DMMD_i: Main function of iterative DMMD algorithm

In justicesuker/DMMD_Package: Double Matched Matrix Decomposition

Main function of iterative DMMD algorithm

Description

Main function of iterative DMMD algorithm

Usage

DMMD_i(
  X1,
  X2,
  r1 = NULL,
  r2 = NULL,
  rc = NULL,
  rr = NULL,
  angle_threshold = 90 * pi/180,
  variance1 = c("equal", "unequal"),
  variance2 = c("equal", "unequal"),
  method = c("PL", "ED"),
  tol = .Machine$double.eps^0.5,
  maxiter = 1000,
  verbose = FALSE
)

Arguments

X1	The first noisy data matrix
X2	The second noisy data matrix
r1	Total rank for X1. Default is NULL, meaning unknown, which will be estimated by rank estimation procedure determined by 'method'
r2	Total rank for X2. Default is NULL, meaning unknown, which will be estimated by rank estimation procedure determined by 'method'
rc	Joint column rank. Default is NULL, meaning unknown, which will be estimated by profile likelihood method
rr	Joint row rank. Default is NULL, meaning unknown, which will be estimated by profile likelihood method
angle_threshold	The threshold angle for principal angles. Principal angles greater than the threshold are not considered as joint signal. Default is 90 degree
variance1	Either "equal" or "unequal". Default is "equal". This argument is the variance assumption used in the profile likelihood method for determining the total rank
variance2	Either "equal" or "unequal". Default is "equal". This argument is the variance assumption used in the profile likelihood method for determining the joint rank
method	The method used for determining the total ranks r1 and r2. Either "PL" (profile likelihood) or "ED" (edge distribution). Default is "PL"
tol	The tolerance used to determine convergence. Default is the square root of the machine precision
maxiter	Maximum number of iterations allowed in the iterative algorithm. Default is 1000
verbose	Do you want to see the calculating progress of the function? Default is FALSE, which means the function stays silent.

Details

This function decomposed double-matched matrices according to Lemma 1 in Dongbang Yuan & Irina Gaynanova (2022) Double-Matched Matrix Decomposition for Multi-View Data, Journal of Computational and Graphical Statistics, DOI: 10.1080/10618600.2022.2067860. This function also updates the joint structures M and N compared to DMMD function.

Value

A list with the following elements:

r1	The estimated total rank for X1, if not specified
r2	The estimated total rank for X2, if not specified
rc	The estimated joint column rank for X1, if not specified
rr	The estimated joint row rank for X1, if not specified
A1	The estimated low-rank signal matrix of X1
A2	The estimated low-rank signal matrix of X2
E1	The noise matrix of X1, X_1 = A_1 + E_1
E2	The noise matrix of X2, X_2 = A_2 + E_2
Jc1	The estimated low-rank joint column signal for X1
Jc2	The estimated low-rank joint column signal for X2
Jr1	The estimated low-rank joint row signal for X1
Jr2	The estimated low-rank joint row signal for X2
Ic1	The estimated low-rank individual column signal for X1
Ic2	The estimated low-rank individual column signal for X2
Ir1	The estimated low-rank individual row signal for X1
Ir2	The estimated low-rank individual row signal for X2
obj_vec	A vector of objective values calculated at each iteration

Examples

data = DoubleDataGen(n = 20, p = 16, rank = c(4, 3), rc = 2, rr = 1, nrep = 1)
X1 = data$X1[[1]]
X2 = data$X2[[1]]
result = DMMD_i(X1,X2, verbose = TRUE)

justicesuker/DMMD_Package documentation built on Aug. 6, 2022, 12:34 p.m.