Dimension Reduction for Beginners: Hitchhiker's Guide to Matrix Factorization and PCA

Instructor(s) name(s) and contact information

• Aedin Culhane
• Lauren Hsu

Description

This workshop will provide a beginner's guide to matrix factorization, principal component analysis (PCA), the difference between singular value decomposition, different forms of PCA and fast PCA for single-cell data as well as correspondence analysis and decomposition of the Pearson Residuals. We will describe how to detect artifacts and select the optimal number of components. It will focus on SVD, PCA, COA applied toy datasets and single-cell data.

Principal component analysis (PCA) is a key step in many bioinformatics pipelines. In this interactive session we will take a deep dive into the various implementations of singular value decomposition (SVD) and principal component analysis (PCA) to clarify the relationship between these methods, and to demonstrate the equivalencies and contrasts between these methods. We will describe correspondence analysis (COA) and demonstrate how it differs from PCA. We will also discuss interpretation of outputs, as well as some common pitfalls and sources of confusion in utilizing these methods.

Pre-requisites

A basic understanding of R syntax would be helpful, but not required. No prior knowledge of PCA necessary.

Workshop Participation

We invite audience members to engage with questions and examples from their own workflows. R notebooks will also be available in advance to run code interactively with the workshop.

R / Bioconductor packages used

• stats (prcomp, princomp, svd)
• FactoMineR
• ade4
• irlba
• corral
• ggplot2

Time outline

• Set-up + package installation (5 min)
• Introduction to matrix factorization and PCA [conceptual] (25 min)
• Interactive demonstration of methods (25 min)
• Potential pitfalls, interpreting outputs, and how to decide what’s right for your pipeline (15 min)

Workshop goals and objectives

Upon completion of this workshop, we expect participants to have gained an understanding of how to apply PCA and other SVD-based methods in research.

Learning goals

1. Understand how PCA works, the variations of PCA, and how it relates to SVD
2. Suggest appropriate use cases for these dimensionality reduction techniques
3. Select appropriate methods for use in bioinformatics pipelines

Learning objectives

1. Describe the similarities and differences between the different implementations of PCA and SVD in R/Bioconductor
2. Perform PCA/SVD on real data
3. Apply COA on real data
4. Creating plots to interpret PCA/SVD outputs, including diagnosis of problems like arch/horseshoe effect

Installation

You can view, install the released version of PCAworkshop from github

or run it interactively on the orchestra cloud platform

Slides are online