---
title: "Normalization Methods"
author: 
- name: Pol Castellano-Escuder, Ph.D.
  affiliation: Duke University
  email: polcaes@gmail.com
date: "`r BiocStyle::doc_date()`"
output: 
    BiocStyle::html_document
vignette: >
  %\VignetteIndexEntry{Normalization Methods}
  %\VignetteEngine{knitr::rmarkdown}
  %\usepackage[utf8]{inputenc}
  %\VignetteEncoding{UTF-8}
bibliography: ["POMA.bib"]
biblio-style: apalike
link-citations: true
---

**Compiled date**: `r Sys.Date()`

**Last edited**: 2023-12-14

**License**: `r packageDescription("POMA")[["License"]]`

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  fig.align = "center",
  comment = ">"
)
```

# Installation

Run the following code to install the Bioconductor version of package.        

```{r, eval = FALSE}
# install.packages("BiocManager")
BiocManager::install("POMA")
```

# Load Packages

```{r, warning = FALSE, message = FALSE, comment = FALSE}
library(POMA)
library(ggtext)
library(patchwork)
```

# Load Data and Imputation

Let's create a cleaned `SummarizedExperiment` object from the sample data `st000336` to explore the normalization effects.  

```{r, warning = FALSE, comment = NA}
example_data <- st000336 %>% 
  PomaImpute() # KNN imputation

example_data
```

# Normalization

Here we will evaluate the normalization methods that POMA offers on the same `SummarizedExperiment` object to compare them [@normalization].  

```{r, warning = FALSE}
none <- PomaNorm(example_data, method = "none")
auto_scaling <- PomaNorm(example_data, method = "auto_scaling")
level_scaling <- PomaNorm(example_data, method = "level_scaling")
log_scaling <- PomaNorm(example_data, method = "log_scaling")
log_transformation <- PomaNorm(example_data, method = "log_transform")
vast_scaling <- PomaNorm(example_data, method = "vast_scaling")
log_pareto <- PomaNorm(example_data, method = "log_pareto")
```

## Normalization effect on data dimensions

When we check for the dimension of the data after normalization we can see that all methods have the same effect on data dimension. `PomaNorm` **only** modifies the data dimension when the dataset contains **only-zero features** or **zero-variance features**.   

```{r, warning = FALSE}
dim(SummarizedExperiment::assay(none))
dim(SummarizedExperiment::assay(auto_scaling))
dim(SummarizedExperiment::assay(level_scaling))
dim(SummarizedExperiment::assay(log_scaling))
dim(SummarizedExperiment::assay(log_transformation))
dim(SummarizedExperiment::assay(vast_scaling))
dim(SummarizedExperiment::assay(log_pareto))
```

## Normalization effect on samples

Here we can evaluate the normalization effects on samples [@normalization].   

```{r, message = FALSE, warning = FALSE}
a <- PomaBoxplots(none, 
                  x = "samples") +
  ggplot2::ggtitle("Not Normalized")

b <- PomaBoxplots(auto_scaling, 
                  x = "samples", 
                  theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Auto Scaling") +
  ggplot2::theme(axis.text.x = ggplot2::element_blank())

c <- PomaBoxplots(level_scaling, 
                  x = "samples", 
                  theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Level Scaling") +
  ggplot2::theme(axis.text.x = ggplot2::element_blank())

d <- PomaBoxplots(log_scaling, 
                  x = "samples", 
                  theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Log Scaling") +
  ggplot2::theme(axis.text.x = ggplot2::element_blank())

e <- PomaBoxplots(log_transformation, 
                  x = "samples", 
                  theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Log Transformation") +
  ggplot2::theme(axis.text.x = ggplot2::element_blank())

f <- PomaBoxplots(vast_scaling, 
                  x = "samples", 
                  theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Vast Scaling") +
  ggplot2::theme(axis.text.x = ggplot2::element_blank())

g <- PomaBoxplots(log_pareto, 
                  x = "samples", 
                  theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Log Pareto") +
  ggplot2::theme(axis.text.x = ggplot2::element_blank())

a  
(b + c + d) / (e + f + g)
```

## Normalization effect on features

Here we can evaluate the normalization effects on features.   

```{r, message = FALSE, warning = FALSE}
h <- PomaDensity(none, 
                 x = "features", 
                 theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Not Normalized")

i <- PomaDensity(auto_scaling, 
                 x = "features", 
                 theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Auto Scaling") +
  ggplot2::theme(axis.title.x = ggplot2::element_blank(),
                 axis.title.y = ggplot2::element_blank())

j <- PomaDensity(level_scaling, 
                 x = "features", 
                 theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Level Scaling") +
  ggplot2::theme(axis.title.x = ggplot2::element_blank(),
                 axis.title.y = ggplot2::element_blank())

k <- PomaDensity(log_scaling, 
                 x = "features", 
                 theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Log Scaling") +
  ggplot2::theme(axis.title.x = ggplot2::element_blank(),
                 axis.title.y = ggplot2::element_blank())

l <- PomaDensity(log_transformation, 
                 x = "features", 
                 theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Log Transformation") +
  ggplot2::theme(axis.title.x = ggplot2::element_blank(),
                 axis.title.y = ggplot2::element_blank())

m <- PomaDensity(vast_scaling, 
                 x = "features", 
                 theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Vast Scaling") +
  ggplot2::theme(axis.title.x = ggplot2::element_blank(),
                 axis.title.y = ggplot2::element_blank())

n <- PomaDensity(log_pareto, 
                 x = "features", 
                 theme_params = list(legend_title = FALSE, legend_position = "none")) +
  ggplot2::ggtitle("Log Pareto") +
  ggplot2::theme(axis.title.x = ggplot2::element_blank(),
                 axis.title.y = ggplot2::element_blank())

h  
(i + j + k) / (l + m + n)
```

# Session Information

```{r}
sessionInfo()
```

# References