L137_tSNE_Mnist_Template.Rmd

---
title: "t-SNE in Comparison to PCA for Handwritten Digits."
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)
```

We will work with Mnist dataset. This is purely because it is highly dimensional (784 dimensions) and shows a very good result for t-SNE.

More information on the data can be found [here](http://yann.lecun.com/exdb/mnist/).

# Data Preparation

First, we import the data.

```{r}
x_train <- read.csv("./data/train.csv", sep = ",")
```

Now we separate dependent and independent variables.

```{r}
y_train <- x_train$label
x_train <- x_train %>% 
  select(-label)
```

## Visualisation of a digit

We want to check that we are dealing with digits.

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


# 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=1, alpha = 0.5) +
  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 = x_train, center = T, scale. = F)

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

We can now visualise the result.

```{r}
ggplot(result_pca, aes(x=PC1, y=PC2, col = factor(label))) +  
  geom_point(size=1, alpha = 0.5) +
  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.