Bioc2021

PCAworkshop

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Aedin Culhane, Lauren Hsu

@AedinCulhane

To run this workshop

• Cloud RStudio http://app.orchestra.cancerdatasci.org/

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• Following Rmarkdown on Website (pkgdown) https://aedin.github.io/PCAworkshop/

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For help on workshops, see Kevin Rue-Albrecht’s Introduction to Workshops presentation

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• Install this workshop package locally

BiocManager::install(‘aedin/PCAworkshop’)

devtools::install_github(’aedin/PCAworkshop’)

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Choose a workshop

Wait for your own workshop instance to launch

Ignore the Google Chrome warning 🙈

IMPORTANT

• Do not share the URL of your session with others.

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• Do not copy the URL from someone who is sharing their screen.

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Navigating to an URL used by someone else will kick them out of their session.

This workshop includes 4 Vignettes

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Matrix Factorization or Dimension reduction methods, including PCA are commonly used and is well suited to finding known & unknown (latent) patterns in large data

Reduce the data matrix to a small number of linear vectors that explain most of the variance in the data

New Axis 1

New Axis 2

Many use

Singular Value Decomposition X= UDV^t

n

p

1

X

=

n

1

k

1

k

k

p

1

1

k

U

D

V^t

1. Short PCA Vignette

Examines a simple data

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data(bordeaux)

bordeaux

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## excellent good mediocre boring

## Cru_Bourgeois 45 126 24 5

## Grand_Cru_classe 87 93 19 1

## Vin_de_table 0 0 52 148

## Bordeaux_d_origine 36 68 74 22

## Vin_de_marque 0 30 111 59

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and shows the relationship between Principal Component Analysis (PCA) and Singular Value Decomposition (SVD)

U,V matrices are orthogonal, uncorrelated

=

n

1

k

p

1

k

U

I

V^t

n

1

k

U^t

=

V

p

1

k

1

k

k

And the inner product (generalization of dot product) between pair of columns in U or V equals 0

The columns and rows are orthogonal unit vectors-> the squared elements of columns U,V sums to 1

Confirm this.. Lets go to Rstudio

Terminology SVD -> PCA

• Left (U), Right (V) singular vectors, singular values (D)

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• PCA computed by linear regression, eigen analysis, SVD, latent factor analysis

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• Vectors are called principal components, principal axes, latent vectors, eigen vector and capture variance (information) in the data

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• Number eigen values selected by scree plot or permutations.

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The "Kaiser rule" criteria

is shown in red.

Scree

Vignette 2. Principal Component Analysis in R

Compares different functions in R that compute PCA

Dimension reduction is indispensable in �large scale data analysis

Ordination

Dimension Reduction

Matrix Factorization

Latent variable analysis

Factor Analysis

Principal Component Analysis

Wavelet Decomposition

Spectral analysis

Eigen analysis

Two forms of PCA; Covariance, Correlation

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Covariance-based PCA

Correlation-based PCA

SVD

Covariance-based PCA used by Sun et al., 2019

https://github.com/xzhoulab/DRComparison/blob/master/algorithms/call_PCA.R

Thank so much for providing reproducible code on github

PCA

Covariance-based PCA

Assessment of the Accuracy, robustness and scalability of dimensionality reduction methods for single-cell RNA-seq analysis

Sun, S., Zhu, J., Ma, Y. et al. . Genome Biol 20, 269 (2019)

Comparison of 18 Methods

Processing steps �impact�results

human lung adenocarcinoma

cell lines

HCC827

H1975

H2228

Hsu & Culhane, 2020

Preprocessing Impacts�on PC1

Arch effect: points on PC1 lie on 1 side of the origin

Centering is important: orthogonal vectors are uncorrelated only when at least one of them has mean 0.

Arches,�Horseshoes,�Guttman effect

curvilinear

relationships

between successive

PCs

Arch

Can arise as a consequence of distance metrics that saturate.

10 nonzero values.

Vignette 3. Correspondence Analysis

From our Briefings in Bioinformatics review. Meng et al., 2016 https://academic.oup.com/bib/article/17/4/628/2240645

Correspondence Analysis of scMix Data

corralm

Unpublished

PCA

corral package

Designed for use on single cell data

• Uses sparse matrices (Matrix)
• Applies fast SVD approximation (irlba)
• Interacts directly with Bioconductor objects

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BiocManager::install(‘corral’)

devtools::install_github(‘laurenhsu/corral’)

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Lauren Hsu

Lets test some scRNAseq data

Compare PCA, corral on Zhengmix (DuoClustering2018)

Zhengmix4eq

Zhengmix4uneq

Zhengmix8eq

Pre-sorted cells, including:

1. B-cells
2. CD14 monocytes
3. CD4 T-helper cells
4. CD56 NK cells
5. memory T-cells
6. naive cytotoxic T-cells
7. naive T- cells
8. regulatory T-cells

4 cell types, in approx. equal proportions

4 cell types, in unequal proportions

8 cell types, in approx. equal proportions

10X sequencing

mixed

Joint Matrix Factorization of >2 datasets

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Meng & Zeleznik et al., (2016) Dimension reduction techniques for the integrative analysis of multi-omics data. Briefings in Bioinformatics, 17(4), 2016, 628–641

Towards Integration of multiple datasets

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Meng et al., BMC Bioinformatics 2014, 15:162

Meng et al., Brief Bioinform. 2016 Jul; 17(4): 628–641.

Culhane AC et al., BMC Bioinformatics 2003, 4:59-74

Meng et al., BMC Bioinformatics 2014, 15:162

Package:mogsa

Find Correlated Structure Across 5 transcriptomics datasets using MCIA tensor Integration

Multiple Factor Analysis, Multiple Coinertia Analysis, Consensus PCA

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BiocManager::install("mogsa")

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moa(lapply(se, exprs), proc.row = "center_ssq1", w.data = "inertia", statis = TRUE) #MCIA

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MFA statis=FALSE (the default setting)..

Parallel (permutation) based selection of components

• Horn's Parallel Analysis for factor retention
• https://www.r-bloggers.com/determining-the-number-of-factors-with-parallel-analysis-in-r/

library(paran)

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• Edgar Dobriban
• https://github.com/dobriban/DPA

Determine Number of Components (by permutation) representing concordant structure between datasets

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bootMoa(

moa = ana,

proc.row = "center_ssq1",

w.data = "inertia",

statis = TRUE,

B = 20,

plot=TRUE) �

Select N Components

with > variance than

expected (permuted)

Meng et al., BMC Bioinformatics 2014, 15:162

Package:mogsa

How to annotate of Genesets in tensor Integration

Project GO Terms (vector of gene) onto each to get a gene set “score” in each space

Simple approach to generate a gene set scores

Fagan et al., (2007) A Multivariate Analysis approach to the Integration of Proteomic and Gene Expression Data. Proteomics. 7(13):2162-71.

Jeffery et al., (2007) Integrating transcription factor binding site information with gene expression datasets. Bioinformatics 23(3):298-305.

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Matrix decomposition of gene expression and proteomics onto same scale

Multiple ‘Omics Gene Set Analysis

MOGSA Meng C, et al., 2019

MCP  DOI: 10.1074/mcp.TIR118.001251

Fast & Performant

Single Sample/Cell Gene Set Scores

Useful Reference Books

Open source (free) at

http://web.stanford.edu/class/bios221/book /