Customer Spending Analysis with R

This project analyzes customer spending behavior using R, employing concepts like normalization, similarity computation, matrix transformation, and eigenvalue analysis. The process includes graphical visualizations to gain insights into the data.

Overview

The analysis is divided into the following steps:

1. Normalization: Scale customer spending vectors to unit length.
2. Similarity (Dot Product): Calculate similarity between customers based on spending patterns.
3. Transformation (Matrix Multiplication): Transform data for feature extraction.
4. Eigenvalues Analysis: Analyze principal components for dimensionality reduction.

R Code

The R script performs the following:

• Normalizes the data.
• Computes pairwise similarities between customers.
• Performs matrix transformation.
• Calculates eigenvalues and eigenvectors for variance analysis.
• Generates plots for visual interpretation.

Required Libraries

• ggplot2 for graphical outputs.

Script

# Load necessary libraries
library(ggplot2)

# Input Data: Customer spending habits
customers <- data.frame(
  Customer = c("A", "B", "C"),
  Product1 = c(2, 3, 5),
  Product2 = c(4, 6, 7),
  Product3 = c(6, 9, 8)
)

# 1. Normalize Spending
normalize <- function(vec) {
  return(vec / sqrt(sum(vec^2)))
}
customers_norm <- data.frame(
  Customer = customers$Customer,
  t(apply(customers[,-1], 1, normalize))
)
colnames(customers_norm)[-1] <- paste0("Normalized_", colnames(customers)[-1])

# 2. Calculate Similarity (Dot Product)
dot_product <- function(vec1, vec2) {
  return(sum(vec1 * vec2))
}
similarity_matrix <- matrix(0, nrow = nrow(customers), ncol = nrow(customers))
rownames(similarity_matrix) <- customers$Customer
colnames(similarity_matrix) <- customers$Customer

for (i in 1:nrow(customers)) {
  for (j in 1:nrow(customers)) {
    similarity_matrix[i, j] <- dot_product(
      as.numeric(customers[i, -1]),
      as.numeric(customers[j, -1])
    )
  }
}

# 3. Transformation (Matrix Multiplication)
weights <- matrix(c(1, 0, 0, 1, 1, 1), nrow = 3)
transformed_data <- as.matrix(customers[,-1]) %*% weights
colnames(transformed_data) <- c("Feature1", "Feature2")

# 4. Eigenvalues of Covariance Matrix
cov_matrix <- cov(as.matrix(customers[,-1]))
eigenvalues <- eigen(cov_matrix)$values
eigenvectors <- eigen(cov_matrix)$vectors

# Graphical Outputs

# a. Plot normalized data
norm_plot <- ggplot(customers_norm, aes(x = Normalized_Product1, y = Normalized_Product2, color = Customer)) +
  geom_point(size = 3) +
  theme_minimal() +
  labs(title = "Normalized Spending (Product1 vs Product2)", x = "Product1", y = "Product2")
print(norm_plot)

# b. Heatmap for Similarity Matrix
heatmap(similarity_matrix, Rowv = NA, Colv = NA, col = heat.colors(256), scale = "none", main = "Customer Similarity")

# c. Bar plot of Eigenvalues
eigen_plot <- ggplot(data.frame(Eigenvalues = eigenvalues, Component = 1:length(eigenvalues)), aes(x = Component, y = Eigenvalues)) +
  geom_bar(stat = "identity", fill = "skyblue") +
  theme_minimal() +
  labs(title = "Eigenvalues of Covariance Matrix", x = "Component", y = "Eigenvalue")
print(eigen_plot)

Outputs

1. Normalized Spending

A scatter plot displaying normalized spending patterns of customers on Product1 and Product2.

2. Similarity Matrix

A heatmap showing the similarity scores between customers based on their spending.

3. Eigenvalues Analysis

A bar plot representing the eigenvalues of the covariance matrix, indicating the variance explained by each component.

Insights

1. Normalized Spending:

   • Customer C dominates normalized spending.
   • Helps in fair comparison of spending behavior.

2. Customer Similarity:

   • Customers B and C are closely related.
   • Customer A shows distinct spending behavior.

3. Eigenvalues Analysis:

   • The first principal component explains most of the variance.
   • Dimensionality reduction is feasible.

How to Use

1. Clone the repository.
2. Install R and required libraries (ggplot2).
3. Run the provided R script.
4. Analyze the generated plots for insights.

Contact

For queries, reach out to TannuWorks at agapaitanveermou@gmail.com.