This pipeline calculates clusters based on a consensus non-negative matrix factorization (NMF) clustering method ##REF##10,##REF##11. This pipeline has the following features:
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Convert input data set to non-negativity matrix by column rank normalization.
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Classify samples into consensus clusters.
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Determine differentially expressed marker genes for each subtype.
The 2363 most variable methylated genes were selected based on variation. The variation cutoff are set for each tumor type empirically by fitting a bimodal distriution. For genes with multiple methylation probes, we chose the most variable one to represent the gene. Consensus NMF clustering of 582 samples and 2363 genes identified 3 subtypes with the stability of the clustering increasing for k = 2 to k = 8 and the average silhouette width calculation for selecting the robust clusters.
Figure 1. Get High-res Image Silhouette width was calculated and the average silhouette width for all samples within one cluster was shown below according to different clusters (left panel). The robust cluster was pointed out by blue symbol (left panel) and the silhouette width of each sample in robust cluster was shown on right panel.
Figure 2. Get High-res Image The gene methylation heatmap with a standard hierarchical clustering for 582 samples and 2363 most variable genes.
Figure 3. Get High-res Image The consensus matrix after clustering shows 3 robust clusters with limited overlap between clusters.
Figure 4. Get High-res Image The correlation matrix also shows 3 robust clusters.
Table 1. Get Full Table List of samples with 3 subtypes and silhouette width.
| SampleName | cluster | silhouetteValue |
|---|---|---|
| TCGA-04-1331-01 | 1 | 0.015 |
| TCGA-04-1341-01 | 1 | 0.019 |
| TCGA-04-1342-01 | 1 | 0.066 |
| TCGA-04-1343-01 | 1 | 0.059 |
| TCGA-04-1347-01 | 1 | 0.2 |
| TCGA-04-1350-01 | 1 | 0.13 |
| TCGA-04-1351-01 | 1 | 0.015 |
| TCGA-04-1364-01 | 1 | 0.074 |
| TCGA-04-1369-01 | 1 | 0.074 |
| TCGA-04-1371-01 | 1 | 0.16 |
Table 2. Get Full Table List of samples belonging to each cluster in different k clusters.
| SampleName | K=2 | K=3 | K=4 | K=5 | K=6 | K=7 | K=8 |
|---|---|---|---|---|---|---|---|
| TCGA-04-1331-01 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| TCGA-04-1332-01 | 1 | 2 | 2 | 2 | 2 | 2 | 1 |
| TCGA-04-1337-01 | 1 | 2 | 1 | 1 | 1 | 1 | 3 |
| TCGA-04-1338-01 | 1 | 2 | 2 | 1 | 4 | 4 | 4 |
| TCGA-04-1346-01 | 1 | 2 | 2 | 2 | 4 | 4 | 4 |
| TCGA-04-1347-01 | 1 | 1 | 2 | 4 | 2 | 2 | 1 |
| TCGA-04-1350-01 | 1 | 1 | 2 | 4 | 2 | 2 | 1 |
| TCGA-04-1351-01 | 1 | 1 | 2 | 4 | 2 | 2 | 1 |
| TCGA-04-1356-01 | 1 | 2 | 2 | 2 | 3 | 4 | 4 |
| TCGA-04-1360-01 | 1 | 2 | 2 | 4 | 4 | 4 | 4 |
Samples most representative of the clusters, hereby called core samples were identified based on positive silhouette width, indicating higher similarity to their own class than to any other class member. Core samples were used to select differentially expressed marker genes for each subtype by comparing the subclass versus the other subclasses, using Student's t-test.
Table 3. Get Full Table List of marker genes with p<= 0.05 (The positive value of column difference means gene is upregulated in this subtype and vice versa).
| Composite.Element.REF | p | difference | q | subclass |
|---|---|---|---|---|
| PCDHGA1 | 6.5e-45 | 0.4 | 6.9e-43 | 1 |
| PCDHGA10 | 6.5e-45 | 0.4 | 6.9e-43 | 1 |
| PCDHGA2 | 6.5e-45 | 0.4 | 6.9e-43 | 1 |
| PCDHGA3 | 6.5e-45 | 0.4 | 6.9e-43 | 1 |
| PCDHGA4 | 6.5e-45 | 0.4 | 6.9e-43 | 1 |
| PCDHGA5 | 6.5e-45 | 0.4 | 6.9e-43 | 1 |
| PCDHGA6 | 6.5e-45 | 0.4 | 6.9e-43 | 1 |
| PCDHGA7 | 6.5e-45 | 0.4 | 6.9e-43 | 1 |
| PCDHGA8 | 6.5e-45 | 0.4 | 6.9e-43 | 1 |
| PCDHGA9 | 6.5e-45 | 0.4 | 6.9e-43 | 1 |
Non-negative matrix factorization (NMF) is an unsupervised learning algorithm that has been shown to identify molecular patterns when applied to gene expression data ##REF##10,##REF##11. Rather than separating gene clusters based on distance computation, NMF detects contextdependent patterns of gene expression in complex biological systems.
Silhouette width is defined as the ratio of average distance of each sample to samples in the same cluster to the smallest distance to samples not in the same cluster. If silhouette width is close to 1, it means that sample is well clustered. If silhouette width is close to -1, it means that sample is misclassified ##REF##12.
This is an experimental feature. The full results of the analysis summarized in this report can be downloaded from the TCGA Data Coordination Center.