From b8f4ed5b435aa06e8b555b74eebbf54aa892f0f5 Mon Sep 17 00:00:00 2001 From: Laurent Modolo <laurent.modolo@ens-lyon.fr> Date: Wed, 8 Jun 2022 17:36:52 +0200 Subject: [PATCH] 3_dimension_reduciton update --- 2_normalization/normalization.Rmd | 4 +- 3_dimension_reduction/dimension_reduction.Rmd | 112 ++++++++++++++++-- 3_dimension_reduction/img/cell_vector.key | Bin 0 -> 463182 bytes .../img/matrix_factorization.png | Bin 0 -> 59855 bytes 3_dimension_reduction/plots.R | 51 ++++++++ 4_clustering/clustering.Rmd | 4 +- 5_pseudo_time/pseudo_time.Rmd | 4 +- 6_dea/dea.Rmd | 4 +- 8 files changed, 161 insertions(+), 18 deletions(-) create mode 100755 3_dimension_reduction/img/cell_vector.key create mode 100644 3_dimension_reduction/img/matrix_factorization.png create mode 100644 3_dimension_reduction/plots.R diff --git a/2_normalization/normalization.Rmd b/2_normalization/normalization.Rmd index b07cd23..c750990 100644 --- a/2_normalization/normalization.Rmd +++ b/2_normalization/normalization.Rmd @@ -262,10 +262,8 @@ Cell barcode corresponding to $n$-plet should be in the minority if the preparat ## Cell filtering -\begin{block}{hypothesis} +### hypothesis Cell barcode corresponding to $n$-plet should be in the minority if the preparation went well. -\end{block} - ### Algorithm diff --git a/3_dimension_reduction/dimension_reduction.Rmd b/3_dimension_reduction/dimension_reduction.Rmd index 574f95c..666787e 100644 --- a/3_dimension_reduction/dimension_reduction.Rmd +++ b/3_dimension_reduction/dimension_reduction.Rmd @@ -8,9 +8,9 @@ output: fig_caption: no highlight: tango latex_engine: xelatex - slide_level: 1 + slide_level: 2 theme: metropolis - ioslides_presentation: + oslides_presentation: highlight: tango slidy_presentation: highlight: tango @@ -28,8 +28,6 @@ classoption: aspectratio=169 5. Pseudo-time and velocity inference (Thursday 30 June 2022 - 14:00) 6. Differental expression analysis (Friday 8 July 2022 - 14:00) -# Introduction - ## Programme 1. Single-cell RNASeq data from 10X Sequencing (Friday 3 June 2022 - 14:00) @@ -38,10 +36,106 @@ classoption: aspectratio=169 - Dimension of the data - Linear dimention reduction - Non-Linear dimention reduction - - t-SNE - - U-MAP - - Auto-encoder - - Variational Auto-encoder + - t-SNE + - UMAP + - Auto-encoder 4. Clustering and annotation (Thursday 23 June 2022 - 14:00) 5. Pseudo-time and velocity inference (Thursday 30 June 2022 - 14:00) -6. Differential expression analysis (Friday 8 July 2022 - 14:00) \ No newline at end of file +6. Differential expression analysis (Friday 8 July 2022 - 14:00) + +# Dimension of the data + +## High dimensional count data + +\begin{center} +\[ + X_{cells \times genes} = + \begin{bmatrix} + x_{1,1} & x_{1,2} & x_{1,3} & \cdots & x_{1,c} \\ + x_{2,1} & x_{2,2} & x_{2,3} & \cdots & x_{2,c} \\ + x_{3,1} & x_{3,2} & x_{3,3} & \cdots & x_{3,c} \\ + \vdots & \vdots & \vdots & \ddots & \vdots \\ + x_{n,1} & x_{n,2} & x_{n,3} & \cdots & x_{n,c} \\ + \end{bmatrix} +\] +\end{center} + +We have $20-30^5$ rows (genes or transcripts) and up to $10^6$ columns (cells) + +## Geometric interpretation of $X_{cells \times genes}$ + +\begin{center} +\begin{columns} +\column{0.5\textwidth} +\begin{center} +\[ + X_{1 \times genes} = + \begin{bmatrix} +x_{1,c} \\ +x_{2,c} \\ +x_{3,c} \\ + \end{bmatrix} +\] +\end{center} + +\column{0.5\textwidth} + +\end{columns} +\end{center} + +## Geometric interpretation of $X_{cells \times genes}$ + +\begin{center} +\begin{columns} +\column{0.5\textwidth} +\begin{center} +\[ + X_{1 \times genes} = + \begin{bmatrix} +x_{1,c} \\ +x_{2,c} \\ +x_{3,c} \\ + \end{bmatrix} +\] +\end{center} + +\column{0.5\textwidth} + +\begin{tikzpicture}[fill=blue,fill opacity=0.7,draw,scale=3,rounded corners=0.5pt] + \def\cubecol{blue} + \def\opacity{0.8} + \filldraw (-0.5,-0.5,-0.5) -- ++(1,0,0) -- ++(0,1,0) -- ++(-1, 0, 0) -- cycle; + \filldraw (-0.5,-0.5,-0.5) -- ++(1,0,0) -- ++(0,0,1) -- ++(-1, 0, 0) -- cycle; + \filldraw (-0.5,-0.5,-0.5) -- ++(0,1,0) -- ++(0,0,1) -- ++(0, -1, 0) -- cycle; + \filldraw[fill=blue!20] (0.5,0.5,0.5) -- ++(-1,0,0) -- ++(0,-1,0) -- ++(1, 0, 0) -- cycle; + \filldraw[fill=blue!50!black!50] (0.5,0.5,0.5) -- ++(-1,0,0) -- ++(0,0,-1) -- ++(1, 0, 0) -- cycle; + \filldraw[fill=blue!20!black!80] (0.5,0.5,0.5) -- ++(0,-1,0) -- ++(0,0,-1) -- ++(0, 1, 0) -- cycle; +\end{tikzpicture} + +\end{columns} +\end{center} + +## Matrix factorization + +### Low dimensional representation +\begin{itemize} + \item Cells: $ {\bf U} \in \mathbb{R}^{n\times \textcolor{red}{K}} $ + \item Genes: $ {\bf V} \in \mathbb{R}^{p\times \textcolor{red}{K}} $ +\end{itemize} + +\vspace{-2em} + +\begin{center} + \includegraphics[height=4cm]{./img/matrix_factorization.png} +\end{center} + +\begin{center} + What is the sens of ${\bf \approx}$ ? +\end{center} + +# Linear dimention reduction +# Non-Linear dimention reduction +# t-SNE +# UMAP +# Auto-encoder +# Variational Auto-encoder \ No newline at end of file diff --git a/3_dimension_reduction/img/cell_vector.key b/3_dimension_reduction/img/cell_vector.key new file mode 100755 index 0000000000000000000000000000000000000000..5bf182d575975c7172fa830f8af7820b9e81ec15 GIT binary patch literal 463182 zcmWIWW@Zs#0D%dq&w~1Le`|{!VqgGaQw9bGm&B4p{oE2=6B9ERX9F{HT{i;*16>ny zQ%hYZV`F1oV?zTACqn}ZS0@WsT{9yK1HG(*^#3>hKVT5>a`SX!U}R)q@L=#@VEF%# z!NIj6GmU}4*Ox(yfq{X8fw4W4frWvAfsuiMK?>vm2Brl}FcHR-1<Wuu!wHb=|F;Yl z0U7xv`NbLe1q#M`1`HNXp1v#~6BrmEY*mmt27xQGJvaLqHnF^H;GFU1hg04EM@%N3 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zSpk!IjA8gqljp4edgMQf+8q{OHlrfXupC@9$QX$J2e~`tzeQ8D&*V#<cXE_Yhx^t% zPb{|ks2codcf)<3RR=3CZ`pD$8C*;^uYME{((tBUdzrzGBq6SAp-;f2&HttQ8Tykw WCYhM7e$2qYz~JfX=d#Wzp$Pyhh?}ke literal 0 HcmV?d00001 diff --git a/3_dimension_reduction/plots.R b/3_dimension_reduction/plots.R new file mode 100644 index 0000000..0f9b27f --- /dev/null +++ b/3_dimension_reduction/plots.R @@ -0,0 +1,51 @@ +library(tidyverse) + +# regression +x <- c(61, 67, 32, 43, 57, 44, 39, 38, 42, 51) +y <- c(30, 33, 15, 23, 26, 18, 23, 17, 27, 37) +plot(x, y, xlim=c(20, 80), ylim=c(10,40), pch=15, las = 1, main = "Le crit`ere d'ajustement") +b <- 1/6 +a <- 17 +ytheo <- b*x + a +abline(a,b) +points(x, ytheo, pch=20, col="blue", cex=1.5) +segments(x,ytheo,x,y) +mess <- paste("Ecart = ",round(mean((y-ytheo)^2),dig=2)) +text(50,12,mess) + + + +library(MASS) +library(rgl) +library(factoextra) + +data <- mvrnorm( + n = 1000, + mu = c(0, 2, -2), + Sigma = matrix( + c( + 1, .8, -.8, + .8, 1, -0.9, + -.8, 0.9, 0.9 + ), + ncol = 3) + ) %>% + scale() %>% + as.data.frame() %>% + as_tibble() +data %>% plot() +plot3d(data, type = "p", ) +plot3d(ellipse3d(cor(data)), col = "blue", alpha = 0.25, add = T) + +pca <- prcomp(data, scale = FALSE) +pca_coord <- prcomp(data, scale = FALSE) %>% get_pca_ind() %>% .$coord +pca_var <- prcomp(data, scale = FALSE) %>% get_pca_var() %>% .$coord +pca_coord %>% + as_tibble() %>% + plot() +plot3d(pca_coord, type = "p") +plot3d(ellipse3d(cor(pca_coord %*% pca_var)), col = "blue", alpha = 0.25, add = T) + +cbind(pca_coord[, 2], data[, 1]) %>% plot() + + diff --git a/4_clustering/clustering.Rmd b/4_clustering/clustering.Rmd index 4cde152..2d23bb3 100644 --- a/4_clustering/clustering.Rmd +++ b/4_clustering/clustering.Rmd @@ -8,9 +8,9 @@ output: fig_caption: no highlight: tango latex_engine: xelatex - slide_level: 1 + slide_level: 2 theme: metropolis - ioslides_presentation: + oslides_presentation: highlight: tango slidy_presentation: highlight: tango diff --git a/5_pseudo_time/pseudo_time.Rmd b/5_pseudo_time/pseudo_time.Rmd index 4b1c02b..4b5b31b 100644 --- a/5_pseudo_time/pseudo_time.Rmd +++ b/5_pseudo_time/pseudo_time.Rmd @@ -8,9 +8,9 @@ output: fig_caption: no highlight: tango latex_engine: xelatex - slide_level: 1 + slide_level: 2 theme: metropolis - ioslides_presentation: + oslides_presentation: highlight: tango slidy_presentation: highlight: tango diff --git a/6_dea/dea.Rmd b/6_dea/dea.Rmd index 39dfe47..1351882 100644 --- a/6_dea/dea.Rmd +++ b/6_dea/dea.Rmd @@ -8,9 +8,9 @@ output: fig_caption: no highlight: tango latex_engine: xelatex - slide_level: 1 + slide_level: 2 theme: metropolis - ioslides_presentation: + oslides_presentation: highlight: tango slidy_presentation: highlight: tango -- GitLab