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

24 CHAPTER 3. MATHEMATICAL MODELING AND ALGORITHMS
Figure 3.1.1: Overview of the pipeline. The colored boxes show the distinct modules:
“(Signal) Preprocessing”, “Peak Seeding”, “Peak Picking” and “Analysis”. The gray
arrows indicate the data flow.
(see section 2.2): at this stage borders of the peaks are detected and
convoluted peaks separated.
Peak Picking: Classify signals found as noise or relevant peaks (sections 3.4,
3.6). This corresponds to the grouping of bricks in the Lego example.
Analyses: Determine significance of relevant peaks to distinguish spectrum
groups, such as “healthy” vs. “diseased” (section 3.7). Select the best
peaks to distinguish between two groups (section 3.8).
Now, one of the first questions jumping to mind when looking at a technology,
some hundred years old usually is: “Isn’t it already fully understood and
haven’t algorithms been developed already that can perfectly analyze these
data ?” The simple answer is “No”. It is still unclear what exactly happens
inside the machine (with respect to physical and biochemical phenomena) and
many approaches have been published that are continuously improving, but
still far from being perfect. To give you a better understanding, the next
section will introduce the main principles and resulting problems we have to
deal with. In the remaining of the chapter we will introduce our approaches
to cope with these issues.
3.1.1 Comparison to Other Concepts
The division into the components (pipeline steps) described above is somewhat
different to what is usually described in the literature. This is because most
algorithms are using one spectrum at a time for analysis in contrast to o ur
approach where we use many spectra simultaneously to refine the quality of
our findings. For example, usually a Peak Picking algorithm is designed to