Alignment Results

We have used the continuous alignment method presented in [1] to align the second cycle to the first cycle using the interpolated and deconvolved results. This method can compute an alignment error value which is the average square integral between the two aligned curve. We fixed the alignment parameters so that the two cycles are assumed to align perfectly well (stretch of 1 and shift of 65). Next, we compute the average alignment error for all cycling genes using these two datasets.
Both datasets resulted in similar alignment error (0.16). However, spline interpolation tends to flatten the expression profile. This leads to low alignment errors (for example, a completely flat curve will have an alignment error of 0). We thus normalized the alignment error for each gene by its average absolute expression values. Note that this procedure will still result in large errors for the deconvolved data if the two cycles do not agree. The normalized error was 25% higher for the interpolated results, indicating that the deconvolved values achieve better agreement between the first and second cycles.

[1] Bar-Joseph, Z., Gerber, G., Jaakkola, T.S., Gifford, D.K. and Simon, I.
A New Approach to Analyzing Gene Expression Time Series Data
RECOMB pp 39-48, 2002