Figure 2

The detailed process for identifying a very important pool (VIP) of genes. X₁ and X₂ are, respectively, the gene expression profiles for class 1 samples and class 2 samples in the training set. X_1mand X_2mare samples randomly selected from X₁ and X₂ in the m^thbagging step. ${\text{X}}_{1m}^{\text{'}}$ and ${\text{X}}_{2m}^{\text{'}}$ are the genes remaining after filtering genes from X_1mand X_2m, respectively. Malinowski's factor indicator function (IND) is calculated with equations $R{E}_k=\sqrt{{\displaystyle \sum _{i=k+1}^g{\lambda }_i}/p(n-k)}$ and IND _k = RE _k /(n - k)², where λ _i is the i^th eigenvalue of the total g eigenvalues; n is the number of samples and p is the number of genes. The optimum number (k) of components corresponds to the IND minimum. E₁₁ and E₂₁ are the residue matrices after projecting X_1mand X_2minto the PCA space for class 1, respectively, while E₂₂ and E₁₂ are the residue matrices after projecting X_2mand X_1minto the PCA space for class 2, respectively. The discrimination power (DP) of a gene j is calculated with the equation: $D{P}_j=[{(e_j^{12})}^{\text{T}}(e_j^{12})+{(e_j^{21})}^{\text{T}}(e_j^{21})]/[{(e_j^{11})}^{\text{T}}(e_j^{11})+{(e_j^{22})}^{\text{T}}(e_j^{22})]$, where $e_j^{11}$, $e_j^{12}$, $e_j^{22}$, and $e_j^{21}$ are the j columns of residue matrices E₁₁, E₁₂, E₂₂, and E₂₁, respectively.