---
title: "5. Generating model summaries"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{5. Generating model summaries}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
options(rmarkdown.html_vignette.check_title = FALSE)
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  warning = FALSE, 
  message = FALSE
)
```

This demonstrates how to generate and inspect model summaries. Summarising models fitted to both the high-dimensional space and its corresponding 2-D embedding is an essential step in evaluating how well a low-dimensional representation captures the structure of the original data.

```{r setup}
library(quollr)
library(dplyr)
library(ggplot2)
```

## Step 1: Fitting the model

Begin by fitting a high-dimensional model and its corresponding 2-D model using the `fit_highd_model()` function. This generates the 2-D bin centroids (the 2-D model) and their corresponding coordinates in the high-dimensional space (the lifted model).

```{r}
model <- fit_highd_model(
  highd_data = scurve, 
  nldr_data = scurve_umap, 
  b1 = 4, 
  q = 0.1, 
  benchmark_highdens = 5
)

df_bin_centroids <- model$model_2d
df_bin <- model$model_highd
```

## Step 2: Predicting 2-D embedding for data

To evaluate model fit, you can predict the 2-D embedding for each observation in the original high-dimensional dataset.

```{r}
pred_df_training <- predict_emb(
  highd_data = scurve, 
  model_highd = scurve_model_obj$model_highd,
  model_2d = scurve_model_obj$model_2d
)

glimpse(pred_df_training)
```

### Visualising predictions

The plot below shows the original UMAP embedding of the training data in grey, overlaid with the predicted 2-D coordinates in red.

```{r, fig.alt="UMAP embedding of the S-curve training data with predictions in red."}
umap_scaled <- scurve_model_obj$nldr_obj$scaled_nldr

umap_scaled |>
  ggplot(aes(x = emb1, y = emb2, label = ID)) +
  geom_point(alpha = 0.5) +
  geom_point(data = pred_df_training, aes(x = pred_emb_1, y = pred_emb_2), 
             color = "red", alpha = 0.5) +
  coord_equal() +
  theme(
    plot.title = element_text(hjust = 0.5, size = 18, face = "bold"),
    axis.text = element_text(size = 5),
    axis.title = element_text(size = 7)
  )
```

## Step 3: Computing model summaries

Use the `glance()` function to compute summary statistics that describe how well the 2-D model captures structure in the high-dimensional space.

```{r}
glance(
  highd_data = scurve, 
  model_highd = scurve_model_obj$model_highd,
  model_2d = scurve_model_obj$model_2d
)
```

## Step 4: Augmenting the dataset

To obtain a detailed data frame that includes the high-dimensional observations, their assigned bins, predicted embeddings, and summary metrics, use the `augment()` function:
  
```{r}
augment(
  highd_data = scurve, 
  model_highd = scurve_model_obj$model_highd,
  model_2d = scurve_model_obj$model_2d
) |>
  head(5)
```