Algorithms and framework for Nonnegative Matrix Factorization (NMF).

Background

Nonnegative Matrix Factorization (NMF) is an unsupervised learning technique that has been applied successfully in several fields, including signal processing, face recognition and text mining. Recent applications of NMF in bioinformatics have demonstrated its ability to extract meaningful information from high-dimensional data such as gene expression microarrays. Developments in NMF theory and applications have resulted in a variety of algorithms and methods. However, most NMF implementations have been on commercial platforms, while those that are freely available typically require programming skills. This limits their use by the wider research community.

Results

Our objective is to provide the bioinformatics community with an open-source, easy-to-use and unified interface to standard NMF algorithms, as well as with a simple framework to help implement and test new NMF methods. For that purpose, we have developed a package for the R/BioConductor platform. The package ports public code to R, and is structured to enable users to easily modify and/or add algorithms. It includes a number of published NMF algorithms and initialization methods and facilitates the combination of these to produce new NMF strategies. Commonly used benchmark data and visualization methods are provided to help in the comparison and interpretation of the results.

Conclusions

The NMF package helps realize the potential of Nonnegative Matrix Factorization, especially in bioinformatics, providing easy access to methods that have already yielded new insights in many applications.

Availability

Documentation, source code and sample data are available from:

• Latest stable release from CRAN: http://cran.r-project.org/package=NMF

• Development versions:

  • project: http://r-forge.r-project.org/projects/nmf
    NOTE: due to some unknown problem on R-forge build system, the package is not being built. Please use the MyCRAN repository until the issue is fixed.
    
    
  • MyCRAN: personal CRAN-like repository at http://web.cbio.uct.ac.za/~renaud/CRAN

Help topics

• advanced-NMF(which.best)
  Advanced Usage of the Package NMF
• aheatmap
  Annotated Heatmaps
• algorithmic-NMF(algorithm, algorithm<-, algorithm<--methods, algorithm-methods, algorithm<-,NMFfit,ANY-method, algorithm,NMFfit-method, algorithm,NMFfitXn-method, algorithm<-,NMFSeed,function-method, algorithm,NMFSeed-method, algorithm<-,NMFStrategyFunction,function-method, algorithm,NMFStrategyFunction-method, algorithm<-,NMFStrategyOctave,character-method, compare, compare-methods, compare,NMFfitXn-method, logs, logs,ANY-method, logs-methods, modelname, modelname,ANY-method, modelname-methods, modelname,NMFfit-method, modelname,NMFfitXn-method, modelname,NMFStrategy-method, niter, niter<-, niter<--methods, niter-methods, niter,NMFfit-method, niter<-,NMFfit,numeric-method, nrun, nrun,ANY-method, nrun-methods, nrun,NMFfit-method, nrun,NMFfitX1-method, nrun,NMFfitX-method, nrun,NMFfitXn-method, objective, objective<-, objective<--methods, objective-methods, objective<-,NMFfit,ANY-method, run, run-methods, runtime, runtime.all, runtime.all-methods, runtime.all,NMFfit-method, runtime.all,NMFfitX-method, runtime-methods, runtime,NMFfit-method, seeding, seeding<-, seeding<--methods, seeding-methods, seeding<-,NMFfit-method, seeding,NMFfit-method, seeding,NMFfitXn-method, seqtime, seqtime-methods, seqtime,NMFfitXn-method, seqtime,NMFList-method)
  Generic Interface for Algorithms
• algorithm,NMFList-method
  Returns the method names used to compute the NMF fits in the list.
• algorithm,NMFStrategyOctave-method
  Returns the name of the Octave/Matlab function that implements the NMF algorithm -- as stored in
• basis(.basis, .basis<-, basis<-, basis<-,ANY-method, basis,ANY-method, .basis<--methods, .basis-methods, basis<--methods, basis-methods, .basis<-,NMFfit,matrix-method, .basis,NMFfit-method, basis,NMFfitXn-method, .basis<-,NMF,matrix-method, .basis,NMF-method, basis,NMF-method, .basis<-,NMFstd,matrix-method, .basis,NMFstd-method, coef, .coef, .coef<-, coef<-, coef<-,ANY-method, coefficients, coefficients-methods, coefficients,NMF-method, .coef<--methods, .coef-methods, coef<--methods, coef-methods, .coef<-,NMFfit,matrix-method, .coef,NMFfit-method, coef,NMFfitXn-method, .coef<-,NMF,matrix-method, .coef,NMF-method, coef,NMF-method, .coef<-,NMFstd,matrix-method, .coef,NMFstd-method, loadings,NMF-method, scoef, scoef,matrix-method, scoef-methods, scoef,NMF-method)
  Accessing NMF Factors
• basiscor(basiscor,matrix,NMF-method, basiscor-methods, basiscor,NMF,matrix-method, basiscor,NMF,missing-method, basiscor,NMF,NMF-method, profcor, profcor,matrix,NMF-method, profcor-methods, profcor,NMF,matrix-method, profcor,NMF,missing-method, profcor,NMF,NMF-method)
  Correlations in NMF Models
• basisnames(basisnames<-, basisnames<-,ANY-method, basisnames,ANY-method, basisnames<--methods, basisnames-methods, dimnames-NMF, dimnames<-,NMF-method, dimnames,NMF-method)
  Dimension names for NMF objects
• bioc-NMF(.atrack,ExpressionSet-method, featureNames,NMFfitX-method, featureNames<-,NMF-method, featureNames,NMF-method, metagenes, metagenes<-, metaprofiles, metaprofiles<-, nmeta, nmf,ExpressionSet,ANY,ANY-method, nmf,matrix,ExpressionSet,ANY-method, nmfModel,ANY,ExpressionSet-method, nmfModel,ExpressionSet,ANY-method, nneg,ExpressionSet-method, rnmf,ANY,ExpressionSet-method, rposneg,ExpressionSet-method, run,NMFStrategy,ExpressionSet,ANY-method, sampleNames<-,NMF,ANY-method, sampleNames,NMFfitX-method, sampleNames,NMF-method, seed,ExpressionSet,ANY,ANY-method)
  Specific NMF Layer for Bioconductor
• canFit(canFit,character,ANY-method, canFit-methods, canFit,NMFStrategy,character-method, canFit,NMFStrategy,NMF-method)
  Testing Compatibility of Algorithm and Models
• compare-NMF(compare,list-method, compare,NMFfit-method, consensusmap,list-method, consensusmap,NMF.rank-method, plot,NMFList,missing-method, summary,NMFList-method)
  Comparing Results from Different NMF Runs
• connectivity(connectivity,ANY-method, connectivity,factor-method, connectivity-methods, connectivity,NMF-method, connectivity,numeric-method, consensus, consensus-methods, consensus,NMFfitX-method, consensus,NMF-method)
  Clustering Connectivity and Consensus Matrices
• consensushc(consensushc,matrix-method, consensushc-methods, consensushc,NMFfitX-method, consensushc,NMF-method)
  Hierarchical Clustering of a Consensus Matrix
• consensus,NMFfitX1-method
  Returns the consensus matrix computed while performing all NMF runs,
• consensus,NMFfitXn-method(plot.NMF.consensus)
  Computes the consensus matrix of the set of fits stored in
• cophcor(cophcor,matrix-method, cophcor-methods, cophcor,NMFfitX-method)
  Cophenetic Correlation Coefficient
• deviance(deviance-methods, deviance,NMFfit-method, deviance,NMFfitX-method, deviance,NMF-method, deviance,NMFStrategy-method, nmfDistance)
  Distances and Objective Functions
• dispersion(dispersion,matrix-method, dispersion-methods, dispersion,NMFfitX-method)
  Dispersion of a Matrix
• esGolub
  Golub ExpressionSet
• fcnnls(fcnnls,ANY,numeric-method, fcnnls,matrix,matrix-method, fcnnls-methods, fcnnls,numeric,matrix-method)
  Fast Combinatorial Nonnegative Least-Square
• .fcnnls
  Internal Routine for Fast Combinatorial Nonnegative Least-Squares
• featureScore(extractFeatures, extractFeatures,matrix-method, extractFeatures-methods, extractFeatures,NMF-method, featureScore,matrix-method, featureScore-methods, featureScore,NMF-method)
  Feature Selection in NMF Models
• fit(fit<-, fit<--methods, fit-methods, fit,NMFfit-method, fit<-,NMFfit,NMF-method, fit,NMFfitX1-method, fit,NMFfitX-method, fit,NMFfitXn-method, minfit, minfit-methods, minfit,NMFfit-method, minfit,NMFfitX1-method, minfit,NMFfitX-method, minfit,NMFfitXn-method)
  Extracting Fitted Models
• fitted(fitted-methods, fitted,NMFfit-method, fitted,NMF-method, fitted,NMFns-method, fitted,NMFOffset-method, fitted,NMFstd-method)
  Fitted Matrix in NMF Models
• getRNG1(.getRNG, getRNG1-methods, getRNG1,NMFfitX1-method, getRNG1,NMFfitX-method, getRNG1,NMFfitXn-method, .getRNG-methods, .getRNG,NMFfitXn-method)
  Extracting RNG Data from NMF Objects
• heatmap-NMF(basismap, basismap-methods, basismap,NMFfitX-method, basismap,NMF-method, coefmap, coefmap-methods, coefmap,NMFfitX-method, coefmap,NMF-method, consensusmap, consensusmap,matrix-method, consensusmap-methods, consensusmap,NMFfitX-method, consensusmap,NMF-method)
  Heatmaps of NMF Factors
• ibterms(bterms, cterms, ibasis, ibterms-methods, ibterms,NMFfit-method, ibterms,NMFfitX-method, ibterms,NMF-method, ibterms,NMFstd-method, icoef, icterms, icterms-methods, icterms,NMFfit-method, icterms,NMF-method, icterms,NMFstd-method, iterms, nbterms, ncterms, nterms)
  Fixed Terms in NMF Models
• is.nmf(hasBasis, hasCoef, is.empty.nmf, isNMFfit, is.partial.nmf)
  Testing NMF Objects
• match_atrack
  Extending Annotation Vectors
• methods-NMF(existsNMFMethod, getNMFMethod, removeNMFMethod, selectNMFMethod)
  Registry for NMF Algorithms
• nbasis(dim-NMF, dim,NMFfitXn-method, dim,NMF-method, nbasis,ANY-method, nbasis-methods, nbasis,NMFfitXn-method)
  Dimension of NMF Objects
• nmf(nmf,data.frame,ANY,ANY-method, nmf,formula,ANY,ANY-method, nmf,matrix,data.frame,ANY-method, nmf,matrix,matrix,ANY-method, nmf,matrix,missing,ANY-method, nmf,matrix,NMF,ANY-method, nmf,matrix,NULL,ANY-method, nmf,matrix,numeric,character-method, nmf,matrix,numeric,function-method, nmf,matrix,numeric,list-method, nmf,matrix,numeric,missing-method, nmf,matrix,numeric,NMFStrategy-method, nmf,matrix,numeric,NULL-method, nmf-methods)
  Running NMF algorithms
• nmfAlgorithm
  Listing and Retrieving NMF Algorithms
• nmfAlgorithm.SNMF_R(nmfAlgorithm.SNMF_L, SNMF/L-nmf, SNMF/R-nmf)
  NMF Algorithm - Sparse NMF via Alternating NNLS
• nmfApply
  Apply Function for NMF Objects
• nmfCheck
  Checking NMF Algorithm
• NMF-class(.DollarNames,NMF-method, misc, $<-,NMF-method, $,NMF-method)
  Generic Interface for Nonnegative Matrix Factorisation Models
• NMF-defunct(metaHeatmap, metaHeatmap,matrix-method, metaHeatmap-methods, metaHeatmap,NMFfitX-method, metaHeatmap,NMF-method)
  Defunct Functions and Classes in the NMF Package
• NMF-deprecated
  Deprecated Functions in the Package NMF
• nmf.equal(nmf.equal,list,list-method, nmf.equal,list,missing-method, nmf.equal-methods, nmf.equal,NMFfit,NMFfit-method, nmf.equal,NMFfit,NMF-method, nmf.equal,NMFfitX1,NMFfitX1-method, nmf.equal,NMFfitX,NMF-method, nmf.equal,NMF,NMFfit-method, nmf.equal,NMF,NMFfitX-method, nmf.equal,NMF,NMF-method)
  Testing Equality of NMF Models
• nmfEstimateRank(plot.NMF.rank)
  Estimate Rank for NMF Models
• NMFfit-class(NMFfit)
  Base Class for to store Nonnegative Matrix Factorisation results
• NMFfitX1-class
  Structure for Storing the Best Fit Amongst Multiple NMF Runs
• NMFfitX-class
  Virtual Class to Handle Results from Multiple Runs of NMF Algorithms
• NMFfitXn-class
  Structure for Storing All Fits from Multiple NMF Runs
• nmfFormals(nmfArgs)
  Showing Arguments of NMF Algorithms
• NMFList-class
  Class for Storing Heterogeneous NMF fits
• [,NMF-method
  Sub-setting NMF Objects
• nmfModel(nmfModel,data.frame,data.frame-method, nmfModel,formula,ANY-method, nmfModel,matrix,ANY-method, nmfModel,matrix,matrix-method, nmfModel-methods, nmfModel,missing,ANY-method, nmfModel,missing,missing-method, nmfModel,NULL,ANY-method, nmfModel,numeric,matrix-method, nmfModel,numeric,missing-method, nmfModel,numeric,numeric-method, nmfModels)
  Factory Methods NMF Models
• NMFns-class
  NMF Model - Nonsmooth Nonnegative Matrix Factorization
• nmfObject
  Updating NMF Objects
• NMFOffset-class(initialize,NMFOffset-method)
  NMF Model - Nonnegative Matrix Factorization with Offset
• NMF-package(NMF)
  Algorithms and framework for Nonnegative Matrix Factorization (NMF).
• nmfSeed(existsNMFSeed, getNMFSeed)
  Seeding Strategies for NMF Algorithms
• NMFSeed(NMFSeed,character-method, NMFSeed-methods, NMFSeed,NMFSeed-method, removeNMFSeed, setNMFSeed)
  NMFSeed
• NMFSeed-class
  Base class that defines the interface for NMF seeding methods.
• NMFstd-class
  NMF Model - Standard model
• NMFStop(nmf.stop.connectivity, nmf.stop.iteration, nmf.stop.stationary, nmf.stop.threshold, stop-NMF)
  Stopping Criteria for NMF Iterative Strategies
• NMFStrategy(NMFStrategy,character,character-method, NMFStrategy,character,function-method, NMFStrategy,character,missing-method, NMFStrategy,character,NMFStrategy-method, NMFStrategy-methods, NMFStrategy,missing,character-method, NMFStrategy,NMFStrategy,missing-method, NMFStrategy,NULL,character-method, NMFStrategy,NULL,NMFStrategy-method, run,NMFStrategyFunction,matrix,NMFfit-method, run,NMFStrategyIterative,matrix,NMFfit-method, run,NMFStrategyIterativeX,matrix,NMFfit-method, run,NMFStrategy,matrix,NMFfit-method, run,NMFStrategy,matrix,NMF-method, run,NMFStrategyOctave,matrix,NMFfit-method)
  Factory Method for NMFStrategy Objects
• NMFStrategyFunction-class
  Interface for Single Function NMF Strategies
• NMFStrategyIterative-class
  Interface for Algorithms: Implementation for Iterative NMF Algorithms
• NMFStrategyOctave-class(show,NMFStrategyOctave-method)
  S4 Interface for Octave-Matlab NMF Algorithms
• nmf_update.brunet_R(brunet_M-nmf, brunet-nmf, brunet_R-nmf, KL-nmf, nmfAlgorithm.brunet, nmfAlgorithm.brunet_M, nmfAlgorithm.brunet_R, nmfAlgorithm.KL, nmf_update.brunet)
  NMF Algorithm/Updates for Kullback-Leibler Divergence
• nmf_update.euclidean.h(nmf_update.euclidean, nmf_update.euclidean.h_R, nmf_update.euclidean.w, nmf_update.euclidean.w_R)
  NMF Multiplicative Updates for Euclidean Distance
• nmf_update.euclidean_offset.h(nmfAlgorithm.offset, nmfAlgorithm.offset_R, nmf_update.euclidean_offset.w, nmf_update.offset, nmf_update.offset_R, offset_R-nmf)
  NMF Multiplicative Update for NMF with Offset Models
• nmf_update.KL.h(nmf_update.KL, nmf_update.KL.h_R, nmf_update.KL.w, nmf_update.KL.w_R)
  NMF Multiplicative Updates for Kullback-Leibler Divergence
• nmf_update.lee_R(Frobenius-nmf, lee-nmf, lee_R-nmf, nmfAlgorithm.Frobenius, nmfAlgorithm.lee, nmfAlgorithm.lee_R, nmf_update.lee)
  NMF Algorithm/Updates for Frobenius Norm
• nmf_update.lsnmf(lsNMF-nmf, nmfAlgorithm.lsNMF, wrss)
  Multiplicative Updates for LS-NMF
• nmf_update.ns(nmfAlgorithm.nsNMF, nmfAlgorithm.nsNMF_R, nmf_update.ns_R, nsNMF_R-nmf)
  NMF Multiplicative Update for Nonsmooth Nonnegative Matrix Factorization (nsNMF).
• nneg(nneg,matrix-method, nneg-methods, nneg,NMF-method, posneg, rposneg, rposneg,matrix-method, rposneg-methods, rposneg,NMF-method)
  Transforming from Mixed-sign to Nonnegative Data
• objective,NMFfit-method
  Returns the objective function associated with the algorithm that computed the
• offset,NMFfit-method
  Returns the offset from the fitted model.
• offset,NMFOffset-method
  Offsets in NMF Models with Offset
• options-NMF(nmf.getOption, nmf.options, nmf.printOptions, nmf.resetOptions)
  NMF Package Specific Options
• parallel-NMF(gVariable, hostfile, ts_eval, ts_tempfile)
  Utilities for Parallel Computations
• plot,NMFfit,missing-method
  Plots the residual track computed at regular interval during the fit of
• predict(predict-methods, predict,NMFfitX-method, predict,NMF-method)
  Clustering and Prediction
• profplot(profplot.default)
  Plotting Expression Profiles
• purity(entropy, entropy,ANY,ANY-method, entropy,factor,ANY-method, entropy-methods, entropy,NMFfitXn,ANY-method, entropy,table,missing-method, purity,ANY,ANY-method, purity,factor,ANY-method, purity-methods, purity,NMFfitXn,ANY-method, purity,table,missing-method)
  Purity and Entropy of a Clustering
• randomize
  Randomizing Data
• residuals(hasTrack, residuals<-, residuals<--methods, residuals-methods, residuals<-,NMFfit-method, residuals,NMFfit-method, residuals,NMFfitX-method, trackError)
  Residuals in NMF Models
• rmatrix(rmatrix,ANY-method, rmatrix-methods, rmatrix,NMF-method, rmatrix,numeric-method)
  Generating Random Matrices
• rnmf(rnmf,ANY,data.frame-method, rnmf,ANY,matrix-method, rnmf,formula,ANY-method, rnmf-methods, rnmf,missing,missing-method, rnmf,NMF,missing-method, rnmf,NMF,numeric-method, rnmf,NMFOffset,numeric-method, rnmf,numeric,missing-method, rnmf,numeric,numeric-method)
  Generating Random NMF Models
• rss(evar, evar,ANY-method, evar-methods, rss,ANY-method, rss,matrix-method, rss-methods)
  Residual Sum of Squares and Explained Variance
• runtime.all,NMFfitXn-method
  Returns the CPU time used to perform all the NMF fits stored in
• runtime,NMFList-method
  Returns the CPU time required to compute all NMF fits in the list.
• scale.NMF
  Rescaling NMF Models
• seed(seed,ANY,ANY,character-method, seed,ANY,ANY,function-method, seed,ANY,ANY,missing-method, seed,ANY,ANY,NULL-method, seed,ANY,ANY,numeric-method, seed,ANY,list,NMFSeed-method, seed,ANY,numeric,NMFSeed-method, seed,matrix,NMF,NMFSeed-method, seed-methods)
  Interface for NMF Seeding Methods
• setNMFMethod(nmfRegisterAlgorithm)
  Registering NMF Algorithms
• setupBackend(setupLibPaths, setupRNG, setupSharedMemory, setupTempDirectory)
  Computational Setup Functions
• show,NMFfit-method
  Show method for objects of class
• show,NMFfitX1-method
  Show method for objects of class
• show,NMFfitX-method
  Show method for objects of class
• show,NMFfitXn-method
  Show method for objects of class
• show,NMFList-method
  Show method for objects of class
• show,NMF-method
  Show method for objects of class
• show,NMFns-method
  Show method for objects of class
• show,NMFOffset-method
  Show method for objects of class
• show,NMFSeed-method
  Show method for objects of class
• show,NMFStrategyIterative-method
  Show method for objects of class
• silhouette.NMF
  Silhouette of NMF Clustering
• smoothing
  Smoothing Matrix in Nonsmooth NMF Models
• sparseness(sparseness,matrix-method, sparseness-methods, sparseness,NMF-method, sparseness,numeric-method)
  Sparseness
• staticVar
  Get/Set a Static Variable in NMF Algorithms
• summary(summary-methods, summary-NMF, summary,NMFfit-method, summary,NMFfitX-method, summary,NMF-method)
  Assessing and Comparing NMF Models
• syntheticNMF
  Simulating Datasets
• t.NMF
  Transformation NMF Model Objects
• utils-NMF(str_args)
  Utility Function in the NMF Package