---
title: "Classification case: Assessing the performance of remote sensing models"
author: "Luciana Nieto & Adrian Correndo"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Classification case}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

## 1. Introduction 
<img src="../man/figures/metrica_logo.png" align="right" height="150" style="float:right; height:150px;"> <br/>
The *`metrica`* package was developed to visualize and compute the level of agreement between observed ground-truth values and model-derived (e.g., mechanistic or empirical) predicted. 

This package is intended to fit into the following workflow:  

1. a data set containing the observed values is used to train a model  
2. the trained model is used to generate predicted  
3. a data frame containing at least the **observed** and model-**predicted** values is created  
4. *`metrica`* package is used to compute and evaluate the classification model based on observed and predicted values  
5. *`metrica`* package is used to visualize model fit and selected fit metrics  

This vignette introduces the functionality of the *`metrica`* package applied to observed and model-predicted values of a binary land cover classification scenario, where the two classes are vegetation (1) and non-vegetation (0)).  

Let's begin by loading the packages needed.  <br/>
## Libraries 
```{r warning=FALSE, message=FALSE}
library(metrica)
library(dplyr)
library(purrr)
library(tidyr)
library(ggplot2)
```

## 2. Example datasets  <br/>

### 2.1. Kansas Land Cover data 

<br/>

<img src="../man/figures/land_cover_example.png" align="right" height="250" style="float:right; height:250px;"> 

<br/>

**Figure 1**. This binary classification dataset corresponds to a Random Forest model using a 70:30 training:testing split to predict vegetation vs. other land coverage. This exercise focused on pixel level classification. The image is showing the classification map where yellow areas are associated to non-vegetation pixels (other), and the green areas to those classified as vegetation. <br/>

Now we load the binary `land_cover` data set already included with the `metrica` package. This data set contains two columns:  <br/>

- `predicted`: model-predicted (random forest) land cover, being vegetation = 1 and other = 0,  <br/>

- `actual`: ground-truth observed land cover, being 0 = vegetation and 1 = other <br/>

```{r load binary data}
# Load
binary_landCover <- metrica::land_cover

# Printing first observations
head(binary_landCover)
```

### 2.2. Maize Phenology 

<br/>

<img src="../man/figures/maize_phenology_example.png" align="right" height="250" style="float:right; height:250px;"> 

<br/>

**Figure 2**. This multiclass classification dataset corresponds to a Random Forest model using a 70:30 training:testing split to predict maize vegetation vs. other land coverage. This exercise focused on field level classification. The image is showing, in dark grey shapes, the fields used as the ground-truth locations to develop the model. <br/>

Now we load the multinomial `maize_phenology` data set, which is also already included with the `metrica` package. This multiclass data set presents 16 different classes corresponding to phenological stages of the maize (*Zea Mays* (L.)) crop.  <br/>

```{r load multiclass data}
# Load
multi_maize_phen <- metrica::maize_phenology

# Printing first observations
head(multi_maize_phen)
```


## 3 Visual assessment of agreement <br/>

### 3.1 Confusion matrix  

The simplest way to visually assess agreement between observed and predicted classes is with a confusion matrix.  <br/>

We can use the function `confusion_matrix()` from the *metrica* package.  <br/>

The function requires specifying:  <br/>

- the data frame object name (`data` argument) <br/>

- the name of the column containing observed values (`obs` argument)  <br/>

- the name of the column containing predicted values (`pred` argument)  <br/>

The output of the `confusion_matrix()` function is either a table (`plot = FALSE`) or
a `ggplot2` object (`plot = TRUE`) that can be further customized: <br/>

### 3.1. Binary

```{r confusion_matrix binary, fig.width=6, fig.height=5, dpi=60}
# a. Print
binary_landCover %>% confusion_matrix(obs = actual, pred = predicted, 
                                      plot = FALSE,
                                      unit = "count")

# b. Plot
binary_landCover %>% confusion_matrix(obs = actual, pred = predicted, 
                                      plot = TRUE,
                                      colors = c(low="#ffe8d6" , high="#892b64"), 
                                      unit = "count")

# c. Unit = proportion
binary_landCover %>% confusion_matrix(obs = actual, pred = predicted, 
                                      plot = TRUE,
                                      colors = c(low="#f9dbbd" , high="#892b64"), 
                                      unit = "proportion")

```

### 3.2. Multiclass

```{r confusion_matrix multiclass, fig.width=6, fig.height=5, dpi=60}  
# a. Print
multi_maize_phen %>% confusion_matrix(obs = actual, pred = predicted, 
                                      plot = FALSE, 
                                      unit = "count")

# b. Plot
multi_maize_phen %>% confusion_matrix(obs = actual, pred = predicted, 
                                      plot = TRUE, 
                                      colors = c(low="grey85" , high="steelblue"), 
                                      unit = "count")

```


## 4. Numerical assessment of agreement  <br/>

The *metrica* package contains functions for **26** scoring rules to assess the agreement between observed and predicted values for classification data.  <br/>

A list with all the the classification metrics including their name, definition, details, formula, and function name, please check [here](https://adriancorrendo.github.io/metrica/articles/available_metrics_classification.html).  <br/>

All of the metric functions take at least three arguments:  <br/>

- the data frame object name (`data` argument, optional) <br/>

- the name of the column containing observed values (`obs` argument)  <br/>

- the name of the column containing predicted values (`pred` argument) <br/>

- an integer (1 or 2) indicating the alphanumerical order of the positive event (`pos_level` argument, Default = 2) <br/>

- a TRUE/FALSE indicating to estimate metrics for each single class (`atom` argument, Default = FALSE). This argument is only functional for multiclass datasets. <br/>

- a TRUE/FALSE indicating to store the numeric result as a list (`tidy` argument, Default = FALSE), or as a data frame (tidy = TRUE). <br/>

### 4.1. Single metrics

The user can choose to calculate a single metric, or to calculate all metrics at once.  <br/>

To calculate a single metric, the metric function can be called. For example, to calculate $accuracy$, we can use the `accuracy()` function:  

```{r accuracy}
# Binary
binary_landCover %>% accuracy(data = ., obs = actual, pred = predicted, tidy = TRUE)

# Multiclass
maize_phenology %>% accuracy(data = ., obs = actual, pred = predicted, tidy = TRUE)
```

Or considering imbalanced observations across classes we can call the `balacc()` function for balanced accuracy:

```{r balanced_accuracy}
# Binary
binary_landCover %>% balacc(data = ., obs = actual, pred = predicted, tidy = TRUE)

# Multiclass
maize_phenology %>% balacc(data = ., obs = actual, pred = predicted, tidy = TRUE)
```

Similarly, to calculate precision, we can use the `precision()` function:  <br/>

```{r precision}
# Binary
binary_landCover %>% precision(data = ., obs = actual, pred = predicted, tidy = TRUE)

# Multiclass
maize_phenology %>% precision(data = ., obs = actual, pred = predicted, tidy = TRUE)
```

### 4.2. Metrics summary

The user can also calculate all metrics at once using the function `metrics_summary()`:  <br/>
``` {r metrics_summary}

# Get all at once with metrics_summary()
# Binary
binary_landCover %>% metrics_summary(data = ., obs = actual, pred = predicted, type = "classification")

# Multiclass
multi_maize_phen %>% metrics_summary(data = ., obs = actual, pred = predicted, type = "classification")
```

Alternatively, if the user is only looking for specific metrics, within the same function `metrics_summary()`, the user can pass a list of desired metrics using the argument "metrics_list" as follows: <br/>  

``` {r metrics_summary_selected}  
# Get a selected list at once with metrics_summary()
selected_class_metrics <- c("accuracy", "precision", "recall", "fscore")

# Binary
bin_sum <- binary_landCover %>% 
  metrics_summary(data = ., 
                  obs = actual, pred = predicted, 
                  type = "classification",
                  metrics_list = selected_class_metrics, pos_level = 1) 

# Multiclass
multi_maize_phen %>% 
  metrics_summary(data = ., 
                  obs = actual, pred = predicted, 
                  type = "classification",
                  metrics_list = selected_class_metrics)

```
### 4.3. Class wise metrics (`atom` = TRUE)

For multiclass cases, most of the classification metrics can (and should) be estimated 
at the class level and not simply as an overall average across classes. With the 
exceptions of kappa (khat), mcc, fmi, and AUC_roc, all classification metrics can be 
estimated at the class level using the argument `atom = TRUE`, as follows:

```{r atom argument}
# Precision
maize_phenology %>% metrica::precision(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# Recall
maize_phenology %>% metrica::recall(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# Specificity
maize_phenology %>% metrica::specificity(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)

# atom = TRUE available for more functions available (remove #)
# F-score
# maize_phenology %>% metrica::fscore(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # Adjusted F-score
# maize_phenology %>% metrica::agf(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # G-mean
# maize_phenology %>% metrica::gmean(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # Negative predictive value
# maize_phenology %>% metrica::npv(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # Prevalence
# maize_phenology %>% metrica::preval(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # Prevalence threshold
# maize_phenology %>% metrica::preval_t(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # False omission rate
# maize_phenology %>% metrica::FOR(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # False detection rate
# maize_phenology %>% metrica::FDR(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # False positive rate
# maize_phenology %>% metrica::FPR(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # Falase negative rate
# maize_phenology %>% metrica::FNR(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # Delta-p
# maize_phenology %>% metrica::deltap(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # Critical Success Index
# maize_phenology %>% metrica::csi(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # Bookmaker Informedness
# maize_phenology %>% metrica::bmi(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # Positive likelihood ratio
# maize_phenology %>% metrica::posLr(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # Negative likelihood ratio
# maize_phenology %>% metrica::negLr(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
# # Diagnostic odds ratio
# maize_phenology %>% metrica::dor(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)

```


### 4.4. Multiple models

In some cases, multiple runs of a model are available to compare vs. observed values (e.g. cross-validation folds). Thus, we can also fit the agreement analysis for several datasets as follows: <br/>

```{r multiple_models nested}

set.seed(15)
# Let's simulated two extra runs of the same model for Land Cover
fold_2 <- data.frame(actual = sample(c(0,1), 285, replace = TRUE),
                     predicted = sample(c(0,1), 285, replace = TRUE))
fold_3 <- data.frame(actual = sample(c(0,1), 285, replace = TRUE),
                     predicted = sample(c(0,1), 285, replace = TRUE))

# a. Create nested df with the folds
binary_nested_folds <- bind_rows(list(fold_1 = binary_landCover, 
                                      fold_2 = fold_2,
                                      fold_3 = fold_3),
                             .id = "id") %>%
  dplyr::group_by(id) %>% tidyr::nest()

head(binary_nested_folds %>% group_by(id) %>% dplyr::slice_head(n=2))

# b. Run 
binary_folds_summary <- binary_nested_folds %>% 
  # Store metrics in new.column "performance"
  dplyr::mutate(performance = 
                  purrr::map(data,
                             ~metrica::metrics_summary(data = ., 
                                                       obs = actual, pred = predicted, 
                                                       type = "classification"))) %>% 
  dplyr::select(-data) %>% 
  tidyr::unnest(cols = performance) %>% 
  dplyr::arrange(Metric)

head(binary_folds_summary)

```

#### 4.4.1. Non-nested data <br/>

#### 4.4.1.1. Using `group_map()` <br/>

```{r multiple_models unnested group_map}
non_nested_folds <- binary_nested_folds %>% unnest(cols = "data") 

# Using group_map()
binary_folds_summary_2 <- non_nested_folds %>% 
  dplyr::group_by(id) %>% 
  dplyr::group_map(~metrics_summary(data = ., obs = actual, pred = predicted, type = "classification"))

binary_folds_summary_2
```

#### 4.4.1.2. Using `summarise()` <br/>

```{r multiple_models unnested summarise}

# Using summarise()
binary_folds_summary_3 <- non_nested_folds %>% 
  dplyr::group_by(id) %>% 
  dplyr::reframe(metrics_summary(obs = actual, pred = predicted, type = "classification")) %>%
  dplyr::arrange(Metric)

binary_folds_summary_3

```
## 5. Visual Assessment <br/>

### 5.1. Customizing the confusion matrix <br/>

To print the metrics on the `confusion_matrix()`, just use print.metrics = TRUE. Warning: do not forget to specify your 'metrics.list' and choice wisely: <br/>  

```{r scatter_plot print_metrics, fig.width=6, fig.height=5, dpi=60}

selected_metrics <- c("accuracy", "precision", "recall", "khat",
                   "mcc", "fscore", "agf", "npv", "FPR", "FNR")

binary_matrix_metrics <- 
  binary_landCover %>% 
  confusion_matrix(obs = actual, pred = predicted, 
                   plot = TRUE,
                   colors = c(low="#ffe8d6" , high="#892b64"), 
                   unit = "count",  
                   # Print metrics_summary
                   print_metrics = TRUE,
                   # List of performance metrics
                   metrics_list = selected_metrics,
                   # Position (bottom or top)
                   position_metrics = "bottom")

binary_matrix_metrics

multinomial_matrix_metrics <-
  maize_phenology %>% 
  confusion_matrix(obs = actual, pred = predicted, 
                   plot = TRUE, 
                   colors = c(low="grey85" , high="steelblue"), 
                   unit = "count",
                   # Print metrics_summary
                   print_metrics = TRUE,
                   # List of performance metrics
                   metrics_list = selected_metrics,
                   # Position (bottom or top)
                   position_metrics = "bottom")
  
multinomial_matrix_metrics

```
Also, as a ggplot element, outputs are flexible of further edition:  

```{r scatter_plot.edit, fig.width=6, fig.height=5, dpi=60}

binary_matrix_metrics +
  # Modify labels
  ggplot2::labs(x = "Observed Vegetation", 
       y = "Predicted Vegetation",
       title = "Binary Confusion Matrix")
  

multinomial_matrix_metrics +
  # Modify labels
  ggplot2::labs(x = "Observed Corn Phenology", 
       y = "Predicted Corn Phenology",
       title = "Multinomial Confusion Matrix")+
  # Modify theme
  ggplot2::theme_light()


```


## 6. Exporting  
To export the metrics summary table, the user can simply write it to file with the function `write.csv()`:  

```{r export metrics_summary, eval=F }
metrics_summary(data = binary_landCover,
                obs = actual, 
                pred = predicted,
                type = "classification") %>%
  write.csv("binary_landcover_metrics_summary.csv")

```


Similarly, to export a plot, the user can simply write it to file with the function `ggsave()`:  

```{r export plot, eval=F}

ggsave(plot = multinomial_matrix_metrics,
       "multinomial_matrix_metrics.png",
       width = 8,
       height = 7)
```
