Results: In this article, we introduce the motivation and rationale of some parametric and nonparametric versions of PCA specifically geared for binary data. Although there are several PCA alternatives for binary data in the psychometric, data analysis and machine learning literature, they are not well known to the bioinformatics community. The special mathematical characteristics of binary data make the direct use of the classical principal component analysis (PCA) model to explore low-dimensional structures less obvious. Genome-wide measurements of genetic and epigenetic alterations are generating more and more high-dimensional binary data.