| Title: | Unbiased Distances for Mixed-Type Data |
|---|---|
| Description: | A comprehensive framework for calculating unbiased distances in datasets containing mixed-type variables (numerical and categorical). The package implements a general formulation that ensures multivariate additivity and commensurability, meaning that variables contribute equally to the overall distance regardless of their type, scale, or distribution. Supports multiple distance measures including Gower's distance, Euclidean distance, Manhattan distance, and various categorical variable distances such as simple matching, Eskin, occurrence frequency, and association-based distances. Provides tools for variable scaling (standard deviation, range, robust range, and principal component scaling), and handles both independent and association-based category dissimilarities. Implements methods to correct for biases that typically arise from different variable types, distributions, and number of categories. Particularly useful for cluster analysis, data visualization, and other distance-based methods when working with mixed data. Methods based on van de Velden et al. (2024) <doi:10.48550/arXiv.2411.00429> "Unbiased mixed variables distance". |
| Authors: | Alfonso Iodice D'Enza [aut], Angelos Markos [aut, cre], Michel van de Velden [aut], Carlo Cavicchia [aut] |
| Maintainer: | Angelos Markos <[email protected]> |
| License: | GPL-3 |
| Version: | 0.4.3 |
| Built: | 2025-02-13 07:07:30 UTC |
| Source: | https://github.com/cran/manydist |
Computes a distance matrix for categorical variables with support for validation data, multiple distance metrics, and variable weighting. The function implements various distance calculation approaches as described in van de Velden et al. (2024), including commensurable distances and supervised options when response variable is provided.
cdist(x, response = NULL, validate_x = NULL, method = "tot_var_dist", commensurable = FALSE, weights = 1)cdist(x, response = NULL, validate_x = NULL, method = "tot_var_dist", commensurable = FALSE, weights = 1)
x |
A data frame or matrix of categorical variables (factors). |
response |
Optional response variable for supervised distance calculations. Default is |
validate_x |
Optional validation data frame or matrix. If provided, distances are computed between observations in |
method |
Character string or vector specifying the distance metric(s). Options include:
Can be a single string or vector for different methods per variable. |
commensurable |
Logical. If |
weights |
Numeric vector or matrix of weights. If vector, must have length equal to number of variables. If matrix, must match the dimension of level-wise distances. Default is 1 (equal weighting). |
The cdist function provides a comprehensive framework for categorical distance calculations:
Supports multiple distance calculation methods that can be specified globally or per variable
Handles validation data through validate_x parameter
Implements supervised distances when response variable is provided
Supports commensurable distances for better comparability across variables
Provides flexible weighting schemes at variable and level granularity
Important notes:
Input variables are automatically converted to factors with dropped unused levels
Different methods per variable is not supported for "none", "st_dev", "HL", "cat_dis", "HLeucl", "mca"
Weight vector length must match the number of variables when specified as a vector
Variables should be factors; numeric variables will cause errors
A list containing:
distance_mat |
Matrix of pairwise distances. If |
delta |
Matrix or list of matrices containing level-wise distances for each variable. |
delta_names |
Vector of level names used in the delta matrices. |
van de Velden, M., Iodice D'Enza, A., Markos, A., Cavicchia, C. (2024). (Un)biased distances for mixed-type data. arXiv preprint. Retrieved from https://arxiv.org/abs/2411.00429.
mdist for mixed-type data distances, ndist for continuous data distances
library(palmerpenguins) library(rsample) # Prepare data with complete cases for both categorical variables and response complete_vars <- c("species", "island", "sex", "body_mass_g") penguins_complete <- penguins[complete.cases(penguins[, complete_vars]), ] penguins_cat <- penguins_complete[, c("species", "island", "sex")] response <- penguins_complete$body_mass_g # Create training-test split set.seed(123) penguins_split <- initial_split(penguins_cat, prop = 0.8) tr_penguins <- training(penguins_split) ts_penguins <- testing(penguins_split) response_tr <- response[penguins_split$in_id] response_ts <- response[-penguins_split$in_id] # Basic usage result <- cdist(tr_penguins) # With validation data val_result <- cdist(x = tr_penguins, validate_x = ts_penguins, method = "tot_var_dist") # ...and commensurability val_result_COMM <- cdist(x = tr_penguins, validate_x = ts_penguins, method = "tot_var_dist", commensurable = TRUE) # Supervised distance with response variable sup_result <- cdist(x = tr_penguins, response = response_tr, method = "supervised") # Supervised with validation data sup_val_result <- cdist(x = tr_penguins, validate_x = ts_penguins, response = response_tr, method = "supervised") # Commensurable distances with custom weights comm_result <- cdist(tr_penguins, commensurable = TRUE, weights = c(2, 1, 1)) # Different methods per variable multi_method <- cdist(tr_penguins, method = c("matching", "goodall_3", "tot_var_dist"))library(palmerpenguins) library(rsample) # Prepare data with complete cases for both categorical variables and response complete_vars <- c("species", "island", "sex", "body_mass_g") penguins_complete <- penguins[complete.cases(penguins[, complete_vars]), ] penguins_cat <- penguins_complete[, c("species", "island", "sex")] response <- penguins_complete$body_mass_g # Create training-test split set.seed(123) penguins_split <- initial_split(penguins_cat, prop = 0.8) tr_penguins <- training(penguins_split) ts_penguins <- testing(penguins_split) response_tr <- response[penguins_split$in_id] response_ts <- response[-penguins_split$in_id] # Basic usage result <- cdist(tr_penguins) # With validation data val_result <- cdist(x = tr_penguins, validate_x = ts_penguins, method = "tot_var_dist") # ...and commensurability val_result_COMM <- cdist(x = tr_penguins, validate_x = ts_penguins, method = "tot_var_dist", commensurable = TRUE) # Supervised distance with response variable sup_result <- cdist(x = tr_penguins, response = response_tr, method = "supervised") # Supervised with validation data sup_val_result <- cdist(x = tr_penguins, validate_x = ts_penguins, response = response_tr, method = "supervised") # Commensurable distances with custom weights comm_result <- cdist(tr_penguins, commensurable = TRUE, weights = c(2, 1, 1)) # Different methods per variable multi_method <- cdist(tr_penguins, method = c("matching", "goodall_3", "tot_var_dist"))
The fifa_nl dataset contains information on players in the Dutch League from the FIFA 21 video game. This dataset includes various attributes of players, such as demographics, club details, skill ratings, and physical characteristics.
data("fifa_nl")data("fifa_nl")
A data frame with observations on various attributes describing the players.
player_positionsPrimary playing positions of the player.
nationalityThe country the player represents.
team_positionPlayer's assigned position within their club.
club_nameName of the club the player is part of.
work_rateThe player's work rate, describing defensive and attacking intensity.
weak_footSkill rating for the player's non-dominant foot, ranging from 1 to 5.
skill_movesSkill moves rating, indicating technical skill and ability to perform complex moves, on a scale of 1 to 5.
international_reputationPlayer's reputation on an international scale, from 1=local to 3=global star.
body_typeBody type of the player ( Lean, Normal, Stocky.
preferred_footDominant foot of the player, either Left or Right.
ageAge of the player in years.
height_cmHeight of the player in centimeters.
weight_kgWeight of the player in kilograms.
overallOverall skill rating of the player out of 100.
potentialPotential skill rating the player may achieve in the future.
value_eurEstimated market value of the player in Euros.
wage_eurPlayer's weekly wage in Euros.
release_clause_eurRelease clause value in Euros, which other clubs must pay to buy out the player's contract.
paceSpeed rating of the player out of 100.
shootingShooting skill rating out of 100.
passingPassing skill rating out of 100.
dribblingDribbling skill rating out of 100.
defendingDefending skill rating out of 100.
physicPhysicality rating out of 100.
This dataset provides a snapshot of player attributes and performance indicators as represented in FIFA 21 for players in the Dutch League. It can be used to analyze player characteristics, compare skills across players, and explore potential relationships among variables such as age, position, and various skill ratings.
Stefano Leone. (2021). FIFA 21 Complete Player Dataset. Retrieved from https://www.kaggle.com/datasets/stefanoleone992/fifa-21-complete-player-dataset.
data(fifa_nl) summary(fifa_nl)data(fifa_nl) summary(fifa_nl)
Computes pairwise distances between observations described by numeric and/or categorical attributes, with support for validation data. The function provides options for computing independent, dependent, and practice-based distances as defined in van de Velden et al. (2024), with support for various continuous and categorical distance metrics, scaling, and commensurability adjustments.
mdist(x, validate_x = NULL, response = NULL, distance_cont = "manhattan", distance_cat = "tot_var_dist", commensurable = FALSE, scaling = "none", ncomp = ncol(x), threshold = NULL, preset = "custom")mdist(x, validate_x = NULL, response = NULL, distance_cont = "manhattan", distance_cat = "tot_var_dist", commensurable = FALSE, scaling = "none", ncomp = ncol(x), threshold = NULL, preset = "custom")
x |
A dataframe or tibble containing continuous (coded as numeric), categorical (coded as factors), or mixed-type variables. |
validate_x |
Optional validation data with the same structure as |
response |
An optional factor for supervised distance calculation in categorical variables, applied only if |
distance_cont |
Character string specifying the distance metric for continuous variables. Options include |
distance_cat |
Character string specifying the distance metric for categorical variables. Options include |
commensurable |
Logical. If |
scaling |
Character string specifying the scaling method for continuous variables. Options include |
ncomp |
Integer specifying the number of components to retain when |
threshold |
Numeric value specifying the percentage of variance explained by retained components when |
preset |
Character string specifying pre-defined combinations of arguments. Options include:
|
A matrix of pairwise distances. If validate_x is provided, rows correspond to validation observations and columns to training observations.
van de Velden, M., Iodice D'Enza, A., Markos, A., Cavicchia, C. (2024). (Un)biased distances for mixed-type data. arXiv preprint. Retrieved from https://arxiv.org/abs/2411.00429.
cdist for categorical-only distances, ndist for continuous-only distances
library(palmerpenguins) library(rsample) # Prepare complete data pengmix <- palmerpenguins::penguins[complete.cases(palmerpenguins::penguins), ] # Create training-test split set.seed(123) pengmix_split <- initial_split(pengmix, prop = 0.8) tr_pengmix <- training(pengmix_split) ts_pengmix <- testing(pengmix_split) # Example 1: Basic usage with validation data dist_matrix <- mdist(x = tr_pengmix, validate_x = ts_pengmix) # Example 2: Gower preset with validation dist_gower <- mdist(x = tr_pengmix, validate_x = ts_pengmix, preset = "gower", commensurable = TRUE) # Example 3: Euclidean one-hot preset with validation dist_onehot <- mdist(x = tr_pengmix, validate_x = ts_pengmix, preset = "euclidean_onehot") # Example 4: Custom preset with standardization dist_custom <- mdist(x = tr_pengmix, validate_x = ts_pengmix, preset = "custom", distance_cont = "manhattan", distance_cat = "matching", commensurable = TRUE, scaling = "std") # Example 5: PCA-based scaling with threshold dist_pca <- mdist(x = tr_pengmix, validate_x = ts_pengmix, distance_cont = "euclidean", scaling = "pc_scores", threshold = 0.85) # Example 6: Categorical variables only cat_vars <- c("species", "island", "sex") dist_cat <- mdist(tr_pengmix[, cat_vars], validate_x = ts_pengmix[, cat_vars], distance_cat = "tot_var_dist") # Example 7: Continuous variables only num_vars <- c("bill_length_mm", "bill_depth_mm", "flipper_length_mm", "body_mass_g") dist_cont <- mdist(tr_pengmix[, num_vars], validate_x = ts_pengmix[, num_vars], distance_cont = "manhattan", scaling = "std") # Example 8: Supervised distance with response response_tr <- tr_pengmix$body_mass_g dist_sup <- mdist(tr_pengmix, validate_x = ts_pengmix, response = response_tr, distance_cat = "supervised")library(palmerpenguins) library(rsample) # Prepare complete data pengmix <- palmerpenguins::penguins[complete.cases(palmerpenguins::penguins), ] # Create training-test split set.seed(123) pengmix_split <- initial_split(pengmix, prop = 0.8) tr_pengmix <- training(pengmix_split) ts_pengmix <- testing(pengmix_split) # Example 1: Basic usage with validation data dist_matrix <- mdist(x = tr_pengmix, validate_x = ts_pengmix) # Example 2: Gower preset with validation dist_gower <- mdist(x = tr_pengmix, validate_x = ts_pengmix, preset = "gower", commensurable = TRUE) # Example 3: Euclidean one-hot preset with validation dist_onehot <- mdist(x = tr_pengmix, validate_x = ts_pengmix, preset = "euclidean_onehot") # Example 4: Custom preset with standardization dist_custom <- mdist(x = tr_pengmix, validate_x = ts_pengmix, preset = "custom", distance_cont = "manhattan", distance_cat = "matching", commensurable = TRUE, scaling = "std") # Example 5: PCA-based scaling with threshold dist_pca <- mdist(x = tr_pengmix, validate_x = ts_pengmix, distance_cont = "euclidean", scaling = "pc_scores", threshold = 0.85) # Example 6: Categorical variables only cat_vars <- c("species", "island", "sex") dist_cat <- mdist(tr_pengmix[, cat_vars], validate_x = ts_pengmix[, cat_vars], distance_cat = "tot_var_dist") # Example 7: Continuous variables only num_vars <- c("bill_length_mm", "bill_depth_mm", "flipper_length_mm", "body_mass_g") dist_cont <- mdist(tr_pengmix[, num_vars], validate_x = ts_pengmix[, num_vars], distance_cont = "manhattan", scaling = "std") # Example 8: Supervised distance with response response_tr <- tr_pengmix$body_mass_g dist_sup <- mdist(tr_pengmix, validate_x = ts_pengmix, response = response_tr, distance_cat = "supervised")
Computes a distance matrix for continuous data with support for multiple distance metrics, scaling methods, dimensionality reduction, and validation data. The function implements various distance calculation approaches as described in van de Velden et al. (2024), including options for commensurable distances and variable weighting.
ndist(x, validate_x = NULL, commensurable = FALSE, method = "manhattan", sig = NULL, scaling = "none", ncomp = ncol(x), threshold = NULL, weights = rep(1, ncol(x)))ndist(x, validate_x = NULL, commensurable = FALSE, method = "manhattan", sig = NULL, scaling = "none", ncomp = ncol(x), threshold = NULL, weights = rep(1, ncol(x)))
x |
A data frame or matrix of continuous input variables. |
validate_x |
Optional data frame or matrix for validation data. If provided, distances are computed between observations in |
commensurable |
Logical. If |
method |
Character string specifying the distance metric. Options include |
sig |
Covariance matrix to be used when |
scaling |
Character string specifying the scaling method. Options:
Default is |
ncomp |
Number of principal components to retain when |
threshold |
Proportion of variance to retain when |
weights |
Numeric vector of weights for each variable. Must have length equal to the number of variables in |
The ndist function provides a comprehensive framework for distance calculations in continuous data:
When validate_x is provided, computes distances between observations in validate_x and x.
Supports multiple scaling methods that can be applied before distance calculation.
PCA-based dimensionality reduction can be controlled either by number of components or variance threshold.
For Mahalanobis distance, handles singular covariance matrices with appropriate error messages.
Implements commensurable distances for better comparability across variables.
Warning: The function validates:
Weight vector length must match the number of variables
Covariance matrix singularity for Mahalanobis distance
Compatibility of x and validate_x dimensions
A distance matrix where element [i,j] represents the distance between:
observation i and j of x if validate_x is NULL
observation i of validate_x and observation j of x if validate_x is provided
van de Velden, M., Iodice D'Enza, A., Markos, A., Cavicchia, C. (2024). (Un)biased distances for mixed-type data. arXiv preprint. Retrieved from https://arxiv.org/abs/2411.00429.
mdist for mixed-type data distances, cdist for categorical data distances.
library(palmerpenguins) library(rsample) penguins_cont <- palmerpenguins::penguins[, c("bill_length_mm", "bill_depth_mm", "flipper_length_mm", "body_mass_g")] penguins_cont <- penguins_cont[complete.cases(penguins_cont), ] # Basic usage dist_matrix <- ndist(penguins_cont) # Commensurable distances with standardization dist_matrix <- ndist(penguins_cont, commensurable = TRUE, scaling = "std") # PCA-based dimensionality reduction dist_matrix <- ndist(penguins_cont, scaling = "pc_scores", threshold = 0.95) # Mahalanobis distance dist_matrix <- ndist(penguins_cont, method = "mahalanobis") # Weighted Euclidean distance dist_matrix <- ndist(penguins_cont, method = "euclidean", weights = c(1, 0.5, 2, 1)) # Training-test split example with validation data set.seed(123) # Create training-test split using rsample penguins_split <- initial_split(penguins_cont, prop = 0.8) tr_penguins <- training(penguins_split) ts_penguins <- testing(penguins_split) # Basic usage with training data only dist_matrix <- ndist(tr_penguins) # Computing distances between test and training sets val_dist_matrix <- ndist(x = tr_penguins, validate_x = ts_penguins, method = "euclidean") # Using validation data with standardization val_dist_matrix_std <- ndist(x = tr_penguins, validate_x = ts_penguins, scaling = "std", method = "manhattan") # Validation with PCA and commensurability val_dist_matrix_pca <- ndist(x = tr_penguins, validate_x = ts_penguins, scaling = "pc_scores", ncomp = 2, commensurable = TRUE) # Validation with robust scaling and custom weights val_dist_matrix_robust <- ndist(x = tr_penguins, validate_x = ts_penguins, scaling = "robust", weights = c(1, 0.5, 2, 1)) # Mahalanobis distance with validation data val_dist_matrix_mahal <- ndist(x = tr_penguins, validate_x = ts_penguins, method = "mahalanobis")library(palmerpenguins) library(rsample) penguins_cont <- palmerpenguins::penguins[, c("bill_length_mm", "bill_depth_mm", "flipper_length_mm", "body_mass_g")] penguins_cont <- penguins_cont[complete.cases(penguins_cont), ] # Basic usage dist_matrix <- ndist(penguins_cont) # Commensurable distances with standardization dist_matrix <- ndist(penguins_cont, commensurable = TRUE, scaling = "std") # PCA-based dimensionality reduction dist_matrix <- ndist(penguins_cont, scaling = "pc_scores", threshold = 0.95) # Mahalanobis distance dist_matrix <- ndist(penguins_cont, method = "mahalanobis") # Weighted Euclidean distance dist_matrix <- ndist(penguins_cont, method = "euclidean", weights = c(1, 0.5, 2, 1)) # Training-test split example with validation data set.seed(123) # Create training-test split using rsample penguins_split <- initial_split(penguins_cont, prop = 0.8) tr_penguins <- training(penguins_split) ts_penguins <- testing(penguins_split) # Basic usage with training data only dist_matrix <- ndist(tr_penguins) # Computing distances between test and training sets val_dist_matrix <- ndist(x = tr_penguins, validate_x = ts_penguins, method = "euclidean") # Using validation data with standardization val_dist_matrix_std <- ndist(x = tr_penguins, validate_x = ts_penguins, scaling = "std", method = "manhattan") # Validation with PCA and commensurability val_dist_matrix_pca <- ndist(x = tr_penguins, validate_x = ts_penguins, scaling = "pc_scores", ncomp = 2, commensurable = TRUE) # Validation with robust scaling and custom weights val_dist_matrix_robust <- ndist(x = tr_penguins, validate_x = ts_penguins, scaling = "robust", weights = c(1, 0.5, 2, 1)) # Mahalanobis distance with validation data val_dist_matrix_mahal <- ndist(x = tr_penguins, validate_x = ts_penguins, method = "mahalanobis")