Dimensionality_Reduction.Rmd

---
title: "Dimensionality_Reduction"
output: html_document
---

GOALS:

- Explore different projections:
  + PCA
    + Screeplot
  - MDS
    - Different distance metrics
    - STRESS
    - Shepard Plot
  - t-SNE
  - LLE
  - ISOMAP
  - NeRV
  - CCA
  - ESOM (?)
  
- Explore other approaches:
  - Wrapper:
    - RFE
    - Genetic
  - Filter:
    - Correlation based (FCBF package)

```{r setup, include=FALSE, message=FALSE, warning=FALSE}
library(ProjectionBasedClustering)
```

Desired dimensions

```{r}
dimensions <-
  c(1:10,
    15,
    20,
    25,
    30,
    35,
    40,
    45,
    50,
    75,
    100,
    125,
    150,
    175,
    200,
    250,
    300,
    350,
    400,
    450,
    500)
```

PCA function

```{r pca}
optimizePCA <- function(train, test) {
  p <- prcomp(train)
  summ.p <- summary(p)
  var.explained <- summ.p$importance[2,]
  
  gg <- ggplot(data = data.frame(x = 1:50, y = (p$sdev ^ 2)[1:50]),
               mapping = aes(x = x, y = y)) + geom_point() + geom_line()
  plot(gg + labs(title = "Screeplot",
                 x = "Components",
                 y = "Eigenvalues"))
  
  no_of_features <- which(cumsum(var.explained) > 0.8)[1]
  
  print(paste(no_of_features, "components account for 80% of total variance"))
  
  train_return <- data.frame(p$x[, 1:no_of_features])
  
  test_return <-
    data.frame(predict(p, newdata = test)[, 1:no_of_features])
  
  return(list("train" = train_return, "test" = test_return))
}
```

PCA ace vaxinpad

```{r}
pca_ace_vaxinpad <- optimizePCA(train = ace_vaxinpad_train, test = ace_vaxinpad_test)
```

MDS functions

```{r mds_funcs}
calculateMDS <- function(original_distances, dimensions) {
  stress <- vector("list", length(dimensions))
  projected_points <- vector("list", length(dimensions))
  
  for (i in 1:length(dimensions)) {
    mds <-
      MDS(as.matrix(original_distances), OutputDimension = dimensions[i])
    stress[[i]] <- mds$Stress
    projected_points[[i]] <- mds$ProjectedPoints
  }
  return(list(
    "stress" = stress,
    "points" = projected_points,
    "dimensions" = dimensions
  ))
}

plotScreeplot <- function(stress, dimensions) {
  p <-
    ggplot(data = data.frame(x = dimensions, y = stress),
           mapping = aes(x = x, y = y)) +
    geom_point() +
    geom_line()
  
  return(
    p + labs(
      title = "Screeplot",
      x = "Dimensions",
      y = "STRESS"
    )
  )
}

determineGoodStressValues <- function(stress, dimensions, cutoff) {
  return(dimensions[stress <= cutoff])
}

plotShepardPlot <- function(original_distances, new_distances) {
  correlation <- cor(original_distances, new_distances)
  p <-
    ggplot(
      data = data.frame(x = original_distances, y = new_distances),
      mapping = aes(x = x, y = y)
    ) +
    geom_point(size = 1, alpha = 0.5) +
    geom_abline(intercept = 0, slope = 1, colour = "grey")
  
  return(
    p + labs(
      title = "Shepard plot",
      subtitle = paste("r =", correlation),
      x = "Original distances",
      y = "Projected distances"
    )
  )
}

optimizeMDS <- function(data, dimensions) {
  distances <- dist(data)
  mds <- calculateMDS(distances, dimensions)
  plot(plotScreeplot(unlist(mds$stress, use.names = F), dimensions))
  opt_stress <-
    determineGoodStressValues(unlist(mds$stress, use.names = F), dimensions, cutoff = 0.1)
  opt_points <- mds$points[[which(dimensions == opt_stress[1])]]
  new_distances <- dist(opt_points)
  plot(plotShepardPlot(as.vector(distances), as.vector(new_distances)))
  return(opt_points)
}
```

MDS ace vaxinpad

```{r}
mds_points_ace_vaxinpad <- optimizeMDS(ace_vaxinpad, dimensions)
dim(mds_points_ace_vaxinpad)
```