90  Week Ten Practical

Agenda

Review Introduction.

Review Clustering.

Review Dimensionality reduction.

Practice cluster analysis

Review Ensemble methods.

Demonstration of Neural Networks.

Practical demonstration - SCO 2023-24.

90.1 Cluster analysis - practice

Download the dataset available here:

rm(list=ls())
df <- read.csv('https://www.dropbox.com/scl/fi/8sf5s4uloq8rgu0tbf45y/sco_prem_2024.csv?rlkey=qvoewxn2nd1f6clqbwo0aib7f&dl=1')

Take some time to figure out what the variables might reflect.

Use the following code to select the variables you wish to explore via cluster analysis, and scale those variables.

# For example....

selected_data <- scale(df[, c("home_team_win_ratio", "away_team_win_ratio", "home_team_points_ratio", "away_team_points_ratio")])

Now, conduct a k-means cluster analysis using k=3.

  • First, conduct the cluster analysis.

  • Then, create a PCA analysis for dimensionality reduction.

  • Create a dataframe with the principal components and cluster assignment.

  • Plot the first two PC components.

  • Assign cluster allocation to the observations in the original dataset.

  • Review the gap score to check the optimum number of clusters.

  • Repeat the cluster analysis with an alternative number of clusters (k), based on the gap score.

  • Finally, review the cluster allocations. What do they tell you about the observations?

show solution 
k <- 3

set.seed(123)

#-----------------------
# Perform cluster analysis
#-----------------------

clusters <- kmeans(selected_data, centers = k, nstart = 25)
#-----------------------
# Perform PCA
#-----------------------
pca_result <- prcomp(selected_data)

#-----------------------
# Create data frame with PCs and cluster assignments
pca_data <- data.frame(pca_result$x[, 1:2], Cluster = clusters$cluster)

#-----------------------
# Plotting the first two principal components
#-----------------------
plot(pca_data[,1], pca_data[,2], col = pca_data$Cluster, pch = 20, xlab = "Principal Component 1", ylab = "Principal Component 2", main = "K-Means Clustering with PCA")

points(clusters$centers[, 1:2], col = 1:k, pch = 8, cex = 2)

show solution 
#-----------------------
# Check n clusters
#-----------------------
library(cluster)
gap_stat <- clusGap(selected_data, FUN = kmeans, nstart = 25, K.max = 10, B = 50)
plot(gap_stat, main = "Plot of Gap Statistic")

#-----------------------
# Adding the cluster assignments to the original dataframe
#-----------------------
df$Cluster <- clusters$cluster

#-----------------------
# Examine features of the clusters
#-----------------------
library(ggplot2)

show solution 
# Using ggplot2 to plot home_team_win_ratio by cluster
ggplot(data = df, aes(x = Cluster, y = home_team_win_ratio, group = Cluster)) +
  geom_point() +  # Add points
  geom_line() +   # Connect points within each cluster with lines
  theme_minimal() +  # Use a minimal theme
  labs(x = "Cluster", y = "Home Team Win Ratio", title = "Home Team Win Ratio by Cluster")

show solution 
# Create scatter plot
ggplot(data = df, aes(x = home_team_win_ratio, y = away_team_win_ratio, color = factor(Cluster))) +
  geom_point() +
  labs(x = "Home Team Win Ratio", y = "Away Team Win Ratio", color = "Cluster") +
  theme_minimal()

show solution 
# Load the ggplot2 package
library(ggplot2)

# Create the scatter plot with labels
ggplot(data = df, aes(x = home_team_win_ratio, y = away_team_win_ratio, color = factor(Cluster))) +
  geom_point() +
  geom_label(aes(label = result_category), nudge_y = 0.02, nudge_x = 0.02) +  # Nudge positions labels slightly to avoid overlap
  labs(x = "Home Team Win Ratio", y = "Away Team Win Ratio", color = "Cluster") +
  theme_minimal()