# biScale: 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

 1 2 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}-α_i-β_j}{γ_iτ_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 hastie@stanford.edu

softImpute,Incomplete,lambda0,impute,complete, and class "SparseplusLowRank"
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 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)