Type: Package
Title: Projected Refinement for Imputation of Missing Entries in PCA
Version: 1.2
Date: 2021-8-5
Author: Ziwei Zhu, Tengyao Wang, Richard J. Samworth
Maintainer: Ziwei Zhu <ziweiz@umich.edu>
Description: Implements the primePCA algorithm, developed and analysed in Zhu, Z., Wang, T. and Samworth, R. J. (2019) High-dimensional principal component analysis with heterogeneous missingness. <doi:10.48550/arXiv.1906.12125>.
Imports: softImpute, Matrix, MASS, methods
RoxygenNote: 7.1.1
License: GPL-3
NeedsCompilation: no
Packaged: 2021-08-05 13:57:37 UTC; ziweizhu
Repository: CRAN
Date/Publication: 2021-08-05 15:10:02 UTC

Center and/or normalize each column of a matrix

Description

Center and/or normalize each column of a matrix

Usage

col_scale(X, center = T, normalize = F)

Arguments

X

a numeric matrix with NAs or "Incomplete" matrix object (see softImpute package)

center

center each column of X if center == TRUE. The default value is TRUE.

normalize

normalize each column of X such that its sample variance is 1 if normalize == TRUE. The default value is False.

Value

a centered and/or normalized matrix of the same dimension as X.

Inverse probability weighted method for estimating the top K eigenspaces

Description

Inverse probability weighted method for estimating the top K eigenspaces

Usage

inverse_prob_method(X, K, trace.it = F, center = T, normalize = F)

Arguments

X

a numeric matrix with NAs or "Incomplete" matrix object (see softImpute package)

K

the number of principal components of interest

trace.it

report the progress if trace.it == TRUE

center

center each column of X if center == TRUE. The default value is TRUE.

normalize

normalize each column of X such that its sample variance is 1 if normalize == TRUE. The default value is False.

Value

Columnwise centered matrix of the same dimension as X.

Examples

X <- matrix(1:30 + .1 * rnorm(30), 10, 3)
X[1, 1] <- NA
X[2, 3] <- NA
v_hat <- inverse_prob_method(X, 1)

primePCA algorithm

Description

primePCA algorithm

Usage

primePCA(
  X,
  K,
  V_init = NULL,
  thresh_sigma = 10,
  max_iter = 1000,
  thresh_convergence = 1e-05,
  thresh_als = 1e-10,
  trace.it = F,
  prob = 1,
  save_file = "",
  center = T,
  normalize = F
)

Arguments

X

an n-by-d data matrix with NA values

K

the number of the principal components of interest

V_init

an initial estimate of the top K eigenspaces of the covariance matrix of X. By default, primePCA will be initialized by the inverse probability method.

thresh_sigma

used to select the "good" rows of X to update the principal eigenspaces \sigma_* in the paper).

max_iter

maximum number of iterations of refinement

thresh_convergence

The algorithm is halted if the Frobenius-norm sine-theta distance between the two consecutive iterates

thresh_als

This is fed into thresh in svd.als of softImpute. is less than thresh_convergence.

trace.it

report the progress if trace.it = TRUE

prob

probability of reserving the "good" rows. prob == 1 means to reserve all the "good" rows.

save_file

the location that saves the intermediate results, including V_cur, step_cur and loss_all, which are introduced in the section of returned values. The algorithm will not save any intermediate result if save_file == "".

center

center each column of X if center == TRUE. The default value is TRUE.

normalize

normalize each column of X such that its sample variance is 1 if normalize == TRUE. The default value is False.

Value

a list is returned, with components V_cur, step_cur and loss_all. V_cur is a d-by-K matrix of the top K eigenvectors. step_cur is the number of iterations. loss_all is an array of the trajectory of MSE.

Examples

X <- matrix(1:30 + .1 * rnorm(30), 10, 3)
X[1, 1] <- NA
X[2, 3] <- NA
v_tilde <- primePCA(X, 1)$V_cur

Frobenius norm sin theta distance between two column spaces

Description

Frobenius norm sin theta distance between two column spaces

Usage

sin_theta_distance(V1, V2)

Arguments

V1

a matrix with orthonormal columns

V2

a matrix of the same dimension as V1 with orthonormal columns

Value

the Frobenius norm sin theta distance between two V1 and V2