pc_evectors.m

来自「用matlab编写的找两个输入量之间的主要特征向量,主要方法采用PCA经典算法.」· M 代码 · 共 125 行

function [Vectors,Values,Psi] = pc_evectors(A,numvecs)
%PC_EVECTORS Get the top numvecs eigenvectors of the covariance matrix
%            of A, using Turk and Pentland's trick for numrows >> numcols
%            Returns the eigenvectors as the colums of Vectors and a
%            vector of ALL the eigenvectors in Values.

% Matthew Dailey 2000

  % Check arguments

  if nargin ~= 2
    error('usage: pc_evectors(A,numvecs)');
  end;

  nexamp = size(A,2);

  % Now compute the eigenvectors of the covariance matrix, using
  % a little trick from Turk and Pentland 1991

  % Compute the "average" vector
  % mean(A) gives you a row vector containing the mean of each column of A

  fprintf(1,'Computing average vector and vector differences from avg...\n');
  Psi = mean(A')';

  % Compute difference with average for each vector

  for i = 1:nexamp
    A(:,i) = A(:,i) - Psi;
  end;


  % Get the patternwise (nexamp x nexamp) covariance matrix

  fprintf(1,'Calculating L=A''A\n');
  L = A'*A;

  % Get the eigenvectors (columns of Vectors) and eigenvalues (diag of Values)

  fprintf(1,'Calculating eigenvectors of L...\n');
  [Vectors,Values] = eig(L);

  % Sort the vectors/values according to size of eigenvalue

  fprintf(1,'Sorting evectors/values...\n');
  [Vectors,Values] = sortem(Vectors,Values);

  % Convert the eigenvectors of A'*A into eigenvectors of A*A'

  fprintf(1,'Computing eigenvectors of the real covariance matrix..\n');
  Vectors = A*Vectors;

  % Get the eigenvalues out of the diagonal matrix and
  % normalize them so the evalues are specifically for cov(A'), not A*A'.

  Values = diag(Values);
  Values = Values / (nexamp-1);

  % Normalize Vectors to unit length, kill vectors corr. to tiny evalues

  num_good = 0;
  for i = 1:nexamp
    Vectors(:,i) = Vectors(:,i)/norm(Vectors(:,i));
    if Values(i) < 0.00001
      % Set the vector to the 0 vector; set the value to 0.
      Values(i) = 0;
      Vectors(:,i) = zeros(size(Vectors,1),1);
    else
      num_good = num_good + 1;
    end;
  end;
  if (numvecs > num_good)
    fprintf(1,'Warning: numvecs is %d; only %d exist.\n',numvecs,num_good);
    numvecs = num_good;
  end;
  Vectors = Vectors(:,1:numvecs);








%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
%The function pc_evectors uses TUrk and Pentland'd trick to get the eigenvectors of A*A' from the eigenvectors
%of the A'*A. It uses the function "sorterm" to sort the eigenvectors and eigenvalues by eigenvalue. To use the function,
%just do:

[Vecs,Vals,Psi]=pc_evectors(Imgs,30);% @get top 30 pc evectors of imgs and to ecplore the eigenvalue spectrum and how much variance the first n vectors account for, try following:
Plot(Vals);   % to plot the eigenvalues
Cvals=zeros(1,length(Vals));  %Allocate a vector same length as Vals
CVals(1)=Vals(1);
for i=2:length(Vals)           %Accumulate the eigenvalue sum
  CVals(i)=CVals(i-1)+Vals(i);
  end;
CVals=Cvals/sum(Vals);         %Normalize total sum to 1.0
plot(CVals);                   %Plot the cumulative sum
ylim([0 1]);                   %Set y-axis limits to be 0-1