# Calculation of Pairwise Distances for Mixed-Type Data 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. ```r mdist(x, validate_x = NULL, response = NULL, distance_cont = "manhattan", distance_cat = "tot_var_dist", commensurable = TRUE, scaling_cont = "none", ncomp = ncol(x), threshold = NULL, preset = "custom") ``` ## Arguments - `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 `x`. If provided, distances are computed between observations in `validate_x` and `x`. Default is `NULL`. - `response`: An optional factor for supervised distance calculation in categorical variables, applied only if `distance_cat = "supervised"`. Default is `NULL`. - `distance_cont`: Character string specifying the distance metric for continuous variables. Options include `"manhattan"` (default) and `"euclidean"`. - `distance_cat`: Character string specifying the distance metric for categorical variables. Options include `"tot_var_dist"` (default), `"HL"`, `"HLeucl"`, `cat_dis`, `mca`, `st_dev`, `"matching"`, `"eskin"`, `"iof"`, `"of"`, `"goodall_3"`, `"goodall_4"`, `"gifi_chi2"`, `"lin"`, `"var_entropy"`, `"var_mutability"`, `"supervised"`, `"supervised_full"`, `"le_and_ho"` and all the options in the package philentropy. - `commensurable`: Logical. If `TRUE`, the function adjusts each variable's contribution to ensure equal average influence in the overall distance. Default is `FALSE`. - `scaling_cont`: Character string specifying the scaling method for continuous variables. Options include `"none"` (default), `"std"`, `"range"`, `"pc_scores"`, and `"robust"`. - `ncomp`: Integer specifying the number of components to retain when `scaling_cont = "pc_scores"`. Default is `ncol(x)`. - `threshold`: Numeric value specifying the percentage of variance explained by retained components when `scaling_cont = "pc_scores"`. Overrides `ncomp` if specified. Default is `NULL`. - `preset`: Character string specifying pre-defined combinations of arguments. Options include: * `"custom"` (default): Use specified distance metrics and parameters * `"gower"`: Gower's distance for mixed data * `"unbiased_dependent"`: Commensurable distance * `"euclidean_onehot"`: Euclidean distance on one-hot encoded categorical and standardized continuous ## Returns A matrix of pairwise distances. If `validate_x` is provided, rows correspond to validation observations and columns to training observations. ## Examples ```r 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_cont = "std") # Example 5: PCA-based scaling with threshold dist_pca <- mdist(x = tr_pengmix, validate_x = ts_pengmix, distance_cont = "euclidean", scaling_cont = "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_cont = "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") ``` ## References 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](https://arxiv.org/abs/2411.00429). ## See Also `cdist` for categorical-only distances, `ndist` for continuous-only distances

mdist function