Sample A: Cover Page of Thesis, Project, or Dissertation Proposal

Information gain ratios (equations 2 and 3) were calculated per probe and ProbeSet, based upon
their performance as implemented in the k-means clustering algorithm, for three distinct clusters.
The average gain ratio for all of the probes in a ProbeSet was determined. However for this
analysis, the gain ratio calculated for the average ProbeSet intensity was evaluated to eliminate
less informative ProbeSets. It is proposed here that the differences observed between the
aggregate ProbeSet and the average probe performance can by utilized in a way similar to the
suggestion for using the ‘Signal’ ProbeSets in Chapter 3, to discern transcript regions relevant to
the phenotype. Prior to calculating the gain ratio, normalization transformation was performed on
the data (probe and ProbeSet). Let xi,j represent the data as 4,258 ProbeSets by 155 samples and
was scaled as
xi, j " (xi,
j - x i )/ * i . (5.1)
Where x is the mean signal intensity across the samples and sigma the variance across samples.
Hartigan-Wong Clustering was done for 50 random centers (nstarts=50) [9], which appeared to
be sufficient to minimize the Euclidean sum of squares. This clustering approach is the default
and according to the R documentation it typically demonstrates the best performance [9]. The
two best solutions were then chosen, and their gain ratios were calculated, given their distinct
cluster centers. These solutions were selected as optimal for the adenocarcinoma clustering,
having the smallest Euclidean sum of squares and sub-optimal for either the squamous or normal
clustering. The decision to use both best solutions was an effort to compensate for the ‘no free
lunch theory’ [10], in that if the clustering was appropriate for both adenocarcinoma and normal
samples, the clustering underperforms for the squamous samples. Fifty clustering attempts were
typically sufficient to find both ‘best’ centers, and the gain ratios for the two centers were
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