Clustering of copy number data by focal peak region with absolute value: consensus NMF
Uveal Melanoma (Primary solid tumor)
13 July 2018 | None
Maintainer Information
Maintained by Broad Institute GDAC (Broad Institute of MIT & Harvard)
Overview
Introduction

This pipeline calculates clusters based on a consensus non-negative matrix factorization (NMF) clustering method [1],[2]. 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 marker genes for each subtype.

Summary

The most robust consensus NMF clustering of 80 samples using the 21 most variable genes was identified for k = 5 clusters. We computed the clustering for k = 2 to k = 10 and used the cophenetic correlation coefficient and the average silhouette width calculation to determine the robust clusters.

Results
Gene expression patterns of molecular subtypes

Figure 1. Get High-res Image Samples were separated into 5 clusters. Shown are 80 samples and 36 marker genes. The color bar of the row indicates the marker genes for the corresponding cluster.

Figure 2. Get High-res Image Heatmap with a standard hierarchical clustering for 80 samples and the 21 most variable genes. *The NA values were changed to 0 for this figure.

Silhouette widths, Cophenetic Correlation Coefficients and Consensus matrix

Figure 3. Get High-res Image The silhouette width was calculated for each sample and each value of k. The left upper panel shows the average silhouette width across all samples for each tested k (left upper panel). The left lower panel shows the Cophenetic Correlation Coefficients for each tested k. The right panel shows assignments of clusters to samples and the silhouette width of each sample for the most robust clustering.

Figure 4. Get High-res Image The consensus matrix after clustering shows 5 clusters with limited overlap between clusters.

Samples assignment with silhouette width

Table 1. Get Full Table List of samples with 5 subtypes and silhouette width.

SampleName | cluster | silhouetteValue
--- | --- | ---
TCGA-RZ-AB0B-01A-11D-A39V-01 | 1 | -0.65
TCGA-V4-A9E8-01A-11D-A39V-01 | 1 | 0.77
TCGA-V4-A9EE-01A-11D-A39V-01 | 1 | 0.26
TCGA-V4-A9EO-01A-12D-A39V-01 | 1 | 0.33
TCGA-V4-A9EQ-01A-11D-A39V-01 | 1 | 0.72
TCGA-V4-A9ES-01A-11D-A39V-01 | 1 | 0.18
TCGA-V4-A9F0-01A-11D-A39V-01 | 1 | 0.6
TCGA-V4-A9F8-01A-11D-A39V-01 | 1 | 0.17
TCGA-VD-A8KD-01A-11D-A39V-01 | 1 | 0.21
TCGA-VD-AA8O-01A-11D-A39V-01 | 1 | 0.67

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

membership | K=1 | K=2 | K=3 | K=4 | K=5 | K=6
--- | --- | --- | --- | --- | --- | ---
1 | 1 | 1 | 1 | 1 | 1 | 1
1 | 2 | 2 | 2 | 2 | 2 | 2
2 | 3 | 3 | 3 | 3 | 3 | 3
2 | 3 | 3 | 3 | 3 | 1 | 4
1 | 2 | 2 | 2 | 2 | 2 | 2
1 | 1 | 1 | 1 | 1 | 1 | 5
2 | 3 | 3 | 3 | 3 | 3 | 3
2 | 3 | 3 | 3 | 3 | 3 | 3
2 | 3 | 3 | 3 | 3 | 3 | 3
1 | 1 | 4 | 4 | 4 | 4 | 6

Marker genes 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 genes for each subtype by comparing the subclass versus the other subclasses, using Student's t-test.

Table 3. Get Full Table List of marker genes with p <= 0.05 (The positive value of column difference means gene is upregulated in this subtype and vice versa).

Hybridization.REF | p | difference | q | subclass
--- | --- | --- | --- | ---
DEL PEAK 13(8P11.22) | 0.000019 | 0.62 | 0.00014 | 1
DEL PEAK 17(17Q12) | 0.0082 | 0.25 | 0.014 | 1
DEL PEAK 2(1P12) | 0.0043 | -0.4 | 0.0082 | 1
DEL PEAK 6(3P22.2) | 0.00011 | -0.44 | 0.00023 | 1
DEL PEAK 8(3Q24) | 0.000079 | -0.45 | 0.00018 | 1
DEL PEAK 10(3Q29) | 0.000059 | -0.45 | 0.00016 | 1
DEL PEAK 7(3P14.2) | 6e-05 | -0.46 | 0.00016 | 1
DEL PEAK 4(3P25.2) | 0.000047 | -0.47 | 0.00016 | 1
DEL PEAK 9(3Q29) | 0.000021 | -0.47 | 0.00014 | 1
DEL PEAK 5(3P25.1) | 0.000062 | -0.49 | 0.00016 | 1
DEL PEAK 1(1P36.12) | 2.1e-06 | -0.61 | 0.000043 | 1
AMP PEAK 1(6P24.3) | 0.000043 | -0.72 | 0.00016 | 1
AMP PEAK 2(8Q11.22) | 1.2e-07 | 1.6 | 3.2e-07 | 2
AMP PEAK 3(8Q24.22) | 5.5e-07 | 1.2 | 1.3e-06 | 2
DEL PEAK 1(1P36.12) | 0.0055 | 0.26 | 0.0097 | 2
DEL PEAK 12(6Q25.3) | 0.014 | -0.34 | 0.023 | 2
DEL PEAK 9(3Q29) | 2.1e-10 | -0.54 | 8.9e-10 | 2
DEL PEAK 8(3Q24) | 9.7e-11 | -0.54 | 7.6e-10 | 2
DEL PEAK 10(3Q29) | 1.1e-10 | -0.55 | 7.6e-10 | 2
DEL PEAK 7(3P14.2) | 1.1e-10 | -0.55 | 7.6e-10 | 2
DEL PEAK 4(3P25.2) | 1.5e-10 | -0.56 | 7.6e-10 | 2
DEL PEAK 5(3P25.1) | 5.1e-10 | -0.57 | 1.8e-09 | 2
DEL PEAK 6(3P22.2) | 6e-10 | -0.59 | 1.8e-09 | 2
AMP PEAK 1(6P24.3) | 0.00019 | -0.63 | 0.00037 | 2
DEL PEAK 13(8P11.22) | 4.4e-06 | -0.83 | 9.2e-06 | 2
AMP PEAK 1(6P24.3) | 3.3e-07 | 1.1 | 7.6e-07 | 3
DEL PEAK 5(3P25.1) | 3.1e-21 | 0.84 | 1.3e-20 | 3
DEL PEAK 6(3P22.2) | 1.2e-19 | 0.82 | 3.6e-19 | 3
DEL PEAK 4(3P25.2) | 3e-22 | 0.82 | 4.7e-21 | 3
DEL PEAK 7(3P14.2) | 5.3e-21 | 0.8 | 1.8e-20 | 3
DEL PEAK 9(3Q29) | 4.4e-22 | 0.8 | 4.7e-21 | 3
DEL PEAK 10(3Q29) | 2e-21 | 0.79 | 1.3e-20 | 3
DEL PEAK 8(3Q24) | 3e-21 | 0.78 | 1.3e-20 | 3
DEL PEAK 17(17Q12) | 0.029 | -0.17 | 0.055 | 3
AMP PEAK 3(8Q24.22) | 0.000036 | -0.94 | 0.000075 | 3
AMP PEAK 2(8Q11.22) | 1.2e-09 | -1.4 | 3.2e-09 | 3

Methods & Data
Input

Copy number data file (the peak region with absolute value was used) = 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.

- Input file = TCGA-UVM-TP.expclu.gct

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 [1],[2]. Rather than separating gene clusters based on distance computation, NMF detects contextdependent patterns of gene expression in complex biological systems.

Cophenetic Correlation Coefficient and How to select the best cluster

We use the cophenetic correlation coefficients to determine the cluster that yields the most robust clustering. The cophenetic correlation coefficient is computed as the Pearson correlation of two distance matric: one is the distance between samples induced by the consensus matrix, and the other is the distance between samples induced by the linkage used in the reordingering of consensus matrix. The cophenetic correlation coefficient lies between 0 and 1. We select the best cluster k where the magnitude of the cophenetic correlation coefficient begins to fall[1]. If there are more than one peak points, we will select one with higer silhouette width. If there is no peak point, we will select the k with max cophenetic correlation coefficient.

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 [3][4].

References
[1] Brunet, J.P., Tamayo, P., Golub, T.R. & Mesirov, J.P., Metagenes and molecular pattern discovery using matrix factorization, Proc Natl Acad Sci U S A 12(101):4164-9 (2004)
[2] Broad Genepattern: NMFConsensus
[3] Rousseeuw, P.J., Silhouettes: A graphical aid to the interpretation and validation of cluster analysis., J. Comput. Appl. Math. 20:53-65 (1987)
[4] R silhouette package
[5] RSEM
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