normnonlin (MatArray Toolbox)

MatArray Toolbox

normnonlin

Removes the dependence of the ratios on the spot intensities.

Syntax

Mnorm = normnonlin(M)
Mnorm = normnonlin(M, options)

Description

normnonlin normalizes the data in order to remove the dependence of the ratios upon the spot intensities. M is a two columns data matrix, each column corresponding to a colour and each line to a spot. options can be used to modify the default behavior of the script. options(1) can be used to modify the alpha parameter in loess (default: .5), and options(2) the order (default: 1). If options(3) is present, figures are displayed for diagnosis. Any value of options below 0 is considered as missing.

Examples

Random intensities and ratios for each spot

I=abs(randn(1000,1));
R=exp(randn(1000,1));

but (horror!) there is a non-linear dependence on the values measured to the intensities

M=[I.*sqrt(R) (I+I.^2)./sqrt(R)];

the matrix M can be normalized based on the average intensity

M=M./repmat(mean(M),[1000 1]);

but the dependence of the ratios on the intensities remains. The values are then normalized non-linearly, using the default parameters values.

Mnorm=normnonlin(M,[-1 -1 1]);

The first graphic shows the loess fit of the data. The second graphic shows the original R/G values in black and the normalized values in red.

The normalized ratios can be compared to the original ratios

mean( (R - M(:,1)./M(:,2)).^2 )
ans =
    0.3453
mean( (R - Mnorm(:,1)./Mnorm(:,2)).^2 )
ans =
    0.0032

The normalized ratios are much closer to the real ones.

Algorithm

A small value is added to the red and green channel (in order to make all of their values positive), then their logarithms are taken. The green vs red graph is then rotated to obtain an intensity (red+green) vs ratio (red-green) graph.

A loess non-linear fit of the ratio to the intensity is made. The value of the ratio predicted from the fit is subtracted from the ratio measured, to obtain the corrected ratio. The values are then rotated back in the original space.