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GitHub - JornLotsch/detectXOR

detectXOR: XOR pattern detection and visualization in R

Provides tools for detecting XOR-like patterns in variable pairs. Includes visualizations for pattern exploration.

Traditional feature selection methods often miss complex non-linear relationships where variables interact to produce class differences. The detectXOR package specifically targets XOR patterns - relationships where class discrimination only emerges through variable interactions, not individual variables alone.

🔍 XOR pattern detection - Statistical identification using χ² and Wilcoxon tests
📈 Correlation analysis - Class-wise Kendall τ coefficients
📊 Visualization - Spaghetti plots and decision boundary visualizations
⚡ Parallel processing - Multi-core acceleration for large datasets
🔬 Robust statistics - Winsorization and scaling options for outlier handling

The R libary can be found on The Comprehensive R Archive Network at https://cran.r-project.org/package=detectXOR

Install the libary from CRAN:

# Install detectXOR
install.packages("detectXOR")

The package requires R ≥ 3.5.0 and depends on:

dplyr, tibble (data manipulation)
ggplot2, ggh4x, scales (visualization)
future, future.apply, pbmcapply, parallel (parallel processing)
reshape2, glue (data processing and string manipulation)
DescTools (statistical tools)
Base R packages: stats, utils, methods, grDevices

Optional packages (suggested):

testthat, knitr, rmarkdown (development and documentation)
doParallel, foreach (additional parallel processing options)

library(detectXOR)
# Load example data
data(XOR_data)
# Detect XOR patterns with default settings
results <- detectXOR(XOR_data, class_col = "class")
# View summary
print(results$results_df)

Usage with custom parameters

# Detection with custom thresholds and parallel processing
results <- detect_xor(
  data = XOR_data,
  class_col = "class",
  p_threshold = 0.01,
  tau_threshold = 0.4,
  max_cores = 4,
  extreme_handling = "winsorize",
  scale_data = TRUE
)

detectXOR() - Main detection function Parameter Type Default Description data data.frame required Input dataset with variables and class column class_col character "class" Name of the class/target variable column check_tau logical TRUE Compute class-wise Kendall τ correlations compute_axes_parallel_significance logical TRUE Perform group-wise Wilcoxon tests p_threshold numeric 0.05 Significance threshold for statistical tests tau_threshold numeric 0.3 Minimum absolute τ for "strong" correlation abs_diff_threshold numeric 20 Minimum absolute difference for practical significance split_method character "quantile" Tile splitting method: "quantile" or "range" max_cores integer NULL Maximum cores for parallel processing (auto-detect if NULL) extreme_handling character "winsorize" Outlier handling: "winsorize", "remove", or "none" winsor_limits numeric vector c(0.05, 0.95) Winsorization percentiles scale_data logical TRUE Standardize variables before analysis use_complete logical TRUE Use only complete cases (remove NA values)

The detectXOR() function returns a list with two components:

results_df - Summary data frame Column Description var1, var2 Variable pair names xor_shape_detected Logical: XOR pattern identified chi_sq_p_value χ² test p-value for tile independence tau_class_0, tau_class_1 Class-wise Kendall τ coefficients tau_difference Absolute difference between class τ values wilcox_p_x, wilcox_p_y Wilcoxon test p-values for each axis significant_wilcox Logical: significant group differences detected pair_list - Detailed results

Contains comprehensive analysis for each variable pair including:

Tile pattern analysis results
Statistical test outputs
Processed data subsets
Intermediate calculations

Function Description Key Parameters generate_spaghetti_plot_from_results() Creates connected line plots showing variable trajectories for XOR-detected pairs results, data, class_col, scale_data = TRUE generate_xy_plot_from_results() Generates scatter plots with decision boundary lines for detected XOR patterns results, data, class_col, scale_data = TRUE, quantile_lines = c(1/3, 2/3), line_method = "quantile"

Both functions return ggplot objects that can be displayed or saved manually.

# Generate plots
generate_spaghetti_plot_from_results(results, XOR_data) 
generate_xy_plot_from_results(results, XOR_data)

Function Description Key Parameters generate_xor_reportConsole() Creates console-friendly formatted report with optional plots results, data, class_col, scale_data = TRUE, show_plots = TRUE generate_xor_reportHTML() Generates comprehensive HTML report with interactive elements results, data, class_col, output_file, open_browser = TRUE

# Generate formatted report 
generate_xor_reportHTML(results, XOR_data, class_col = "class")

The report will be automaticlaly opened in the system standard web browser.

Pairwise dataset creation - Extract all variable pairs with preprocessing
Tile pattern analysis - Divide variable space into 2×2 tiles and test for XOR-like distributions
Statistical validation - Apply χ² tests for independence and Wilcoxon tests for group differences
Correlation analysis - Compute class-wise Kendall τ to quantify relationship strength
Result aggregation - Combine findings into interpretable summary format

χ² Test: Tests independence of tile patterns vs. random distribution
Wilcoxon rank sum: Evaluates group differences along variable axes
Kendall τ: Measures monotonic correlation within each class separately

Feature selection enhancement - Identify interaction features that complement traditional univariate methods
Variable interaction discovery - Find synergistic variable pairs where class separation emerges only through combined effects
Preprocessing for ensemble methods - Generate interaction features for boosting algorithms and neural networks
Dimensionality reduction guidance - Preserve important variable interactions when reducing feature space

Cross-platform compatibility

Windows: Uses future::multisession for parallel processing
Unix/Linux/macOS: Uses pbmcapply::pbmclapply with fork-based parallelism
Memory management: Automatic chunk-based processing for large datasets

detectXOR/
├── R/                 # Package source code
├── man/               # Package documentation
├── data/              # Example dataset
├── issues/            # Problem reporting
└── analyses/          # Files used to generate or plot publictaion data sets (not in library)

This project is licensed under the GNU General Public License v3.0 (GPL-3.0)

Lötsch, J, Kringel D & Ultsch A. (2025). Generalized extended OR (XOR) pattern discovery: Accurate predictors without statistical significance in multivariate data. [submitted]

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