logisticPCA is an R package for dimensionality reduction
of binary data. Please note that it is still in the very early stages of
development and the conventions will possibly change in the future. A
manuscript describing logistic PCA can be found here.
To install R, visit r-project.org/.
The package can be installed by downloading from CRAN.
install.packages("logisticPCA")To install the development version, first install
devtools from CRAN. Then run the following commands.
# install.packages("devtools")
library("devtools")
install_github("andland/logisticPCA")Three types of dimensionality reduction are given. For all the
functions, the user must supply the desired dimension k.
The data must be an n x d matrix comprised of binary
variables (i.e. all 0’s and 1’s).
logisticPCA() estimates the natural parameters of a
Bernoulli distribution in a lower dimensional space. This is done by
projecting the natural parameters from the saturated model. A
rank-k projection matrix, or equivalently a
d x k orthogonal matrix U, is solved for to
minimize the Bernoulli deviance. Since the natural parameters from the
saturated model are either negative or positive infinity, an additional
tuning parameter m is needed to approximate them. You can
use cv.lpca() to select m by cross validation.
Typical values are in the range of 3 to
10.
mu is a main effects vector of length d and
U is the d x k loadings matrix.
logisticSVD() estimates the natural parameters by a
matrix factorization. mu is a main effects vector of length
d, B is the d x k loadings
matrix, and A is the n x k principal component
score matrix.
convexLogisticPCA() relaxes the problem of solving for a
projection matrix to solving for a matrix in the
k-dimensional Fantope, which is the convex hull of
rank-k projection matrices. This has the advantage that the
global minimum can be obtained efficiently. The disadvantage is that the
k-dimensional Fantope solution may have a rank much larger
than k, which reduces interpretability. It is also
necessary to specify m in this function.
mu is a main effects vector of length d,
H is the d x d Fantope matrix, and
U is the d x k loadings matrix, which are the
first k eigenvectors of H.
Each of the classes has associated methods to make data analysis easier.
print(): Prints a summary of the fitted model.fitted(): Fits the low dimensional matrix of either
natural parameters or probabilities.predict(): Predicts the PCs on new data. Can also
predict the low dimensional matrix of natural parameters or
probabilities on new data.plot(): Either plots the deviance trace, the first two
PC loadings, or the first two PC scores using the package
ggplot2.In addition, there are functions for performing cross validation.
cv.lpca(), cv.lsvd(),
cv.clpca(): Run cross validation over the rows of the
matrix to assess the fit of m and/or k.plot.cv(): Plots the results of the cv()
method.