# dispersion: Dispersion of a Matrix

Description Usage Arguments Details Methods References

### Description

Computes the dispersion coefficient of a – consensus – matrix object, generally obtained from multiple NMF runs.

### Usage

 1  dispersion(object, ...) 

### Arguments

 object an object from which the dispersion is computed ... extra arguments to allow extension

### Details

The dispersion coefficient is based on the consensus matrix (i.e. the average of connectivity matrices) and was proposed by Kim et al. (2007) to measure the reproducibility of the clusters obtained from NMF.

It is defined as:

ρ = ∑_{i,j=1}^n 4 (C_{ij} - \frac{1}{2})^2 ,

where n is the total number of samples.

By construction, 0 ≤q ρ ≤q 1 and ρ = 1 only for a perfect consensus matrix, where all entries 0 or 1. A perfect consensus matrix is obtained only when all the connectivity matrices are the same, meaning that the algorithm gave the same clusters at each run. See Kim et al. (2007).

### Methods

dispersion

signature(object = "matrix"): Workhorse method that computes the dispersion on a given matrix.

dispersion

signature(object = "NMFfitX"): Computes the dispersion on the consensus matrix obtained from multiple NMF runs.

### References

Kim H and Park H (2007). "Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis." _Bioinformatics (Oxford, England)_, *23*(12), pp. 1495-502. ISSN 1460-2059, <URL: http://dx.doi.org/10.1093/bioinformatics/btm134>, <URL: http://www.ncbi.nlm.nih.gov/pubmed/17483501>.

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