Implementation of PCA algorithm in MATLAB

function [V,s,e]=princa (x) [M,n]=size (x); The% calculates the row m and column n% of the matrix-------------the first step: the normalized matrix-----------------%mv=mean (X); % calculates the mean value of each variable st=std (X); % calculates the standard deviation of each variable x= (X-repmat (mv,m,1))./repmat (st,m,1); % normalized matrix x-------------Second step: Calculate the correlation coefficient matrix-----------------percent r1=x ' *x/(m-1); % method One: Covariance matrix calculation formula% R2=cov (X);     % method Two: Covariance matrix calculation function R=corrcoef (X); % method Three: correlation coefficient matrix function%-------------third step: compute eigenvectors and eigenvalues-----------------%[v,d]=eig (R);       The% computes the characteristic vector matrix V of the matrix R and the eigenvalue Matrix D, with eigenvalues from small to large v= (Rot90 (V)) ';      % The eigenvector Matrix V is sorted from large to small d=rot90 (Rot90 (D));  % The eigenvalue matrix is sorted from large to small e=diag (D);          % convert eigenvalue matrix to eigenvalue vector%-------------Fourth step: Calculate contribution rate and accumulative contribution rate-----------------%ratio=0; % cumulative contribution rate for k=1:n    r=e (k)/sum (E);   % K principal component contribution rate    ratio=ratio+r;  % Cumulative Contribution    if (ratio>=0.9)  % take the cumulative contribution rate greater than or equal to 90% of the main component break        ;    endend%-------------Fifth step: Calculate the score-----------------%s=x*v;

If principal component analysis is required, a function (Princomp) with Matlab comes in. The Princomp call is as follows:
[Coeff,score,latent,tsquare] = Princomp (Zscore (X))

Zscore (x) is a standardized operation on the Matrix X.
Coeff is the matrix of all eigenvectors of the covariance matrix corresponding to the X-matrices, i.e., the transformation matrix or the projection matrix, each column corresponds to a characteristic vector of eigenvalues, and the order of the columns is descending by the size of the eigenvalues.
The equivalent of V in the above program, which represents the coefficient of the principal component.
Score is the scoring of the principal component, i.e. the expression of the original X matrix in the principal component space. Each row corresponds to a sample observation, and each column corresponds to a main component (variable), and its number of rows and columns is the same as the number of lines in X. (equivalent to S in the above program)
A latent is a vector of eigenvalues of the covariance matrix corresponding to X. (equivalent to E in a program)
Relationship between eigenvalues and fractions: Latent=diag (CoV (score));
Tsquare is the T-square statistic representing the hotelling of each sample point
When calculating PCA, if there is a ready-made covariance matrix directly, the function Pcacov is used to calculate.

Implementation of PCA algorithm in MATLAB