biScale: Standardize a matrix to have optionally row means zero and...

In softImpute: Matrix Completion via Iterative Soft-Thresholded SVD

Standardize a matrix to have optionally row means zero and variances one, and/or column means zero and variances one.

Description

A function for standardizing a matrix in a symmetric fashion. Generalizes the scale function in R. Works with matrices with NAs, matrices of class "Incomplete", and matrix in "sparseMatrix" format.

Usage

biScale(
  x,
  maxit = 20,
  thresh = 1e-09,
  row.center = TRUE,
  row.scale = TRUE,
  col.center = TRUE,
  col.scale = TRUE,
  trace = FALSE
)

Arguments

x	matrix, possibly with NAs, also of class "Incomplete" or "sparseMatrix" format.
maxit	When both row and column centering/scaling is requested, iteration is may be necessary
thresh	Convergence threshold
row.center	if row.center==TRUE (the default), row centering will be performed resulting in a matrix with row means zero. If row.center is a vector, it will be used to center the rows. If row.center=FALSE nothing is done. See details for more info.
row.scale	if row.scale==TRUE, the rows are scaled (after possibly centering, to have variance one. Alternatively, if a positive vector is supplied, it is used for row centering. See details for more info.
col.center	Similar to row.center
col.scale	Similar to row.scale
trace	with trace=TRUE, convergence progress is reported, when iteration is needed.

Details

This function computes a transformation

\frac{X_{ij}-\alpha_i-\beta_j}{\gamma_i\tau_j}

to transform the matrix X. It uses an iterative algorithm based on "method-of-moments". At each step, all but one of the parameter vectors is fixed, and the remaining vector is computed to solve the required condition. Although in genereal this is not guaranteed to converge, it mostly does, and quite rapidly. When there are convergence problems, remove some of the required constraints. When any of the row/column centers or scales are provided, they are used rather than estimated in the above model.

Value

A matrix like x is returned, with attributes:

biScale:row	a list with elements "center" and "scale" (the alpha and gamma above. If no centering was done, the center component will be a vector of zeros. Likewise, of no row scaling was done, the scale component will be a vector of ones.
biScale:column	Same details as biScale:row

For matrices with missing values, the constraints apply to the non-missing entries. If x is of class "sparseMatrix", then the sparsity is maintained, and an object of class "SparseplusLowRank" is returned, such that the low-rank part does the centering.

Note

This function will be described in detail in a forthcoming paper

Author(s)

Trevor Hastie, with help from Andreas Buja and Steven Boyd
, Maintainer: Trevor Hastie [e-mail]

References

Trevor Hastie, Rahul Mazumder, Jason Lee, Reza Zadeh (2015) Matrix Completion and Low-rank SVD via Fast Alternating Least Squares, https://arxiv.org/abs/1410.2596
Journal of Machine Learning Research, 16, 3367-3402

See Also

softImpute,Incomplete,lambda0,impute,complete, and class "SparseplusLowRank"

Examples

set.seed(101)
n=200
p=100
J=50
np=n*p
missfrac=0.3
x=matrix(rnorm(n*J),n,J)%*%matrix(rnorm(J*p),J,p)+matrix(rnorm(np),n,p)/5
xc=biScale(x)
ix=seq(np)
imiss=sample(ix,np*missfrac,replace=FALSE)
xna=x
xna[imiss]=NA
xnab=biScale(xna,row.scale=FALSE,trace=TRUE)
xnaC=as(xna,"Incomplete")
xnaCb=biScale(xnaC)
nnz=trunc(np*.3)
inz=sample(seq(np),nnz,replace=FALSE)
i=row(x)[inz]
j=col(x)[inz]
x=rnorm(nnz)
xS=sparseMatrix(x=x,i=i,j=j)
xSb=biScale(xS)
class(xSb)

softImpute documentation built on June 10, 2025, 9:10 a.m.