# nmfdiv: Non-negative Matrix Factorization: Kullback-Leibler... In fabia: FABIA: Factor Analysis for Bicluster Acquisition

## Description

nmfdiv: R implementation of nmfdiv.

## Usage

 1 nmfdiv(X,p=5,cyc=100)

## Arguments

 X the data matrix. p number of hidden factors = number of biclusters; default = 5. cyc maximal number of iterations; default = 100.

## Details

Non-negative Matrix Factorization represents positive matrix X by positive matrices L and Z.

Objective for reconstruction is Kullback-Leibler divergence.

Essentially the model is the sum of outer products of vectors:

X = ∑_{i=1}^{p} λ_i z_i^T

where the number of summands p is the number of biclusters. The matrix factorization is

X = L Z

Here λ_i are from R^n, z_i from R^l, L from R^{n \times p}, Z from R^{p \times l}, and X from R^{n \times l}.

The model selection is performed according to D. D. Lee and H. S. Seung, 1999, 2001.

The code is implemented in R.

## Value

 object of the class Factorization. Containing LZ (estimated noise free data L Z), L (loading L), Z (factors Z), U (noise X-LZ), X (scaled data X).

Sepp Hochreiter

## References

D. D. Lee and H. S. Seung, ‘Algorithms for non-negative matrix factorization’, In Advances in Neural Information Processing Systems 13, 556-562, 2001.

D. D. Lee and H. S. Seung, ‘Learning the parts of objects by non-negative matrix factorization’, Nature, 401(6755):788-791, 1999.