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The following normalization methods will generate different results depending on whether the transformation was performed on samples or on features:

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Normalization Methods

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1. 1. Normalize the reads by the length of feature, it generate reads per kilobase
      RPK_sf  = X_sf / L_f;
   2. Sum up all the RPKsf in a sample
      PRK_s =  ∑^F_f=1 FRPK_sf
   3. Generate a scaling factor for each sample by normalizing the PRK of the sample to the sum PRK of all the samples
      Image RemovedImage Added,
      where TR is the total reads across all samples
   4. Divide raw reads by the scaling factor to get TPM
      TX_sf = X_sf/K_s
      

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Expression signal

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Sample histogram

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References

• Bolstad BM, Irizarry RA, Astrand M, Speed, TP. A Comparison of Normalization Methods for High Density Oligonucleotide Array Data Based on Bias and Variance. Bioinformatics. 2003; 19(2): 185-193.

• Mortazavi A, Williams BA, McCue K, Schaeffer L, Wold B. Mapping and quantifying mammalian transcriptomes by RNA-Seq. Nat Methods. 2008; 5(7): 621–628.

• Bullard JH, Purdom E, Hansen KD, Dudoit S. Evaluation of statistical methods for normalization and differential expression in mRNA-Seq experiments. BMC Bioinformatics. 2010; 11: 94.
• Robinson MD, Oshlack A. A scaling normalization method for differential expression analysis of RNA-seq data. Genome Biol. 2010; 11: R25.
• Dillies MA, Rau A, Aubert J et al. A comprehensive evaluation of normalization methods for Illumina high-throughput RNA sequencing data analysis. Brief Bioinform. 2013; 14(6): 671-83.
• Wagner GP, Kin K, Lynch VJ. Measurement of mRNA abundance using RNA-seq data. Theory Biosci. 2012; 131(4): 281-5.
• Ritchie ME, Phipson B, Wu D et al. Limma powers differential expression analyses for RNA-sequencing and microarray studies. Nucleic Acids Res. 2015; 43(15):e97.

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