = m(k);
    if indexa < indexb
     d(k) = D(indexa,indexb);
   else
    d(k) = D(indexb,indexa);
   end
  end
  dmin(j) = min(d);
 end
 % At each iteration, the sample with the largest dmin value is selected.
 [dummy,index] = max(dmin);
 m(i) = pool(index);
end