L136_tSNE_Circles_Template.Rmd

---
title: "t-SNE in Comparison to PCA for Circles"
output: 
  html_document:
    toc: true
    toc_float: true
    code_folding: hide
    number_sections: true
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = T, message = F, warning = F)
```

# Introduction

```{r}
library(Rtsne)
library(keras)
library(tidyverse)
library(plotly)
```

# Data Preparation

First, we create the data.

```{r}
set.seed(123)
df <- dplyr::tibble(x = runif(n = 1000, min = -10, max = 10),
                    y = runif(n = 1000, min = -10, max = 10),
                    z = runif(n = 1000, min = -10, max = 10)) %>%
    dplyr::mutate(r = x^2+y^2+z^2) %>% 
      dplyr::mutate (class = ifelse(r < 20, 1, 0)) %>%
  dplyr::filter(r < 100) %>% 
  dplyr::filter(r < 20 | r > 70) %>% 
  select(-r)
```

Now we visualise the data.

```{r}
df %>% 
  filter (z > -2 & z < 2) %>% 
  ggplot(aes(x, y, col = factor(class))) + 
  geom_point() +
  theme_bw() + 
  scale_color_discrete(name = "Class")
```

We can also create a three-dimensional plot with plotly.

```{r}
plotly::plot_ly(df, x = ~x, y =~y, z=~z, color = ~class)
```


# t-SNE Model

A t-SNE model is created. The function **Rtsne()** is applied.

```{r}
# code here
```

Now we can create the results plot.

```{r}
ggplot(result_tsne, aes(x=V1, y=V2, col = as.factor(label))) +  
  geom_point(size=2) +
  labs(x = "", y = "", title = "t-SNE") + 
  theme_bw() + 
  scale_color_discrete(name = "Label")
```

All classes are nicely separated.

# PCA Model

A PCA model is created with **prcomp()**.

```{r}
pca_model <- prcomp(x = df, center = T, scale. = F)

result_pca <- tibble(PC1 = pca_model$x[, 1],
                     PC2 = pca_model$x[, 2],
                     label = df$class)
```

We can now visualise the result.

```{r}
ggplot(result_pca, aes(x=PC1, y=PC2, col = factor(label))) +  
  geom_point(size=2) +
  labs(x = "", y = "", title = "PCA") + 
  theme_bw() + 
  scale_color_discrete(name = "Label")
```

The labels are overlapping a lot. They are not as nicely separated as for t-SNE.