For [Affymetrix] microarray, the broadly accepted method of normalisation is known as Robust Multiarray Average (RMA):

- background correction
- quantile normalisation
- probe summarisation (i.e. across transcripts)
- log (base 2) transformation

Extra notes:

- An alternative to this which also adjusts for the GC content, and how it affects probe-binding affinities, is called GC-RMA.
- Other types of normalisation (step 2) exist, namely: Qspline; LOESS; VSN (variance stabilising normalisation);
*et cetera*
- Step 3 is usually a 'median polish'
- There are intricate differences in each step based on different
microarray platforms

Log transformation is *not* performed prior to normalisation.

For more, read the really great review by Professor Quackenbush: Microarray data normalization and transformation.

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Current RNA-seq normalisaton methods / expression measures differ quite a bit from each other. We have:

- FPKM
- RPKM
- FPKM-UQ
- RSEM
- TPM
- CPM
- TMM
- Median normalisation (DESeq2)

**NB (added November 6th, 2019) - some of these are not considered normalisation procedures, ***per se*, and are instead referred to as count measures / abundance measures / expression units that are produce from otherwise un-named normalisation procedures, e.g., FPKM

A log transformation is not typically involved in the normalisation process for RNA-seq. Statistical comparisons are performed on the normalised, unlogged counts, which generally do not follow a binomial distribution. RNA-seq count data, in fact, follows a negative binomial distribution, akin to a Poisson. However, one can later log the normalised counts, e.g. for plotting functions, in order to bring them to a binomial distribution. DESeq2, for example, implements a regularised log transformation.

For more, read A comprehensive evaluation of normalization methods for Illumina high-throughput RNA sequencing data analysis

Kevin