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Creating the WQI involves three main steps (US EPA 2009): (1) obtain measurements on individual water quality indicators (2) transform measurements into "subindex" values to represent them on a common scale (3) aggregate the individual subindex values into an overall WQI value.
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The covariance of the transformed measurements is L(R)−1 R L(R)−I=I.
The goal of compressive sensing is to recover the sparse vector using small number of linearly transformed measurements.
Normalized Cy3 and Cy5 signal intensities from replicate experiments were normalized and log2 transformed (measurements with negative values were changed to a value of 1).
When the number of imputations was large, we did not observe a statistical difference between imputing the missing data using untransformed or squared root transformed measurements, although we noticed a slightly tighter variance when untransformed data was used.
The reference range was obtained using log transformed measurements and back transformed to give limits for the percentage relative difference of the actual measurements.
The standard deviations for the log2 transformed measurements were varied from 0.25 to 1.0, which is in-line with observed standard deviation:mean ratios in other studies.
By transforming measurements into standardised uncorrelated data which is used to estimate Euclidean distances, scale differences are taken into account when estimating distances.
Data were then transformed (measurements less than 0.01 set to 0.01), normalized per chip to the 50 th percentile, and per gene to control samples.
If the original measurement error covariance is R, then the transformed measurement error covariance is (hat {R}=ARA^{T}).
Thus, we transformed measurement data into Z values in order to assess the comparability of change in measured values.
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