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Normalization Z-score (mean=0, var=1) calculations
Here is a small example with explanations for the calculations:
The matrix to normalize:
v1 v2 v3
s1 2 5 6
s2 6 7 2
s3 4 9 1
vm1 = (2 + 4 + 6) / 3 = 4
vs1 = sqrt(((2 - vm1)^2 + (4 - vm1) ^2 + (6 - vm1) ^2) / (N - 1)) = sqrt((4 + 4) / (2)) = sqrt(4) = 2
vm2 = (5 + 7 + 9) / 3 = 7
vs2 = sqrt(((5 - vm2)^2 + (7 - vm2) ^2 + (9 - vm2) ^2) / (N - 1)) = sqrt((4 + 4) / (2)) = sqrt(4) = 2
vm3 = (6 + 2 + 1) / 3 = 3
vs3 = sqrt(((6 - vm3)^2 + (2 - vm3) ^2 + (1 - vm3) ^2) / (N - 1)) = sqrt((9 + 1 + 4) / (2)) = sqrt(7) ~=2.6458
where vmX is the mean for the variable X, vsX is the standard deviation of variable X and N = the number of samples.
We then apply:
vnXY = (vXY - vmX) / vsX
where vnXY is the normalized value and vXY is the original value for the variable number X and sample number Y. For example, variable 1 in sample 1 is transformed like this:
vn11 = (v11 - vm1) / vs1 = (2 - 4) / 2 = -1
This gives the new matrix:
vn1 vn2 vn3
s1 -1 -1 1.1339
s2 1 0 -0.3780
s3 0 1 -0.756
Each variable value is the delta from mean expressed in unit variance (meaning 1 equals the standard deviation).
The original matrix above was imported into Omics Explorer and plotted as a heat map just to show how the scale fits with the data:
Notice that s2v2 and s3v1 are black since their normalized values are 0 and that the positive values are shades of red and the negative values shades of green.
If you look at the color legend, you will see that it goes from -2.0 to 2.0 which means the scale goes from two standard deviations less than the mean to two standard deviations greater than the mean.
The actual color legend scale is calculated based on a quite complex algorithm. If you are not happy with the scale, you can set it manually from the "More plot Settings" dock window.
Qlucore Omics Explorer
How is the normalization (mean=0, Var=1) done in Omics Explorer?
Data pre-processing for expression data
How does Qlucore calculate the length of the gene to do the normalization?
Normalization of RNAseq data in Qlucore Omics Explorer
Normalization using housekeeping genes
Normalizing PCR data
Quantile normalization and eliminated factors
TPM values for RNASeq
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