Kidney Renal Clear Cell Carcinoma: Clustering of copy number data: consensus NMF
Maintained by TCGA GDAC Team (Broad Institute/MD Anderson Cancer Center/Harvard Medical School)
Overview
Introduction

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

1. Convert input data set to a non-negitive matrix by column rank normalization.

2. Classify samples into consensus clusters.

3. Determine differentially expressed focal events for each subtype.

Summary

The most robust consensus NMF clustering of 493 samples using the 30 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.

Results
Copy number focal events of molecular subtypes
Consensus and correlation matrix
Silhouette widths
Samples assignment with silhouette width

Table 1.  Get Full Table List of samples with 3 subtypes and silhouette width.

SampleName cluster silhouetteValue
TCGA-A3-3306-01A-01D-0858-01 1 0.3
TCGA-A3-3311-01A-02D-1322-01 1 -0.1
TCGA-A3-3316-01A-01D-0858-01 1 0.18
TCGA-A3-3317-01A-02D-1322-01 1 0.21
TCGA-A3-3319-01A-02D-1322-01 1 0.2
TCGA-A3-3320-01A-02D-1322-01 1 0.13
TCGA-A3-3335-01A-01D-0858-01 1 0.18
TCGA-A3-3336-01A-01D-0858-01 1 0.17
TCGA-A3-3346-01A-01D-0858-01 1 0.12
TCGA-A3-3352-01A-01D-0858-01 1 0.12

Table 2.  Get Full Table List of samples belonging to each cluster in different k clusters.

SampleName K=2 K=3 K=4 K=5 K=6 K=7 K=8
TCGA-A3-3306-01A-01D-0858-01 1 1 1 1 1 1 1
TCGA-A3-3311-01A-02D-1322-01 1 1 1 1 2 1 1
TCGA-A3-3313-01A-02D-1322-01 1 3 1 3 3 3 3
TCGA-A3-3316-01A-01D-0858-01 1 1 1 1 1 1 1
TCGA-A3-3317-01A-02D-1322-01 1 1 1 1 1 1 1
TCGA-A3-3319-01A-02D-1322-01 1 1 1 1 1 1 1
TCGA-A3-3320-01A-02D-1322-01 1 1 1 4 4 1 1
TCGA-A3-3325-01A-01D-0858-01 1 3 3 3 3 4 4
TCGA-A3-3335-01A-01D-0858-01 1 1 1 4 1 2 1
TCGA-A3-3336-01A-01D-0858-01 1 1 1 1 1 1 1
Marker focal events of each subtype

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 t-test.

Table 3.  Get Full Table List of marker focal events with p <= 0.05.

Composite.Element.REF p difference q subclass
AMP PEAK 2(1Q32.1) 9.3e-06 0.19 0.000023 1
AMP PEAK 5(5Q35.1) 0.000015 0.18 0.000034 1
AMP PEAK 6(7Q36.3) 0.000024 0.17 0.000052 1
AMP PEAK 7(8Q24.22) 5.4e-08 0.16 1.8e-07 1
AMP PEAK 1(1Q24.1) 2.7e-07 0.15 8.1e-07 1
DEL PEAK 3(1Q43) 6.2e-07 0.14 1.7e-06 1
DEL PEAK 4(2Q37.3) 0.016 0.066 0.024 1
DEL PEAK 18(XQ23) 0.00043 -0.052 0.00086 1
DEL PEAK 9(4Q34.3) 0.0083 -0.061 0.014 1
DEL PEAK 15(10Q23.31) 0.013 -0.062 0.02 1
Methods & Data
Input

Copy number data file = All Lesions File actual copy number part (all_lesions.conf_##.txt, where ## is the confidence level). The all lesions file is from GISTIC pipeline and summarizes the results from the GISTIC run. It 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

CNMF Method

Non-negative 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.

Cophenetic Correlation Coefficient

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

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 .