Quantile normalization makes the statistical distribution of values in each column identical by replacing the original values with the mean of the values at the same rank across all columns. This removes technical variation while preserving relative differences between features.
Steps:
Rank the values within each column (average taken in case of ties)
Calculate the mean of values at the same rank across all columns
Replace each value with the mean value corresponding to its rank
$$\LARGE q_{i,j} = \bar{x}_{rank(i,j)} $$
Where:
(\(rank(i,j)\)) is the rank of feature \(i\) within column \(j\)
(\(\bar{x}_{r}\)) where \(r = rank(i,j)\) is the mean of values with rank \(r\) across all columns
(\(q_{i,j}\)) is the quantile-normalized value
Library normalization and log normalization is recommended prior to this normalization.
None
Bolstad, B.M., Irizarry, R.A., Astrand, M. et al. A comparison of normalization methods for high density oligonucleotide array data based on variance and bias. Bioinformatics 19, 185–193 (2003). https://doi.org/10.1093/bioinformatics/19.2.185
Other normalization parameters:
norm_arcsinh,
norm_default,
norm_l2,
norm_library,
norm_log,
norm_osmfish,
norm_pearson,
norm_tfidf