62 lines
1.6 KiB
Matlab
62 lines
1.6 KiB
Matlab
function pca3d( x, y, z )
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% computes covariance matrix from the triples x, y, z
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% diagonalizes covariance matrix, i.e. performs pca on [ x, y, z ]
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% x, y and z are column vectors
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% covariance matrix:
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cv = cov( [ x y z ] );
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% eigen values:
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[ v , d] = eig( cv )
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% plots:
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subplot( 1, 2, 1 );
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hold on;
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% scatter plot:
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view( 3 );
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scatter3( x, y, z ); % , 1.0, 'b', 'filled' ); %, 'MarkerEdgeColor', 'blue' );
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xlabel( 'x' );
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ylabel( 'y' );
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zlabel( 'z' );
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grid on;
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% plot eigenvectors:
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quiver3( ones( 1, 3 ).*mean( x ), ones( 1, 3 )*mean(y), ones( 1, 3 )*mean(z), v(1,:).*sqrt(diag(d))', v(2,:).*sqrt(diag(d))', v(3,:).*sqrt(diag(d))', 'r' ); %, 'LineWidth', 3, 'AutoScale', 'off', 'AutoScaleFactor', 1.0, 'MaxHeadSize', 0.7 )
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%axis( 'equal' );
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hold off;
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% 2D scatter plots:
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subplot( 2, 6, 4 );
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scatter( x, y, 'b', 'filled' ); %, 'MarkerEdgeColor', 'white' );
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xlabel( 'x' )
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ylabel( 'y' )
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subplot( 2, 6, 5 );
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scatter( x, z, 'b', 'filled' ); %, 'MarkerEdgeColor', 'white' );
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xlabel( 'x' )
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ylabel( 'z' )
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subplot( 2, 6, 6 );
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scatter( y, z, 'b', 'filled' ); %, 'MarkerEdgeColor', 'white' );
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xlabel( 'y' )
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ylabel( 'z' )
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% sort the eigenvalues:
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[d,inx] = sort( diag(d), 'descend' );
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subplot( 2, 2, 4 );
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hold on;
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% subtract means:
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x = x - mean( x );
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y = y - mean( y );
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% project onto eigenvectors:
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nx = [ x y z ] * v(:,inx);
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scatter( nx(:,1), nx(:,2), 'b', 'filled' ); %, 'MarkerEdgeColor', 'white' );
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xlabel( 'ex' )
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ylabel( 'ey' )
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axis( 'equal' );
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hold off;
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end
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