dispersion: Dispersion of a Matrix
In renozao/NMF: Algorithms and Framework for Nonnegative Matrix Factorization (NMF)

Description Usage Arguments Details Methods (by generic) References

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

dispersion(object, ...)

## S4 method for signature 'matrix'
dispersion(object, ...)

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

The dispersion coefficient is based on the consensus matrix (i.e. the average of connectivity matrices) and was proposed by Kim and Park (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 and Park (2007).

dispersion(object = NMFfitX): Computes the dispersion on the consensus matrix obtained from multiple NMF runs.
dispersion(object = matrix): Workhorse method that computes the dispersion on a given matrix.

Kim H, Park H (2007). “Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis.” _Bioinformatics (Oxford, England)_, *23*(12), 1495-502. ISSN 1460-2059, doi: 10.1093/bioinformatics/btm134 (URL: https://doi.org/10.1093/bioinformatics/btm134).

renozao/NMF documentation built on June 14, 2020, 9:35 p.m.