Archetypal analysis for single-cell RNA sequencing data

This thesis explores the application of archetypal analysis (AA) as a tool to analyze single-cell RNA sequencing (scRNAseq) dataset, with the objective of assessing its validity and effec- tiveness in capturing significant biological patterns. The study tests archetypal analysis on two scRNAseq datasets to evaluate its performance. The introductory section sets the biological context, discussing the fundamental principles of cellular biology, scRNAseq sequencing and analysis. Subsequently, a comprehensive introduction to archetypal analysis is provided, detail- ing its mathematical formulation and various computational approaches, including convex least squares, penalized nonnegative least squares, and projected gradient methods. The FurthestSum initialization method is also discussed, a technique used to improve the accuracy and computa- tion times of AA. Then the available software implementations for AA are introduced, with a particular focus on the archetypal package in the R programming language, which is used in this thesis. After having described the dataset used for testing, in the result section are presented the conclusions obtained from the AA alongside an overview on the computational burden of the method. The result obtained demonstrates that AA can capture significant biological trends and patterns in both tested datasets, suggesting its potential as a valuable tool in the analysis of scRNAseq data.