Semi-Parametric Factor Analysis via Vintage Sparse PCA

This code implements TODO.

Usage

vsp(x, rank, ...)

# Default S3 method
vsp(x, rank, ...)

# S3 method for class 'matrix'
vsp(
  x,
  rank,
  ...,
  center = FALSE,
  recenter = FALSE,
  degree_normalize = TRUE,
  renormalize = FALSE,
  tau_row = NULL,
  tau_col = NULL,
  kaiser_normalize_u = FALSE,
  kaiser_normalize_v = FALSE,
  rownames = NULL,
  colnames = NULL,
  match_columns = TRUE
)

# S3 method for class 'Matrix'
vsp(
  x,
  rank,
  ...,
  center = FALSE,
  recenter = FALSE,
  degree_normalize = TRUE,
  renormalize = FALSE,
  tau_row = NULL,
  tau_col = NULL,
  kaiser_normalize_u = FALSE,
  kaiser_normalize_v = FALSE,
  rownames = NULL,
  colnames = NULL,
  match_columns = TRUE
)

# S3 method for class 'dgCMatrix'
vsp(
  x,
  rank,
  ...,
  center = FALSE,
  recenter = FALSE,
  degree_normalize = TRUE,
  renormalize = FALSE,
  tau_row = NULL,
  tau_col = NULL,
  kaiser_normalize_u = FALSE,
  kaiser_normalize_v = FALSE,
  rownames = NULL,
  colnames = NULL,
  match_columns = TRUE
)

# S3 method for class 'igraph'
vsp(x, rank, ..., edge_weights = NULL)

Arguments

x: Either a graph adjacency matrix, igraph::igraph or tidygraph::tbl_graph. If x is a matrix or Matrix::Matrix then x[i, j] should correspond to the edge going from node i to node j.
rank: The number of factors to calculate.
...: These dots are for future extensions and must be empty.
center: Should the adjacency matrix be row and column centered? Defaults to FALSE.
recenter: Should the varimax factors be re-centered around the original factor means? Only used when center = TRUE, defaults to FALSE.
degree_normalize: Should the regularized graph laplacian be used instead of the raw adjacency matrix? Defaults to TRUE. If center = TRUE, A will first be centered and then normalized.
renormalize: Should the regularized graph laplacian be used instead of the raw adjacency matrix? Defaults to TRUE. If center = TRUE, A will first be centered and then normalized.
tau_row: Row regularization term. Default is NULL, in which case we use the row degree. Ignored when degree_normalize = FALSE.
tau_col: Column regularization term. Default is NULL, in which case we use the column degree. Ignored when degree_normalize = FALSE.
kaiser_normalize_u: Whether or not to use Kaiser normalization when rotating the left singular vectors U. Defaults to FALSE.
kaiser_normalize_v: Whether or not to use Kaiser normalization when rotating the right singular vectors V. Defaults to FALSE.
rownames: Character vector of row names of x. These row names are propagated into the row names of the U and Z. Defaults to NULL.
colnames: Character vector of column names of x. These column names are propagated into the row names of the V and Y. Defaults to NULL.
match_columns: Should the columns of Y be re-ordered such that Y[, i] corresponds to Z[, i] to the extent possible? Defaults to TRUE. Typically helps with interpretation, and often makes B more diagonally dominant.
edge_weights: When x is an igraph::igraph, an edge attribute to use to form a weighted adjacency matrix.

Value

An object of class vsp. TODO: Details

Details

Sparse SVDs use RSpectra for performance.

Examples


library(LRMF3)
#> Loading required package: Matrix

vsp(ml100k, rank = 2)
#> Vintage Sparse PCA Factor Analysis
#> 
#> Rows (n):   943
#> Cols (d):   1682
#> Factors (rank): 2
#> Lambda[rank]:   0.2994
#> Components
#> 
#> Z: 943 x 2 [matrix] 
#> B: 2 x 2 [matrix] 
#> Y: 1682 x 2 [matrix] 
#> u: 943 x 2 [matrix] 
#> d: 2      [numeric] 
#> v: 1682 x 2 [matrix] 
#>