nmf_update_euclidean: NMF Multiplicative Updates for Euclidean Distance
In renozao/NMF: Algorithms and Framework for Nonnegative Matrix Factorization (NMF)

Description Usage Arguments Details Value Author(s) References

Multiplicative updates from Lee and Seung (2001) for standard Nonnegative Matrix Factorization models V \approx W H, where the distance between the target matrix and its NMF estimate is measured by the – euclidean – Frobenius norm.

nmf_update.euclidean.h(
  v,
  w,
  h,
  eps = 10^-9,
  nbterms = 0L,
  ncterms = 0L,
  copy = TRUE
)

nmf_update.euclidean.h_R(v, w, h, wh = NULL, eps = 10^-9)

nmf_update.euclidean.w(
  v,
  w,
  h,
  eps = 10^-9,
  nbterms = 0L,
  ncterms = 0L,
  weight = NULL,
  copy = TRUE
)

nmf_update.euclidean.w_R(v, w, h, wh = NULL, eps = 10^-9)

`v`	target matrix
`w`	current basis matrix
`h`	current coefficient matrix
`eps`	small numeric value used to ensure numeric stability, by shifting up entries from zero to this fixed value.
`nbterms`	number of fixed basis terms
`ncterms`	number of fixed coefficient terms
`copy`	logical that indicates if the update should be made on the original matrix directly (`FALSE`) or on a copy (`TRUE` - default). With `copy=FALSE` the memory footprint is very small, and some speed-up may be achieved in the case of big matrices. However, greater care should be taken due the side effect. We recommend that only experienced users use `copy=TRUE`.
`wh`	already computed NMF estimate used to compute the denominator term.
`weight`	numeric vector of sample weights, e.g., used to normalise samples coming from multiple datasets. It must be of the same length as the number of samples/columns in `v` – and `h`.

nmf_update.euclidean.w and nmf_update.euclidean.h compute the updated basis and coefficient matrices respectively. They use a C++ implementation which is optimised for speed and memory usage.

The coefficient matrix (H) is updated as follows:

H_kj <- max(H_kj (W^T V)_kj, eps) / ( (W^T W H)_kj + eps )

These updates are used by the built-in NMF algorithms Frobenius and lee.

The basis matrix (W) is updated as follows:

W_ik <- max(W_ik (V H^T)_ik, eps) / ( (W H H^T)_ik + eps )

a matrix of the same dimension as the input matrix to update (i.e. w or h). If copy=FALSE, the returned matrix uses the same memory as the input object.

Update definitions by Lee2001.

C++ optimised implementation by Renaud Gaujoux.

Lee DD, Seung H (2001). “Algorithms for non-negative matrix factorization.” _Advances in neural information processing systems_. <URL: http://scholar.google.com/scholar?q=intitle:Algorithms+for+non-negative+matrix+factorization\#0>.

renozao/NMF documentation built on June 14, 2020, 9:35 p.m.