%
% Problem epage 70
% Example epage 51
% 
% Written by:
% -- 
% John L. Weatherwax                2005-08-14
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

addpath( '../../Code/eda_data' ); 

close all; drawnow; 
clc; 
clear; 

load yeast; X = data; 
[n,p] = size(X);         % [n,p] = [number of samples=384; dimension of each sample=17]
% Normalize columns (the z-scores):
X = X - repmat(mean(X),size(X,1),1);
X = X ./ repmat(std(X),size(X,1),1); 
% with the pre-calculations above this matrix is the correlation matrix ... 
covm = cov( X );

[eigvec,eigval] = eig( covm ); 
eigval = diag(eigval); 
% Order in decending order: 
eigval = flipud(eigval); 
eigvec = eigvec(:,p:-1:1); 
transformX = X * eigvec; 

% Plot a scree plot: 
figure; plot( eigval, '-ok' ); title( 'scree plot' ); 

% Plot the slopes in the scree plot: 
eigSlopes = abs( diff( eigval ) ); 
figure; plot( eigSlopes, '-ok' ); 
xlabel( 'eigen component' ); 
title( 'absolute scree difference' );