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

Figure 4.1: Non-traditional PCA analysis of Bhattacharjee data. PCA analysis of the Bhattacharjee data
for ProbeSets based upon sample correlation, using singular value decomposition of the data matrix (R
prcomp function) [17]. Latent structure can be observed in all three graphs. Top to bottom: RMA, dCHIP,
and BaFL produced values used as input to the data matrix.
PCA is a linear method, but not all gene relationships are linear [5-7]. The results of using a
Laplacian, non-linear reduction, method are presented for the Bhattacharjee data (Figure 4.2),
applied according to [7]. In this approach single value decomposition (SVD) of the correlation
matrix is performed [17] and normalized to the first column (ProbeSet) [7]. The first 2 Laplacian
dimensions are then projected into 2 dimensional space. Again, the BaFL produced data was
transformed with the simple log first.
97