Projection pursuit with applications to scRNA sequencing data

In this paper, we explore the limitations of PCA as a dimension reduction technique and study its extension, projection pursuit (PP), which is a broad class of linear dimension reduction methods. PCA is a popular dimension reduction technique commonly applied to scRNA sequencing data. Despite of huge success in practice, we will illustrate three drawbacks of PCA. It is well known that the eigenvalues of sample covariance matrix is not consistent in high dimensional cases. Every principal component is uncorrelated with each other but not independent.