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