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 371 samples using the 1500 most variable genes was identified for k = 5 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 

TCGA2VA95S01  1  0.074 
TCGA2YA9GS01  1  0.015 
TCGA2YA9GY01  1  0.22 
TCGA2YA9H001  1  0.12 
TCGA5CAAPD01  1  0.22 
TCGABC407301  1  0.16 
TCGABCA10U01  1  0.2 
TCGABCA10W01  1  0.1 
TCGABCA11201  1  0.21 
TCGABCA21601  1  0.098 
SampleName  K=2  K=3  K=4  K=5  K=6  K=7  K=8 

TCGA2VA95S01  1  1  1  1  1  1  1 
TCGA2YA9GU01  1  1  1  3  4  4  4 
TCGA2YA9GW01  1  3  3  4  1  1  1 
TCGA2YA9GX01  1  3  3  4  5  5  5 
TCGA2YA9GY01  1  1  1  1  2  2  2 
TCGA2YA9H201  1  3  3  4  5  4  6 
TCGA2YA9H301  1  1  1  3  4  6  7 
TCGA2YA9H501  1  3  3  3  4  6  7 
TCGA2YA9H601  1  3  3  4  4  5  4 
TCGA2YA9H701  1  1  1  3  4  6  7 
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 

?10357  0.0024  0.27  0.0087  1 
?57714  0.000016  0.81  0.00013  1 
?645851  0.04  0.41  0.087  1 
?653553  0.0034  0.52  0.012  1 
?8225  0.018  0.24  0.045  1 
A1BG1  0.00017  1.7  0.00094  1 
A2LD187769  1.5e06  0.77  0.000018  1 
AAAS8086  0.009  0.15  0.025  1 
AACS65985  1.1e11  0.78  9.2e10  1 
AADAC13  0.000057  1.4  0.00038  1 
RSEM is used to estimate gene and transcript abundances and these values are normalized to a fixed upper quaritile value of 1000 for gene and 300 for transcript level estimates. RPKM for a given GeneX is calculated by: (raw read counts * 10^9) / (total reads * length of GeneX). Total reads is the lane yield after removing poor quality reads and the length of GeneX is defined as the median length of all transcripts associated with GeneX.

Input file for selecting top 1500 genes = *.uncv2.mRNAseq_RSEM_normalized_log2.txt (quantile normalized RSEM with log2 transformed) / *.mRNAseq_RPKM_log2.txt (RPKM value with log2 transformed) from mRNAseq_preprocess pipeline

Input file for the clustering module = /xchip/cga/gdacprod/tcgagdac/jobResults/GDAC_TopgenesforCluster/LIHCTP/22507508/LIHCTP.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.