Projection Pursuit with Applications to scRNA Sequencing Data

TL;DR

This paper examines the limitations of PCA and explores projection pursuit, applying it to single-cell RNA sequencing data to improve linear dimension reduction techniques.

Contribution

It introduces the use of negative standardized Shannon's entropy as a projection index in projection pursuit and applies it to scRNA sequencing data.

Findings

PP can overcome PCA limitations in certain data structures

Shannon's entropy effectively identifies informative projections

Application to scRNA data demonstrates practical utility

Abstract

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. We first discuss the relevant concepts and theorems and then apply PCA and PP (with negative standardized Shannon's entropy as the projection index) on single cell RNA sequencing data.