Rank Principal Component Analysis for Mixed Data Types

Description

This function performs Principal Component Analysis (PCA) on datasets containing both categorical and continuous variables. It facilitates data preprocessing, encoding of categorical variables, and computes PCA to determine the optimal number of principal components based on a specified variance threshold. The function also computes composite indices for ranking observations.

Usage

rankPCA(data, range_cat_var, range_continuous_var, threshold)

Arguments

Value

A list containing PCA results and composite index.

References

Garai, S., & Paul, R. K. (2023). Development of MCS based-ensemble models using CEEMDAN decomposition and machine intelligence. Intelligent Systems with Applications, 18, 200202, https://doi.org/10.1016/j.iswa.2023.200202.

Examples

# Create a sample dataset
set.seed(123)
sample_data <- data.frame(
  Category1 = sample(c("A", "B", "C"), 100, replace = TRUE),
  Category2 = sample(c("X", "Y", "Z"), 100, replace = TRUE),
  Category3 = sample(c("M", "N", "O"), 100, replace = TRUE),
  Continuous1 = rnorm(100),
  Continuous2 = runif(100, min = 0, max = 100),
  Continuous3 = rnorm(100, mean = 50, sd = 10),
  Continuous4 = rpois(100, lambda = 5),
  Continuous5 = rbinom(100, size = 10, prob = 0.5)
)
result <- rankPCA(data = sample_data,
                  range_cat_var = 1:3,
                  range_continuous_var = 4:8,
                  threshold = 80)

# Access the results
eigenvalues_pca <- result$eigenvalues_pca
pca_max_dim <- result$pca_max_dim
coordinates <- result$coordinates
eigenvalues <- result$eigenvalues
weighted_coordinates <- result$weighted_coordinates
weighted_sums <- result$weighted_sums
composite_index <- result$composite_index
loading_vectors <- result$loading_vectors

Calculate Variable Ranking

Description

This function calculates the ranking of variables based on the sum of absolute values for each row of loading vectors.

Usage

variable_ranking(loading_vectors)

Arguments

Value

A data frame containing the ranked variables.

Examples

# Define row and column names
row_names <- c("Category1A", "Category1B", "Category1C", "Category2X", "Category2Y",
               "Category2Z", "Category3M", "Category3N", "Category3O", "Continuous1",
               "Continuous2", "Continuous3", "Continuous4", "Continuous5")

col_names <- paste0("PC", 1:8)

# Define the data matrix
loading_vectors <- matrix(c(
  0.199, 0.268, 0.189, 0.641, 0.092, 0.171, 0.079, -0.070,
  0.244, -0.371, 0.042, -0.426, 0.358, -0.070, 0.016, 0.371,
  -0.435, 0.099, -0.227, -0.216, -0.441, -0.100, -0.094, -0.294,
  0.087, -0.338, 0.458, 0.083, -0.515, -0.150, 0.007, 0.029,
  -0.473, 0.170, -0.164, 0.172, 0.296, 0.006, -0.044, 0.462,
  0.407, 0.155, -0.279, -0.261, 0.198, 0.141, 0.039, -0.510,
  0.101, -0.487, -0.465, 0.302, -0.117, 0.062, 0.036, 0.035,
  0.145, 0.546, 0.057, -0.211, -0.123, -0.325, 0.287, 0.191,
  -0.274, -0.003, 0.491, -0.134, 0.271, 0.272, -0.349, -0.245,
  0.290, 0.207, 0.001, -0.048, -0.250, -0.090, -0.275, 0.330,
  -0.134, 0.099, -0.277, -0.072, -0.180, 0.485, 0.134, 0.147,
  0.006, 0.051, -0.216, 0.007, 0.008, -0.278, -0.712, 0.004,
  0.320, 0.145, -0.061, 0.146, -0.078, 0.215, -0.414, 0.096,
  0.061, 0.044, 0.096, -0.271, -0.273, 0.603, -0.064, 0.245
), ncol = 8, byrow = TRUE)

# Assign row and column names
rownames(loading_vectors) <- row_names
colnames(loading_vectors) <- col_names

# Now you can use the loading_vectors variable in your code
print(loading_vectors)
# rank the variables
ranked_variables <- variable_ranking(loading_vectors)
print(ranked_variables)