2.4.4. Variance stabilization normalization (VSN)

The VSN method overcomes the limitations of log transformations by accommodating negative values and minimizing the inflated variance around low signal intensities. It calibrates between-feature variation through shifting and scaling mechanism in which all the data are adjusted.

Huber et al. and Durbin et al. independently proposed the VSN approach which is a variant of the log-transform (glog2). A two-component model to explain the proportional increase in the variance with the mean intensity of the proteins was proposed [9], [17], [27]; yijkr=αijkr⌢+μijkreη+εijkr, where αijkr⌢ is the background signal and μijkr=yijkr⌢ is the actual signal. η=Norm0,ση and εijkr=Norm0,σ2 are the proportional error and background error respectively. However, with background corrected data this can be modelled as yijkr≈μijkreη. A transformation h is used to produce values such that Varhyijkr is approximately independent of the mean, Ehyijkr. In general, for a matrix, μijkr the function implemented fits a normalisation transformation μijkr→hμijkr=glog2μijkr-aibi where bi is the scaling parameter for array i which is always ensured to be positive with a parameter transformation f(b)=exp(b), ai is the background offset included if the data is not background corrected and glog2u=log2u+u2+1=arsinhu/log2 is the generalised transformation h. A robust variant of the maximum likelihood estimator for the 2 parameters is utilised [1]. Each slide is treated independently and slide to slide variation is not considered [10].