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

56 CHAPTER 3. MATHEMATICAL MODELING AND ALGORITHMS
3.8 Extracting Fingerprints
3.8.1 What are Fingerprints ?
A Fingerprint, with respect to this thesis, is a set of masterpeaks of a particular
set of spectra (for example spectra of lung cancer patients of a certain age)
that are not present (or differentiate) in some control group (for example
healthy patients of the same age). That is, given an unknown spectrum S (of
a patient P ) and a fingerprint F of, say a particular disease, we can judge just
by checking the occurrence of the peaks of F whether the patient P is likely
to have this disease. The following sections will explain how we determine a
fingerprint given two sets of spectra (e.g. cancer patients vs. healthy patients).
3.8.2 Our Approach
After the preprocessing steps we now have information about assigned masterpeaks
from the two patient (spectra) groups. With these information we
can analyze for patterns (fingerprints) by detection and subsequent selection
of significant features.
1. Creation of Fingerprint
� Requires Feature Detection, described in the previous section and
detects potential features that can be used to discriminate two
groups based on their properties (e.g. differences in average height,
see Fig. 3.6.13)
� Feature Selection: Selection of an optimal subset of features detected
(see Figure 3.18(a)).
2. Reduce Complexity: Dimensionality Reduction of fingerprint data by
projecting fingerprint data to a low-dimensional space (see Fig. 3.18(b)).
This is done because it is usually not reliable to cluster in high dimensions.
3. Evaluation by clustering: Clustering of low-dimensional projections to
get a performance measure. The clusters found can then be used to
derive classification rules. (See also section 4.3.3.)
The feature detection step identifies a set of masterpeaks that differ significantly
in particular properties (e.g. height, width) between two groups of
spectra.
Feature Selection
Generally speaking, feature selection approaches try to find a subset of the
original features of the given data. Thus, this step selects a small and efficient 16
set of features from the previous feature detection step. This step is also called
modeling since we build a reduced model of the (real) full feature set. By
removing irrelevant and redundant features from the data, feature selection
helps to improve performance of learning models by
� Reducing the effect of the curse of dimensionality
16 The less features used while maintaining the same discrimination power the more efficient
is the set.