lambda0 {softImpute}

compute the smallest value for lambda such that softImpute(x,lambda) returns the zero solution.

Description

this determines the "starting" lambda for a sequence of values for softImpute, and all nonzero solutions would require a smaller value for lambda.

Usage

lambda0(x, lambda = 0, maxit = 100, trace.it = FALSE, thresh = 1e-05)

Arguments

x

An m by n matrix. Large matrices can be in "sparseMatrix" format, as well as "SparseplusLowRank". The latter arise after centering sparse matrices, for example with biScale, as well as in applications such as softImpute.

The remaining arguments only apply to matrices x in "sparseMatrix", "Incomplete", or "SparseplusLowRank" format.

lambda

As in svd.als, using a value for lambda can speed up iterations. As long as the solution is not zero, the value returned adds back this value.

maxit

maximum number of iterations.

trace.it

with trace.it=TRUE, convergence progress is reported.

thresh

convergence threshold, measured as the relative changed in the Frobenius norm between two successive estimates.

Details

It is the largest singular value for the matrix, with zeros replacing missing values. It uses svd.als with rank=2.

Value

a single number, the largest singular value

Author(s)

Trevor Hastie, Rahul Mazumder
Maintainer: Trevor Hastie [e-mail]

References

Rahul Mazumder, Trevor Hastie and Rob Tibshirani (2010) Spectral Regularization Algorithms for Learning Large Incomplete Matrices, https://web.stanford.edu/~hastie/Papers/mazumder10a.pdf
Journal of Machine Learning Research 11 (2010) 2287-2322

See Also

softImpute,Incomplete, and svd.als.

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
ix=seq(np)
imiss=sample(ix,np*missfrac,replace=FALSE)
xna=x
xna[imiss]=NA
lambda0(xna)