This pipeline calculates clusters based on a consensus nonnegative matrix factorization (NMF) clustering method , . This pipeline has the following features:

Convert input data set to a nonnegitive matrix by column rank normalization.

Classify samples into consensus clusters.

Determine differentially expressed marker genes for each subtype.
The most robust consensus NMF clustering of 124 samples using the 6498 most variable genes was identified for k = 8 clusters. We computed the clustering for k = 2 to k = 10 and uused the cophenetic correlation coefficient and the average silhouette width calculation to determine the robust clusters.
SampleName  cluster  silhouetteValue 

TCGA3GAB0O01  1  0.62 
TCGA3QA9WF01  1  0.74 
TCGA3SAAYX01  1  0.23 
TCGA3TAA9L01  1  0.26 
TCGA4VA9QI01  1  0.52 
TCGA4VA9QJ01  1  0.58 
TCGA4VA9QQ01  1  0.28 
TCGA4VA9QT01  1  0.63 
TCGA4XA9F901  1  0.64 
TCGA4XA9FB01  1  0.6 
SampleName  K=2  K=3  K=4  K=5  K=6  K=7  K=8 

TCGA3GAB0O01  1  1  1  1  1  1  1 
TCGA3GAB0T01  1  1  3  3  3  3  3 
TCGA3QA9WF01  1  1  1  1  1  1  1 
TCGA3SAAYX01  1  1  1  1  1  1  1 
TCGA3TAA9L01  1  1  1  1  1  1  1 
TCGA4VA9QI01  1  1  1  1  1  1  1 
TCGA4VA9QJ01  1  1  1  1  1  1  1 
TCGA4VA9QQ01  1  1  1  1  1  1  1 
TCGA4VA9QS01  1  1  3  3  3  3  3 
TCGA4VA9QT01  1  1  1  1  1  1  1 
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 ttest.
Composite.Element.REF  p  difference  q  subclass 

A2BP1  6.4e08  0.23  7.7e08  1 
A2M  9.5e07  0.19  1.1e06  1 
A4GNT  4.5e13  0.27  1.2e12  1 
AACS  8.2e12  0.29  1.6e11  1 
AACSL  8.2e15  0.31  3.5e14  1 
AARSD1  1.1e18  0.33  4.8e17  1 
ABAT  2.6e14  0.35  9.6e14  1 
ABCA13  1.9e07  0.2  2.2e07  1 
ABCA17P  3.4e08  0.25  4.1e08  1 
ABCA4  4.8e14  0.39  1.6e13  1 
For a given gene, we select the probe with the maximum standard deviation across all beta values. Then we discard any probes with a standard deviation below a specified cutoff. The default cutoff is .2, but it can be tuned based on the desired output file size.

Input file for selecting top 6498 genes = *.meth.by_max_stddev.data.txt and *.meth.by_max_stddev.num_genes.txt from Methylation_Preprocess

Input file for the clustering module = /xchip/cga/gdacprod/tcgagdac/jobResults/GDAC_TopgenesforCluster/THYMTP/22507723/THYMTP.expclu.gct
Nonnegative matrix factorization (NMF) is an unsupervised learning algorithm that has been shown to identify molecular patterns when applied to gene expression data , . Rather than separating gene clusters based on distance computation, NMF detects contextdependent patterns of gene expression in complex biological systems.
We use the cophenetic correlation coefficients to determine the cluster that yields the most robust clustering. The cophenetic correlation coefficient is computed based on the consensus matrix of the CNMF clustering, and measures how reliably the same samples are assigned to the same cluster across many iterations of the clustering lgorithm with random initializations. The cophenetic correlation coefficients and average silhouette values are used to determine the k with the most robust clusterings. From the plot of cophenetic correlation versus k, we select modes and the the point preceding the greatest decrease in cophenetic correlation coefficient, and from these choose the k with the highest average silhouette value.
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 .
In addition to the links below, the full results of the analysis summarized in this report can also be downloaded programmatically using firehose_get, or interactively from either the Broad GDAC website or TCGA Data Coordination Center Portal.