Logistic PCA

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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.

logisticPCA projection


To install R, visit r-project.org/.

The package can be installed by downloading from CRAN.


To install the development version, first install devtools from CRAN. Then run the following commands.

# install.packages("devtools")


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.


Each of the classes has associated methods to make data analysis easier.

In addition, there are functions for performing cross validation.