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Figure 5 | BMC Bioinformatics

Figure 5

From: Methodological study of affine transformations of gene expression data with proposed robust non-parametric multi-dimensional normalization method

Figure 5

Parallel translation normalization of affine transformed data. Parallel translation normalization of A 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbWenfgDOvwBHrxAJfwnHbqeg0uy0HwzTfgDPnwy1aqee0evGueE0jxyaibaieYdOi=BH8vipeYdI8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0lXdbba9pGe9qqFf0dXdHuk9fr=xfr=xfrpiWZqaaeaabiGaaiaacaqabeaadaqacqaaaOqaaGWaaiab=bq8bnaaBaaaleaatCvAUfKttLearCWrP9MDH5MBPbIqV92AaGqbaiab+fdaXaqabaaaaa@43C0@ transformed data. The optimal amount of normalization shift in the raw data is a = 220, which corresponds to an effective shift of ( a G MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGHbqygaqbamaaBaaaleaacqWGhbWraeqaaaaa@2F46@ , a R MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGHbqygaqbamaaBaaaleaacqWGsbGuaeqaaaaa@2F5C@ ) = (420, 240). Left: Log-ratios as a function of log-intensities for certain fold changes. The r = 1 curve (dot-dash blue) is horizontal, that is, for this specific value of r and a the log-ratios are independent of the log-intensities. Right: Normalized log-ratios versus true log-ratios. From this graph it is clear that we obtain the minimum error in log-ratios at zero-fold change.

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