MATLAB 中的主成分分析 [英] Principal Component Analysis in MATLAB

问题描述

我正在使用稀疏数据的特征值分解来实现 PCA.我知道 matlab 实现了 PCA，但它可以帮助我在编写代码时理解所有技术细节.我一直在遵循 here，但与内置函数 princomp 相比，我得到了不同的结果.

I'm implementing PCA using eigenvalue decomposition for sparse data. I know matlab has PCA implemented, but it helps me understand all the technicalities when I write code. I've been following the guidance from here, but I'm getting different results in comparison to built-in function princomp.

任何人都可以看看它并指出正确的方向.

Could anybody look at it and point me in the right direction.

代码如下:

function [mu, Ev, Val ] = pca(data)

% mu - mean image
% Ev - matrix whose columns are the eigenvectors corresponding to the eigen
% values Val 
% Val - eigenvalues

if nargin ~= 1
 error ('usage: [mu,E,Values] = pca_q1(data)');
end

mu = mean(data)';

nimages = size(data,2);

for i = 1:nimages
 data(:,i) = data(:,i)-mu(i);
end

L = data'*data;
[Ev, Vals]  = eig(L);    
[Ev,Vals] = sort(Ev,Vals);

% computing eigenvector of the real covariance matrix
Ev = data * Ev;

Val = diag(Vals);
Vals = Vals / (nimages - 1);

% normalize Ev to unit length
proper = 0;
for i = 1:nimages
 Ev(:,i) = Ev(:,1)/norm(Ev(:,i));
 if Vals(i) < 0.00001
  Ev(:,i) = zeros(size(Ev,1),1);
 else
  proper = proper+1;
 end;
end;

Ev = Ev(:,1:nimages);

推荐答案

我会这样做:

function [V newX D] = myPCA(X)
    X = bsxfun(@minus, X, mean(X,1));           %# zero-center
    C = (X'*X)./(size(X,1)-1);                  %'# cov(X)

    [V D] = eig(C);
    [D order] = sort(diag(D), 'descend');       %# sort cols high to low
    V = V(:,order);

    newX = X*V(:,1:end);
end

还有一个与统计工具箱中的 PRINCOMP 函数进行比较的示例:

and an example to compare against the PRINCOMP function from the Statistics Toolbox:

load fisheriris

[V newX D] = myPCA(meas);
[PC newData Var] = princomp(meas);

<小时>

您可能还对这篇关于执行 SVD 的 PCA.

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