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Bipartition a sample set

Source: R/bipartition.R
bipartition.Rd

Spectral biparitioning by rank-2 matrix factorization

Usage

bipartition(data, tol = 1e-05, nonneg = TRUE, ...)

Arguments

data

dense or sparse matrix of features in rows and samples in columns. Prefer matrix or Matrix::dgCMatrix, respectively

tol

tolerance of the fit

nonneg

enforce non-negativity of the rank-2 factorization used for bipartitioning

...

development parameters

Value

A list giving the bipartition and useful statistics:

  • v : vector giving difference between sample loadings between factors in a rank-2 factorization

  • dist : relative cosine distance of samples within a cluster to centroids of assigned vs. not-assigned cluster

  • size1 : number of samples in first cluster (positive loadings in 'v')

  • size2 : number of samples in second cluster (negative loadings in 'v')

  • samples1: indices of samples in first cluster

  • samples2: indices of samples in second cluster

  • center1 : mean feature loadings across samples in first cluster

  • center2 : mean feature loadings across samples in second cluster

Details

Spectral bipartitioning is a popular subroutine in divisive clustering. The sign of the difference between sample loadings in factors of a rank-2 matrix factorization gives a bipartition that is nearly identical to an SVD.

Rank-2 matrix factorization by alternating least squares is faster than rank-2-truncated SVD (i.e. irlba).

This function is a specialization of rank-2 nmf with support for factorization of only a subset of samples, and with additional calculations on the factorization model relevant to bipartitioning. See nmf for details regarding rank-2 factorization.

Advanced Parameters

Several parameters may be specified in the ... argument:

  • diag = TRUE: scale factors in \(w\) and \(h\) to sum to 1 by introducing a diagonal, \(d\). This should generally never be set to FALSE. Diagonalization enables symmetry of models in factorization of symmetric matrices, convex L1 regularization, and consistent factor scalings.

  • samples = 1:ncol(A): samples to include in bipartition, numbered from 1 to ncol(A). Default is all samples.

  • calc_dist = TRUE: calculate the relative cosine distance of samples within a cluster to either cluster centroid. If TRUE, centers for clusters will also be calculated.

  • seed = NULL: random seed for model initialization, generally not needed for rank-2 factorizations because robust solutions are recovered when diag = TRUE

  • maxit = 100: maximum number of alternating updates of \(w\) and \(h\). Generally, rank-2 factorizations converge quickly and this should not need to be adjusted.

References

Kuang, D, Park, H. (2013). "Fast rank-2 nonnegative matrix factorization for hierarchical document clustering." Proc. 19th ACM SIGKDD intl. conf. on Knowledge discovery and data mining.

See also

nmf, dclust

Author

Zach DeBruine

Examples

if (FALSE) {
library(Matrix)
data(iris)
A <- as(as.matrix(iris[,1:4]), "dgCMatrix")
bipartition(A, calc_dist = TRUE)
}