Clustering of RPPA data: consensus NMF
Prostate Adenocarcinoma (Primary solid tumor)
17 October 2014  |  analyses__2014_10_17
Maintainer Information
Citation Information
Maintained by TCGA GDAC Team (Broad Institute/MD Anderson Cancer Center/Harvard Medical School)
Cite as Broad Institute TCGA Genome Data Analysis Center (2014): Clustering of RPPA data: consensus NMF. Broad Institute of MIT and Harvard. doi:10.7908/C1H130ZR

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 marker proteins for each subtype.


The most robust consensus NMF clustering of 164 samples using 189 proteins 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.

Protein expression patterns of molecular subtypes

Figure 1.  Get High-res Image Samples were separated into 3 clusters. Shown are 164 samples and 189 marker proteins. The color bar of the row indicates the marker proteins for the corresponding cluster.

Figure 2.  Get High-res Image Heatmap with a standard hierarchical clustering for 164 samples and the 189 proteins.

Consensus and correlation matrix

Figure 3.  Get High-res Image The consensus matrix after clustering shows 3 clusters with limited overlap between clusters.

Figure 4.  Get High-res Image The correlation matrix also shows 3 clusters.

Silhouette widths

Figure 5.  Get High-res Image The silhouette width was calculated for each sample and each value of k. The left panel shows the average silhouette width across all samples for each tested k (left panel). The right panels shows assignments of clusters to samples and the silhouette width of each sample for the most robust clustering.

Samples assignment with silhouette width

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

SampleName cluster silhouetteValue
TCGA-CH-5737-01A-22-A303-20 1 0.38
TCGA-CH-5739-01A-21-A303-20 1 0.36
TCGA-CH-5740-01A-21-A303-20 1 0.4
TCGA-CH-5743-01A-11-A303-20 1 0.43
TCGA-CH-5744-01A-21-A303-20 1 0.45
TCGA-CH-5745-01A-21-A303-20 1 0.34
TCGA-CH-5748-01A-21-A303-20 1 0.38
TCGA-CH-5750-01A-21-A303-20 1 0.45
TCGA-CH-5753-01A-21-A303-20 1 0.25
TCGA-CH-5762-01A-21-A303-20 1 0.34

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-CH-5737-01A-22-A303-20 1 1 1 1 1 1 1
TCGA-CH-5738-01A-21-A303-20 1 2 2 2 2 2 2
TCGA-CH-5739-01A-21-A303-20 1 1 2 2 2 2 3
TCGA-CH-5740-01A-21-A303-20 1 1 2 2 2 2 3
TCGA-CH-5743-01A-11-A303-20 1 1 2 2 2 2 3
TCGA-CH-5744-01A-21-A303-20 1 1 2 2 2 2 3
TCGA-CH-5745-01A-21-A303-20 1 1 2 2 2 2 3
TCGA-CH-5748-01A-21-A303-20 1 1 1 1 1 1 1
TCGA-CH-5750-01A-21-A303-20 1 1 2 2 2 2 3
TCGA-CH-5753-01A-21-A303-20 1 1 2 4 2 2 3
Marker proteins 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 proteins for each subtype by comparing the subclass versus the other subclasses, using Student's t-test.

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

Composite.Element.REF p difference q subclass
AKT1 AKT2 AKT3|AKT_PS473-R-V 9.8e-16 1.2 2.1e-14 1
RPS6|S6_PS235_S236-R-V 8.3e-11 1.1 7.9e-10 1
MAPK1 MAPK3|MAPK_PT202_Y204-R-V 1.1e-13 1.1 1.6e-12 1
PDCD4|PDCD4-R-C 7.3e-18 0.99 3.5e-16 1
RPS6|S6_PS240_S244-R-V 9.5e-08 0.95 4.8e-07 1
AKT1 AKT2 AKT3|AKT_PT308-R-V 7.2e-13 0.93 9.1e-12 1
EIF4EBP1|4E-BP1_PT37_T46-R-V 1.9e-18 0.91 1.2e-16 1
SRC|SRC_PY527-R-V 2.4e-21 0.89 2.3e-19 1
STAT3|STAT3_PY705-R-V 1.8e-08 0.69 1.1e-07 1
GSK3A GSK3B|GSK3-ALPHA-BETA_PS21_S9-R-V 2.8e-15 0.66 5.2e-14 1
Methods & Data

The RPPA Level 3 data was used as the input for clustering; protein measurements corrected by median centering across antibodies.

CNMF Method

Non-negative 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.

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 .

Download Results

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.

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[3] Rousseeuw, P.J., Silhouettes: A graphical aid to the interpretation and validation of cluster analysis., J. Comput. Appl. Math. 20:53-65 (1987)