AdaptiveInitialize

An implementation of the AdaptiveInitialize algorithm for matrix imputation for sparse matrices. At the moment the implementation is only suitable for small matrices with on the order of thousands of rows and columns at most.

Usage

adaptive_initialize(
  X,
  rank,
  ...,
  p_hat = NULL,
  alpha_method = c("exact", "approximate"),
  additional = NULL
)

# S3 method for class 'sparseMatrix'
adaptive_initialize(
  X,
  rank,
  ...,
  p_hat = NULL,
  alpha_method = c("exact", "approximate"),
  additional = NULL
)

Arguments

X

A sparse matrix of sparseMatrix class. Explicit (observed) zeroes in X can be dropped for

rank

Desired rank (integer) to use in the low rank approximation. Must be at least 2L and at most the rank of X.

...

Ignored.

p_hat

The portion of X that is observed. Defaults to NULL, in which case p_hat is set to the number of observed elements of X. Primarily for internal use in citation_impute() or advanced users.

alpha_method

Either "exact" or "approximate", defaulting to "exact". "exact" is computationally expensive and requires taking a complete SVD of matrix of size nrow(X) x nrow(X), and matches the AdaptiveInitialize algorithm exactly. "approximate" departs from the AdaptiveInitialization algorithm to compute a truncated SVD of rank rank + additional instead of a complete SVD. This reduces computational burden, but the resulting estimates of singular-ish values will not be penalized as much as in the AdaptiveInitialize algorithm.

additional

Ignored except when alpha_method = "approximate" in which case it controls the precise of the approximation to alpha. The approximate computation of alpha will always understand alpha, but the approximation will be better for larger values of additional. We recommend making additional as large as computationally tolerable.

Value

A low rank matrix factorization represented by an adaptive_imputation() object.

Examples

mf <- adaptive_initialize(
  ml100k,
  rank = 3,
  alpha_method = "approximate",
  additional = 2
)
#> INFO [2025-05-02 19:14:27] Beginning AdaptiveInitialize.
#> INFO [2025-05-02 19:14:27] p_hat = 0.0630466936422453, non-zero entries = 100000, total entries = 1586126
#> INFO [2025-05-02 19:14:27] Calculating nuclear norm (slow step). Using approximate method.
#> INFO [2025-05-02 19:14:27] Approximating alpha using rank 5 approximation.
#> INFO [2025-05-02 19:14:27] Computation complete, alpha = 26.8743096027455
#> INFO [2025-05-02 19:14:27] lambda_hat = 10116.1988316315, 3785.64278402791, 3359.13438021896

mf
#> 
#> Adaptively Imputed Low Rank Matrix Factorization
#> ------------------------------------------------
#> 
#> Rank: 3
#> 
#> Rows: 943
#> Cols: 1682
#> 
#> d[rank]: 3359.134
#> alpha:   26.874
#> 
#> Components
#> 
#> u: 943 x 3 [matrix] 
#> d: 3      [numeric] 
#> v: 1682 x 3 [matrix]