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)

# 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
)

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

Contains comprehensive analysis for each variable pair including:

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

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)

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

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

1. Pairwise dataset creation - Extract all variable pairs with preprocessing
2. Tile pattern analysis - Divide variable space into 2×2 tiles and test for XOR-like distributions
3. Statistical validation - Apply χ² tests for independence and Wilcoxon tests for group differences
4. Correlation analysis - Compute class-wise Kendall τ to quantify relationship strength
5. 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

• 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]