3_dimension_reduciton update

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
 

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

3_dimension_reduction/plots.R

+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()
+
+

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

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

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