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 proteins for each subtype.
The most robust consensus NMF clustering of 106 samples using 193 proteins was identified for k = 5 clusters. We computed the clustering for k = 2 to k = 8 and used the cophenetic correlation coefficient to determine the best solution.
SampleName  cluster  silhouetteValue 

TCGA2LAAQA01A11A39L20  1  0.22 
TCGA2LAAQI01A21A39L20  1  0.21 
TCGA2LAAQL01A21A39L20  1  0.098 
TCGA3AA9IH01A21A39L20  1  0.27 
TCGA3EAAAZ01A21A39L20  1  0.15 
TCGAF2687901A21A39M20  1  0.098 
TCGAF2A8YN01A21A39L20  1  0.14 
TCGAFBA4P501A21A39L20  1  0.063 
TCGAFBA4P601A21A39L20  1  0.27 
TCGAFBA5VM01A21A39L20  1  0.22 
SampleName  K=2  K=3  K=4  K=5  K=6  K=7  K=8 

TCGA2LAAQA01A11A39L20  1  1  1  1  1  1  1 
TCGA2LAAQI01A21A39L20  1  1  1  1  1  1  1 
TCGA2LAAQL01A21A39L20  1  1  3  1  1  1  1 
TCGA2LAAQM01A21A39L20  1  1  3  3  3  3  3 
TCGA3AA9I501A21A39L20  1  3  3  4  4  4  4 
TCGA3AA9IH01A21A39L20  1  1  1  1  1  1  1 
TCGA3AA9IN01A21A39L20  1  1  3  4  4  4  3 
TCGA3AA9IX01A21A39L20  1  1  3  4  1  1  1 
TCGA3EAAAZ01A21A39L20  1  1  1  1  1  1  6 
TCGAF2687901A21A39M20  1  1  1  1  1  6  6 
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 proteins for each subtype by comparing the subclass versus the other subclasses, using Student's ttest.
Composite.Element.REF  p  difference  q  subclass 

VHLVHLMC  7.7e11  1.2  1.7e09  1 
CDH1ECADHERINRV  6e12  1.2  1.9e10  1 
ERBB2HER2MV  7.9e13  0.92  5.9e11  1 
CTNNB2BETACATENINRV  1.7e09  0.88  1.6e08  1 
STAT5ASTAT5ALPHARV  5.1e08  0.8  3.3e07  1 
RAB25RAB25RV  3.3e08  0.78  2.3e07  1 
EIF4G1EIF4GRC  1.1e10  0.76  2.2e09  1 
KDRVEGFR2RV  2.6e08  0.7  1.8e07  1 
RBM15RBM15RV  9.2e13  0.7  5.9e11  1 
ERBB3HER3RV  1.8e09  0.66  1.6e08  1 
The RPPA Level 3 data was used as the input for clustering; protein measurements corrected by median centering across antibodies.
Nonnegative matrix factorization (NMF) is an unsupervised learning algorithm that has been shown to identify molecular patterns when applied to protein expression data , . Rather than separating protein clusters based on distance computation, NMF detects contextdependent patterns of protein expression in complex biological systems.
We use the cophenetic correlation coefficient 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 coefficient lies between 0 and 1, with higher values indicating more stable cluster assignments. We select the number of clusters k based on the largest observed correlation coefficient for all tested values of k.
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.