logisticSVD: Logistic Singular Value Decomposition
In andland/logisticPCA: Binary Dimensionality Reduction

Description Usage Arguments Value References Examples

Dimensionality reduction for binary data by extending SVD to minimize binomial deviance.

logisticSVD(
  x,
  k = 2,
  quiet = TRUE,
  max_iters = 1000,
  conv_criteria = 1e-05,
  random_start = FALSE,
  start_A,
  start_B,
  start_mu,
  partial_decomp = TRUE,
  main_effects = TRUE,
  use_irlba
)

`x`	matrix with all binary entries
`k`	rank of the SVD
`quiet`	logical; whether the calculation should give feedback
`max_iters`	number of maximum iterations
`conv_criteria`	convergence criteria. The difference between average deviance in successive iterations
`random_start`	logical; whether to randomly inititalize the parameters. If `FALSE`, algorithm will use an SVD as starting value
`start_A`	starting value for the left singular vectors
`start_B`	starting value for the right singular vectors
`start_mu`	starting value for mu. Only used if `main_effects = TRUE`
`partial_decomp`	logical; if `TRUE`, the function uses the RSpectra package to more quickly calculate the SVD. When the number of columns is small, the approximation may be less accurate and slower
`main_effects`	logical; whether to include main effects in the model
`use_irlba`	depricated. Use `partial_decomp` instead

An S3 object of class lsvd which is a list with the following components:

`mu`	the main effects
`A`	a `k`-dimentional orthogonal matrix with the scaled left singular vectors
`B`	a `k`-dimentional orthonormal matrix with the right singular vectors
`iters`	number of iterations required for convergence
`loss_trace`	the trace of the average negative log likelihood of the algorithm. Should be non-increasing
`prop_deviance_expl`	the proportion of deviance explained by this model. If `main_effects = TRUE`, the null model is just the main effects, otherwise the null model estimates 0 for all natural parameters.

de Leeuw, Jan, 2006. Principal component analysis of binary data by iterated singular value decomposition. Computational Statistics & Data Analysis 50 (1), 21–39.

Collins, M., Dasgupta, S., & Schapire, R. E., 2001. A generalization of principal components analysis to the exponential family. In NIPS, 617–624.

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic SVD on it
lsvd = logisticSVD(mat, k = 1, main_effects = FALSE, partial_decomp = FALSE)

# Logistic SVD likely does a better job finding latent features
# than standard SVD
plot(svd(mat_logit)$u[, 1], lsvd$A[, 1])
plot(svd(mat_logit)$u[, 1], svd(mat)$u[, 1])