softImpute.x.matrix: Internal softImpute functions

In softImpute: Matrix Completion via Iterative Soft-Thresholded SVD

Internal softImpute functions

Description

These functions are not intended to be called directly, but they can be useful for understanding the structure of the models used. rdname softImpute-internal

Usage

softImpute.x.matrix(
  x,
  J,
  lambda,
  type,
  thresh,
  maxit,
  trace.it,
  warm.start,
  final.svd
)

Arguments

x	An m by n matrix with NAs. For large matrices can be of class "Incomplete", in which case the missing values are represented as pseudo zeros leading to dramatic storage reduction. x can have been centered and scaled via biScale, and this information is carried along with the solution.
J	Trevor to document this param
lambda	nuclear-norm regularization parameter. If lambda=0, the algorithm reverts to "hardImpute", for which convergence is typically slower, and to local minimum. Ideally lambda should be chosen so that the solution reached has rank slightly less than rank.max. See also lambda0() for computing the smallest lambda with a zero solution.
type	two algorithms are implements, type="svd" or the default type="als". The "svd" algorithm repeatedly computes the svd of the completed matrix, and soft thresholds its singular values. Each new soft-thresholded svd is used to re-impute the missing entries. For large matrices of class "Incomplete", the svd is achieved by an efficient form of alternating orthogonal ridge regression. The "als" algorithm uses this same alternating ridge regression, but updates the imputation at each step, leading to quite substantial speedups in some cases. The "als" approach does not currently have the same theoretical convergence guarantees as the "svd" approach.
thresh	convergence threshold, measured as the relative change in the Frobenius norm between two successive estimates.
maxit	maximum number of iterations.
trace.it	with trace.it=TRUE, convergence progress is reported.
warm.start	an svd object can be supplied as a warm start. This is particularly useful when constructing a path of solutions with decreasing values of lambda and increasing rank.max. The previous solution can be provided directly as a warm start for the next.
final.svd	only applicable to type="als". The alternating ridge-regressions do not lead to exact zeros. With the default final.svd=TRUE, at the final iteration, a one step unregularized iteration is performed, followed by soft-thresholding of the singular values, leading to hard zeros.

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