logisticPCA (version 0.2)

logisticPCA: Logistic Principal Component Analysis

Description

Dimensionality reduction for binary data by extending Pearson's PCA formulation to minimize Binomial deviance

Usage

logisticPCA(x, k = 2, m = 4, quiet = TRUE, partial_decomp = FALSE, max_iters = 1000, conv_criteria = 1e-05, random_start = FALSE, start_U, start_mu, main_effects = TRUE, validation, M, use_irlba)

Arguments

x

matrix with all binary entries

k

number of principal components to return

m

value to approximate the saturated model. If m = 0, m is solved for

quiet

logical; whether the calculation should give feedback

partial_decomp

logical; if TRUE, the function uses the rARPACK package to more quickly calculate the eigen-decomposition. This is usually faster than standard eigen-decomponsition when ncol(x) > 100 and k is small

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, function will use an eigen-decomposition as starting value

start_U

starting value for the orthogonal matrix

start_mu

starting value for mu. Only used if main_effects = TRUE

main_effects

logical; whether to include main effects in the model

validation

optional validation matrix. If supplied and m = 0, the validation data is used to solve for m

M

depricated. Use m instead

use_irlba

depricated. Use partial_decomp instead

Value

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

mu

the main effects

U

a k-dimentional orthonormal matrix with the loadings

PCs

the princial component scores

m

the parameter inputed or solved for

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.

References

Landgraf, A.J. & Lee, Y., 2015. Dimensionality reduction for binary data through the projection of natural parameters. arXiv preprint arXiv:1510.06112.

Examples

# 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 PCA on it
lpca = logisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

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