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How to read PCA.Rmd
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---
title: "R Notebook"
output: html_notebook
---
```{r}
library(dplyr)
library(tidyr)
library(ggplot2)
library(ggfortify)
library(viridis)
library(mvtnorm)
```
```{r}
G <- 100
S <- diag(G)
mu1 <- rep(0.5, G)
mu2 <- rep(-0.5, G)
```
```{r}
1
```
```{r}
image(S)
```
```{r}
data1 <- rmvnorm(300, mu1, S)
data2 <- rmvnorm(300, mu2, S)
data <- rbind(data1, data2)
```
```{r}
image(data)
```
```{r}
df <- gather(as.data.frame(data))
ggplot(df, aes(x='V1', y='V2')) + geom_point()
```
```{r}
as.data.frame(data)
```
```{r}
df <- as.data.frame(data)
df <- mutate(df, cell = row_number())
df <- gather(df, 'gene', 'expression', -cell)
```
```{r}
ggplot(df, aes(x=cell, y=gene)) + geom_tile(aes(fill=expression)) + theme_minimal() + scale_fill_viridis()
```
```{r}
autoplot(prcomp(data, scale. = TRUE)) + theme_classic()
```
```{r}
F_G <- 20
A11 <- matrix(0.9, F_G, F_G)
O12 <- matrix(0, F_G, G - F_G)
O22 <- matrix(0, G - F_G, G - F_G)
S1 <- rbind(cbind(A11, O12),
cbind(t(O12), O22))
diag(S1) <- 1.
S2 <- rbind(cbind(O22, t(O12)),
cbind(O12, A11))
diag(S2) <- 1.
```
```{r}
```
```{r}
image(S2)
```
```{r}
data1 <- rmvnorm(300, mu1, S1)
data2 <- rmvnorm(300, mu1, S2)
data <- rbind(data1, data2)
```
```{r}
image(data)
```
```{r}
autoplot(prcomp(data)) + theme_classic()
```
```{r}
S <- diag(G)
mu1 <- c(rep(1., F_G), rep(0, G - F_G))
mu2 <- c(rep(0, G - F_G), rep(1., F_G))
data1 <- rmvnorm(300, mu1, S)
data2 <- rmvnorm(300, mu2, S)
data <- rbind(data1, data2)
image(data)
```
```{r}
autoplot(prcomp(data)) + theme_classic()
```
```{r}
S <- matrix(0.9, G, G)
diag(S) <- 1
data1 <- rmvnorm(300, mu1, S)
data2 <- rmvnorm(300, mu2, S)
data <- rbind(data1, data2)
image(data)
```
```{r}
autoplot(prcomp(data)) + theme_classic()
```
```{r}
mu1 <- c(rep(0.5, F_G), rep(0, G - F_G))
mu2 <- c(rep(-0.5, F_G), rep(0, G - F_G))
data1 <- rmvnorm(300, mu1, S1)
data2 <- rmvnorm(300, mu2, S1)
data <- rbind(data1, data2)
image(data)
```
```{r}
autoplot(prcomp(data)) + theme_classic()
```
```{r}
mu1 <- c(rep(1, F_G), rep(0, G - F_G))
mu2 <- c(rep(0, G - F_G), rep(1, F_G))
```
```{r}
data1 <- rmvnorm(300, mu1, S1)
data2 <- rmvnorm(300, mu2 , S2)
data <- rbind(data1, data2)
image(data)
```
\[
y_n \sim [c = 1] \cdot \mathcal{N}(\mu_1, \Sigma_1) + [c=2] \cdot \mathcal{N}(\mu_2, \Sigma_2)
\]
```{r}
autoplot(prcomp(data)) + theme_classic()
```