Note: The original LIHC RPPA data used on 2016_01_28 was reported to be mislabelled Mesothelioma RPPA data. The affected analyses were patched on 10/13/2016, and contain this notice. For more details see our analysis release notes.
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 184 samples using the 219 most variable proteins was identified for k = 6 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 

TCGABC407201B21A40L20  1  0.013 
TCGABCA10U01A21A40L20  1  0.42 
TCGABCA10W01A21A40N20  1  0.41 
TCGABCA21601A21A40N20  1  0.067 
TCGABCA8YO01A21A40N20  1  0.43 
TCGACC526201A21A40L20  1  0.24 
TCGACC526301A21A40L20  1  0.089 
TCGACCA1HT01A21A40N20  1  0.54 
TCGACCA3MA01A21A40M20  1  0.01 
TCGACCA3MC01A21A40M20  1  0.025 
SampleName  K=2  K=3  K=4  K=5  K=6  K=7  K=8 

TCGABC407201B21A40L20  1  1  1  1  1  1  1 
TCGABCA10S01A11A40N20  1  1  1  3  3  3  3 
TCGABCA10U01A21A40L20  1  1  3  1  1  1  1 
TCGABCA10W01A21A40N20  1  1  3  1  1  1  1 
TCGABCA11001A21A40N20  1  1  1  3  3  3  3 
TCGABCA21601A21A40N20  1  1  3  1  1  1  1 
TCGABCA21701A21A40L20  1  3  4  4  5  5  5 
TCGABCA3KG01A21A40M20  1  3  4  4  5  5  5 
TCGABCA69H01A21A40M20  1  3  4  4  5  5  1 
TCGABCA8YO01A21A40N20  1  1  4  1  1  1  5 
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 

SERPINE1PAI1  9.6e06  0.93  0.000058  1 
FN1FIBRONECTIN  2.5e06  0.68  2e05  1 
GAPDHGAPDH  0.000021  0.63  0.00011  1 
BCL2A1BCL2A1  6.3e10  0.5  6.9e08  1 
SYKSYK  0.000021  0.48  0.00011  1 
SQSTM1P62LCKLIGAND  0.037  0.46  0.059  1 
TFRCTFRC  0.000034  0.44  0.00014  1 
TIGARTIGAR  0.000027  0.44  0.00013  1 
YWHAZ1433_ZETA  0.000038  0.43  0.00015  1 
ACACAACC1  0.0049  0.42  0.01  1 
The RPPA Level 3 data was protein measurements corrected by median centering across antibodies.

Input file for selecting top 219 genes = *.antibody_annotation.txt from RPPA_AnnotateWithGene

Input file for the clustering module = /xchip/cga/gdacprod/tcgagdac/jobResults/GDAC_TopgenesforCluster/LIHCTP/26850662/LIHCTP.expclu.gct
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 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.