generalizedPCA: Generalized Principal Component Analysis

In andland/generalizedPCA: Generalized PCA

Description

Dimension reduction for exponential family data by extending Pearson's PCA formulation

Usage

generalizedPCA(x, k = 2, M = 4, family = c("gaussian", "binomial",
  "poisson", "multinomial"), weights, quiet = TRUE, majorizer = c("row",
  "all"), partial_decomp = FALSE, max_iters = 1000, conv_criteria = 1e-05,
  random_start = FALSE, start_U, start_mu, main_effects = TRUE,
  normalize = FALSE, validation, val_weights)

Arguments

x	matrix of either binary, proportions, count, or continuous data
k	number of principal components to return
M	value to approximate the saturated model
family	exponential family distribution of data
weights	an optional matrix of the same size as the x with data weights
quiet	logical; whether the calculation should give feedback
majorizer	how to majorize the deviance. "row" gives tighter majorization, but may take longer to calculate each iteration. "all" may be faster per iteration, but take more iterations
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
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
normalize	logical; whether to weight the variables to they all have equal influence
validation	a validation dataset to select m with
val_weights	weights associated with validation data

Value

An S3 object of class gpca 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
family	the exponential family used
iters	number of iterations required for convergence
loss_trace	the trace of the average deviance 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.

Examples

# construct a low rank matrix in the natural parameter space
rows = 100
cols = 10
set.seed(1)
mat_np = outer(rnorm(rows), rnorm(cols))

# generate a count matrix
mat = matrix(rpois(rows * cols, c(exp(mat_np))), rows, cols)

# run Poisson PCA on it
gpca = generalizedPCA(mat, k = 1, M = 4, family = "poisson")

andland/generalizedPCA documentation built on May 12, 2019, 2:42 a.m.