Computes the dispersion coefficient of a -- consensus --
matrix object, generally obtained from multiple
NMF runs.
dispersion(object, ...)
an object from which the dispersion is computed
extra arguments to allow extension
signature(object = "matrix"):
Workhorse method that computes the dispersion on a given
matrix.
signature(object = "NMFfitX"):
Computes the dispersion on the consensus matrix obtained
from multiple NMF runs.
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: $$\rho = \sum_{i,j=1}^n 4 (C_{ij} - \frac{1}{2})^2 , $$ where \(n\) is the total number of samples.
By construction, \(0 \leq \rho \leq 1\) and \(\rho = 1\) 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).
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>.