Logistic PCA
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.
Installation
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")
Classes
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).
Logistic PCA
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.
Logistic SVD
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.
Convex Logistic PCA
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
.
Methods
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 packageggplot2
.
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 ofm
and/ork
.plot.cv()
: Plots the results of thecv()
method.