nnTensor (version 1.0.4)

NMF: Non-negative Matrix Factorization Algorithms (NMF)

Description

The input data is assumed to be non-negative matrix. NMF decompose the matrix to two low-dimensional factor matices. This function is also used as initialization step of tensor decomposition (see also NTF and NTD).

Usage

NMF(X, J = 3, rank.method=c("all", "ccc", "dispersion", "rss",
  "evar", "residuals", "sparseness.basis", "sparseness.coef",
  "sparseness2.basis",  "sparseness2.coef",  "norm.info.gain.basis",
  "norm.info.gain.coef",  "singular",  "volume",  "condition"),
  runtime=30, algorithm = "KL", Alpha = 1, Beta = 2, eta = 1e-04, thr1 = 1e-10,
  thr2 = 1e-10, tol = 1e-04, num.iter = 100, viz = FALSE, figdir = NULL,
  verbose = FALSE)

Arguments

X

The input Matrix which has N-rows and M-columns.

J

The number of low-dimension (J < N, M). If a numerical vector is specified (e.g. 2:6), the appropriate rank is estimated.

rank.method

The rank estimation method (Default: "all"). Only if the J option is specified as a numerical vector longer than two, this option will be active.

runtime

The number of trials to estimate rank (Default: 10).

algorithm

NMF algorithms. "Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "HALS", "PGD", "Alpha", "Beta", and "GCD" are available (Default: "KL").

Alpha

The parameter of Alpha-divergence.

Beta

The parameter of Beta-divergence.

eta

The stepsize for PGD algorithm (Default: 0.0001).

thr1

When error change rate is lower than thr1, the iteration is terminated (Default: 1E-10).

thr2

If the minus-value is generated, replaced as thr2 (Default: 1E-10). This value is used within the internal function .positive().

tol

The tolerance parameter used in GCD algorithm.

num.iter

The number of interation step (Default: 100).

viz

If viz == TRUE, internal reconstructed matrix can be visualized.

figdir

the directory for saving the figure, when viz == TRUE.

verbose

If verbose == TRUE, Error change rate is generated in console windos.

Value

U : A matrix which has N-rows and J-columns (J < N, M). V : A matrix which has M-rows and J-columns (J < N, M). J : The number of dimension (J < N, M). RecError : The reconstruction error between data tensor and reconstructed tensor from U and V. RelChange : The relative change of the error. Trial : All the results of the trials to estimate the rank. Runtime : The number of the trials to estimate the rank. RankMethod : The rank estimation method.

References

Andrzej CICHOCK, et. al., (2009). Nonnegative Matrix and Tensor Factorizations. John Wiley & Sons, Ltd

Keigo Kimura, (2017). A Study on Efficient Algorithms for Nonnegative Matrix/Tensor Factorization. Hokkaido University Collection of Scholarly and Academic Papers

Examples

# NOT RUN {
  if(interactive()){
    # Test data
    matdata <- toyModel(model = "NMF")

    # Simple usage
    out <- NMF(matdata, J=5)

    # Rank estimation mode (single method)
    out2 <- NMF(matdata, J=2:10, rank.method="ccc", runtime=3)
    plot(out2)

    # Rank estimation mode (all method)
    out3 <- NMF(matdata, J=2:10, rank.method="all", runtime=10)
    plot(out3)
  }
# }