a set consisting of all of the breast tumors, as well as the 775-sample data set consisting of all triple negative tumors. The R function kmeans was used for clustering. To ensure that the algorithm converged to the global minimum instead of a local minimum, clustering was performed 50 times and the solution with the lowest within-class sum of squares was used to determine the cluster membership of each sample. Consensus K-means clustering was used to assess the stability of the clusters. This consisted of performing the clustering algorithm 100 times on different subsets of the data set, and then computing the fraction of iterations in which any pair of samples were found in the same cluster. At each iteration, the sample subsets were determined by taking a random sample without replacement whose size was 80% of the data set. The consensus matrix is a visual representation of the fraction of iterations in which any pair of samples co-clustered. The cumulative distribution of the consensus matrix across all possible sample pairs was used to determine the number of clusters. The appropriate number of clusters was the cluster number at which no further increases in the area under the cumulative distribution curve occurred. Typically, the relative change in area is close to zero above a IMR-1 certain value of K. For example, in the all-tumor data set and the TNBC-only data set, values of K greater than and equal to 5 resulted in low relative area changes. To select the appropriate number of clusters from these cases, the consensus matrices were investigated to determine which cluster number resulted in the most off-diagonal white space . PAM50 Intrinsic Subtypes A previously used classifier for 9682837 breast cancer involves the use of 50 genes to place tumors into one of five categories: basal, luminal A, luminal B, HER2-like, and normal-like. The method 9504387 for classifying a new sample is to take the Spearman correlation coefficient of the expression of the 50 genes in the sample with each of the five class centroids. The class whose correlation coefficient is the highest is the class to which the sample belongs, unless all correlation coefficients are less than 0.1, in which case the sample is unclassified. It should be noted that no genes in the PAM50 classifier overlap with the VEGF- and semaphorinrelated genes that we consider here; thus when we compare VEGF- and semaphorin-based clusters, we are considering two completely independent methods of classification. Differential Expression Genes for VEGF and semaphorin ligands and receptors that were significantly different between two groups were determined by the Wilcoxon rank sum test. This was carried out using the wilcox.test function in R. Visualization of Data Gene expression differences between tumor and normal samples were plotted in Principal Component Analysis Principal component analysis was used to reduce the dimensionality of the data sets from the 31 VEGF- and semaphorin-related genes under consideration to a smaller number of components that can reproduce most of the variability in the data. The components are linear combinations of the expression of the genes, and capture patterns of co-expression. The prcomp function in R was used to perform PCA. The columns of the x matrix returned by this function corresponded to the scores, while the columns of the rotation matrix corresponded to the gene loadings. For 2-D score plots where colors were used to show different groups of samples, the stat
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