New Statistical Algorithms for the Analysis of Mass - FU Berlin, FB MI ...

48 CHAPTER 3. MATHEMATICAL MODELING AND ALGORITHMS
Figure 3.6.15: This shows a spectrum alignment using key reference key peaks.
The top left picture show the reference key peaks and their respective distances in xdirection.
The top right picture show a new spectrum to be aligned with the reference.
The result of this alignment process is shown in the bottom picture.
peaks. As can be seen, the part in range a1 is compressed while range b1 is
stretched and partly filled with zero elements.
Other Alignment Algorithms
The problem of spectra alignment appears not only in mass spectrometry but
for many other data, such as in NMR spectra alignment (see (Kim et al., 2006)
for an Bayesian approach) or electrophoretic lane alignment (see (Aittokallio
et al., 2001) for a dynamic time warping approach). In all of these domains
(and many more) different and similar algorithms have been developed (see
e.g. (Mäkinen, 2007) for an example derived from sequence alignment). One
large family of algorithms we have analyzed during this work have the following
drawbacks:
� They are operating globally, that is, local changes (during alignment)
of an ordered spectrum x0 . . . xn at a particular position xi affects all
positions xi+1 . . . xn.
� They align exactly two spectra, that is, a new spectrum to a reference
spectrum.
� They can not incorporate any statistical information.
As we have shown above, our approach allows to circumvent these shortcomings
while using statistical information which are incorporated naturally by
aligning groups of peaks (masterpeaks) opposed to single peaks from two single
spectra.