Assignment 4

Load libraries

library(tidyverse)
library(jpeg)  # For reading JPEG files
library(reshape2)  # For data manipulation
library(pracma)  # For eigenvector calculation
library(OpenImageR)

Read the data

file_paths <- list.files(
  path = "C:/Users/akpla/Documents/data605/Assignment_4/jpg",
  pattern = "*.jpg", full.names = TRUE)

images <- lapply(file_paths, readJPEG)

Flatten images into vectors

image_vectors <- lapply(images, function(x) {
  as.vector(x)
})

Calculate covariance matrix

image_matrix <- matrix(unlist(image_vectors),
                       nrow = length(image_vectors[[1]]))

cor_matrix <- cor(scale(image_matrix, center = TRUE, scale = TRUE))

Compute eigenvectors and eigenvalues

eigen_res <- eigen(cor_matrix)

Select top eigenvectors capturing 80% of the variability

total_variance <- sum(eigen_res$values)
cumulative_variance <- cumsum(eigen_res$values) / total_variance
num_eigenvectors <- which.max(cumulative_variance >= 0.8)
num_eigenvectors

## [1] 3

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