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 focal events for each subtype.
The most robust consensus NMF clustering of 370 samples using the 61 copy number focal regions was identified for k = 3 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 

TCGA2VA95S01A11DA36W01  1  0.16 
TCGA2YA9GT01A11DA38101  1  0.09 
TCGA2YA9GU01A11DA38101  1  0.042 
TCGA2YA9GX01A11DA38101  1  0.077 
TCGA2YA9H401A11DA38101  1  0.033 
TCGA4RAA8I01A11DA38101  1  0.21 
TCGA5RAA1D01A11DA38101  1  0.28 
TCGA5RAAAM01A12DA40Q01  1  0.12 
TCGABC407301B02DA12Y01  1  0.056 
TCGABCA10X01A11DA12Y01  1  0.12 
SampleName  K=2  K=3  K=4  K=5  K=6  K=7  K=8 

TCGA2VA95S01A11DA36W01  1  1  1  1  1  1  1 
TCGA2YA9GT01A11DA38101  1  1  1  1  1  1  1 
TCGA2YA9GU01A11DA38101  1  1  3  3  3  3  3 
TCGA2YA9GV01A11DA38101  1  2  1  1  1  4  1 
TCGA2YA9GW01A11DA38101  1  3  4  4  4  5  4 
TCGA2YA9GX01A11DA38101  1  1  3  3  3  3  5 
TCGA2YA9H101A11DA38101  1  3  4  4  4  5  7 
TCGA2YA9H401A11DA38101  1  1  1  5  1  1  1 
TCGA2YA9H601A11DA38W01  1  3  4  4  3  3  5 
TCGA2YA9H701A11DA38W01  1  3  4  4  3  3  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 focal events for each subtype by comparing the subclass versus the other subclasses, using Student's ttest.
Composite.Element.REF  p  difference  q  subclass 

DEL PEAK 8(4Q24)  5.2e21  0.32  3.2e19  1 
DEL PEAK 9(4Q35.1)  7.8e16  0.29  1.6e14  1 
DEL PEAK 7(4Q21.3)  3e18  0.29  9.1e17  1 
DEL PEAK 26(16Q23.1)  8.8e14  0.28  1.3e12  1 
DEL PEAK 27(17P13.1)  1.4e06  0.24  7.3e06  1 
DEL PEAK 2(1P36.11)  7.6e09  0.23  7.8e08  1 
DEL PEAK 14(9P21.3)  1.8e07  0.22  1.1e06  1 
DEL PEAK 22(13Q14.2)  5.7e06  0.21  0.000027  1 
DEL PEAK 28(17P11.2)  0.000026  0.2  0.000098  1 
DEL PEAK 23(14Q23.3)  9.4e07  0.17  5.2e06  1 
The actual copy number part from all_lesions.conf_##.txt was used in this clustering. The all lesions file contains data about the significant regions of amplification and deletion as well as which samples are amplified or deleted in each of these regions. The identified regions are listed down the first column, and the samples are listed across the first row, starting in column 10.

Input file for whole clustering pipeline = all_lesions.conf_##.txt (where ## is the confidence level) from GISTIC pipeline

Input file for the clustering module = /xchip/cga/gdacprod/tcgagdac/jobResults/GDAC_TopgenesforCluster/LIHCTP/22532712/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 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.