normgeo (MatArray Toolbox)

MatArray Toolbox

normgeo

Removes the dependence of the ratio on the position of the spot on the slide.

Syntax

[Mnorm, fact] = normgeo(M, format)
[Mnorm, fact] = normgeo(M, format, options)

Description

normgeo normalizes the data in order to remove the dependence of the ratios upon the position on the slide. M is a two columns data matrix, each column corresponding to a colour and each line to a spot. format indicates the physical layout of the slide as [ Rows Columns MetaRows MetaColumns ], in a manner similar to table2grid.

Mnorm contains the resulting normalized data. fact is a vector containing the normalization factors used for each point.

options(1) can be used to choose the radius of the neighbourhood (default: 7).

If options(2) is different from 0, figures are displayed which show the effect of the normalization.

Examples

Creation of the red and green matrices

R = exp(randn(100,100));
G = exp(randn(100,100));

Say there is a gradient in the ratios from left to right

grad = exp(repmat(((1:100)-50.5),[100 1])/50);
R2 = R./sqrt(grad);
G2 = G.*sqrt(grad);
median(R2(:)./G2(:))
ans =
    1.0086

The median ratio is still around one, but there is a large dependence of the ratios upon the position of the spots. Say the data is organized as 8 blocs of 25x50 spots

M = [ grid2table(R2,[25 50 4 2]) grid2table(G2,[25 50 4 2]) ];

Usually M is what the quantification programs gives as input. Now use normgeo to normalize the data

[Mnorm, fact] = normgeo(M, [25 50 4 2], [7 1]);

The correction factor is given in pseudo-color, using the jet look-up-table. The results here are not very smooth because the variance of the ratios is high compared to the gradient.

The normalized ratios can be compared to the original ratios

O = [ grid2table(R,[25 50 4 2]) grid2table(G,[25 50 4 2]) ];
mean( (O(:,1)./O(:,2) - M(:,1)./M(:,2)).^2 )
ans =
   29.5491
mean( (O(:,1)./O(:,2) - Mnorm(:,1)./Mnorm(:,2)).^2 )
ans =
    1.2858

the normalized ratios obtained with Mnorm are much closer to the original ratios O than the M ratios were. In this case the error could be further diminished by raising the radius, because the variance of the ratios is quite high.

Algorithm

A circle neighbourhood is taken around each point, where the median ratio is calculated. This median should ideally be 1. To normalize, the red channel is divided by the square root of this median ratio, and the green channel multiplied by the same value.