mmpca {mmpca}

Multiview principal component analysis

Description

Analyzes several related matrices of data.

Usage

mmpca(
  x,
  inds,
  k,
  lambda = NULL,
  trace = 0,
  max_iter = 20000,
  init_theta = NULL,
  cachepath = NULL,
  enable_rank_selection = TRUE,
  enable_sparsity = TRUE,
  enable_variable_selection = FALSE,
  parallel = TRUE
)

Arguments

x

List of matrices to analyze

inds

Matrix containing view indices. The matrix should have two columns and the same number of rows as the length of x. The first (second) column contains the view index of the rows (columns) of the corresponding matrix.

k

Integer giving the maximum rank of the analysis, i.e. the maximum number of principal components for each view.

lambda

Vector or matrix of lambda values. The length (or width if it is a matrix) depends on the number of active penalties (2, 3 or 4). If it is a matrix, try different lambda values (one try for each row). Default: a matrix where each column is the sequence exp(seq(-6, 0))).

trace

Integer selecting the amount of log messages. 0 (default): no output, 3: all output.

max_iter

Maximum number of iterations

init_theta

NULL, functions or numeric. NULL (default) use initial values based on ordinary SVD. If init_theta is a list of three functions (CMF, matrix_to_triplets and getCMFopts from package CMF) use the supplied functions to find initial values with collaborative matrix factorization (CMF). If init_theta is a numeric vector it is used as initial value.

cachepath

Character vector with path to directory to store intermediate results. If NULL (default) intermediate results are not stored. For caching to work it is required that the random number generation seed is constant between calls to mmpca, so set.seed needs to be called before mmpca.

enable_rank_selection

Boolean deciding if the second penalty that imposes a low rank model should be enabled.

enable_sparsity

Boolean deciding if the third penalty that imposes sparsity in V should be enabled.

enable_variable_selection

Boolean deciding if the fourth penalty that increases the tendency for sparsity structure of different V columns to be similar. Defaults to FALSE meaning this penalty is not used.

parallel

Boolean deciding if computations should be run on multiple cores simultaneously.

Value

A list with components

initial

initial values used in optimization

cmf

solution found with CMF (if init_theta == c(CMF, matrix_to_triplets, getCMFopts))

training

solutions for different values of lambda

solution

solution for optimal lambda value

Author(s)

Jonatan Kallus, [e-mail]

Examples

# Create model with three views, two data matrices of low-rank 3
max_rank <- 3
v <- list(
  qr.Q(qr(matrix(rnorm(10 * max_rank), 10, max_rank))),
  qr.Q(qr(matrix(rnorm(11 * max_rank), 11, max_rank))),
  qr.Q(qr(matrix(rnorm(12 * max_rank), 12, max_rank)))
)
d <- matrix(
  c(1, 1, 1, 1, 1, 0, 1, 0, 1),
  nrow = max_rank, ncol = 3
)
x <- list(
  v[[1]] %*% diag(d[, 1] * d[, 2]) %*% t(v[[2]]),
  v[[1]] %*% diag(d[, 1] * d[, 3]) %*% t(v[[3]])
)
inds <- matrix(c(1, 1, 2, 3), 2, 2)
result <- mmpca::mmpca(
  x, inds, max_rank, parallel = FALSE,
  lambda = c(1e-3, 1e-5), enable_sparsity = FALSE,
  trace = 3
)
# Investigate the solution
result$solution$D