README.md

In ragnhildlaursen/SFS: Sampling the set of feasible solutions from a non-negative matrix factorization

SFS Package

Introduction

This package is developed for a new sampling algorithm to find the set of feasible solutions (SFS) from an initial solution of non-negative matrix factorization (NMF). Remember, non-negative matrix factorization takes a non-negative matrix M(K x G) and approximates it by two other non-negative matrices P(K x N) and E(N x G) such that

M = PE

Other solutions with the same approximation could be construct with an invertible matrix A(N x N) such that

\tilde{P} = PA \geq 0 \quad \tilde{E} = A^{-1}E \geq 0,

are new solutions. There exist trivial ambiguities where A is either a diagonal matrix or a permutation matrix, but besides these trivial ambiguities others could exist as well. The scaling ambiguity is removed by assuming the columns of P sum to one. The goal of the main function sampleSFS in this package is to approximate the whole SFS that exist for P and E besides the ambiguities. The advantage of this algorithm is that is has a simple implementation and can be applied for an arbitrary dimension of N. A further desciption can be found in the corresponding paper R. Laursen and A. Hobolth, A sampling algorithm to compute the set of feasible solutions for non-negative matrix factorization with an arbitrary rank..

The package includes the following functions:

• sampleSFS is the main function that can find the SFS from an initial NMF
• NMFPois can find an initial NMF solution from a data matrix
• gkl.dev is an internal function for NMFPois, that calculates the generalized Kullback-Leibler
• samplesToSVD will transform SFS solutions from sampleSFS relative to SVD solution

Workflow of the package

Installation

The most simple way to install the package is using the package devtools .

devtools::install_github("ragnhildlaursen/SFS")
library(SFS)

Example of how to use functions

To illustrate the functions let us assume we have given a matrix of data M (4 x 6)

M = matrix(c(20, 3, 24, 19,  2, 15, 
             9, 14, 25, 30, 15, 10,
             30, 6, 12, 10, 11,  7,
             9, 27, 5, 11, 19, 15),
           nrow = 4, ncol = 6)

First, we need to create an initial NMF solution which is made using the function NMFPois. The input for this function is a matrix M and a rank N, that we here choose to be 3.

initial.fit = NMFPois(M,3)
initial.fit$P
initial.fit$E
initial.fit$P%*%initial.fit$E #approximation of M

Now, as an initial solution has been constructed one can find the SFS with the function sampleSFS. Here, we just need the initial solutions of P and E.

sfs.result = sampleSFS(initial.fit$P,initial.fit$E) 

ragnhildlaursen/SFS documentation built on Nov. 15, 2021, 8:28 p.m.