Introduction

Overview

The Clustermatch Correlation Coefficient (CCC) is a highly-efficient, next-generation correlation coefficient that captures not-only-linear relationships and can work on numerical and categorical data types. CCC-GPU is a GPU-accelerated implementation that provides significant performance improvements for large-scale datasets using CUDA.

CCC is based on the simple idea of clustering data points and then computing the Adjusted Rand Index (ARI) between the two clusterings. It is a robust and efficient method that can detect linear and non-linear relationships, making it suitable for a wide range of applications in genomics, machine learning, and data science.

Key Features

  • Non-linear Correlation Detection: Unlike traditional correlation methods, CCC can capture complex non-linear relationships

  • Mixed Data Type Support: Seamlessly handles numerical and categorical data in the same analysis

  • GPU Acceleration: CUDA-powered implementation provides 16x-74x speedups over CPU versions

  • Scalable: Efficiently processes large genomics datasets with 20k+ features

  • Robust: Handles edge cases and provides stable results across different data distributions

  • Easy Integration: Simple API compatible with existing scientific Python workflows

Scientific Applications

CCC-GPU is particularly valuable for:

Genomics and Bioinformatics

  • Gene expression correlation analysis

  • Multi-omics data integration

  • Biomarker discovery

  • Pathway analysis

Machine Learning

  • Feature selection and dimensionality reduction

  • Data preprocessing for complex datasets

  • Non-linear dependency detection

  • Mixed-type data analysis

General Data Science

  • Exploratory data analysis

  • Complex pattern recognition

  • Time series analysis with non-linear trends

  • Social network analysis

Performance Benchmarks

CCC-GPU provides significant performance improvements over CPU-only implementations:

Performance Comparison (CCC-GPU vs. CCC with 12 CPU cores)

Number of Genes

Speedup Factor

500

16.52×

1,000

30.65×

2,000

45.72×

4,000

59.46×

6,000

67.46×

8,000

71.48×

10,000

72.38×

16,000

73.83×

20,000

73.88×

Benchmarks performed on synthetic gene expression data with 1000 fixed samples. Hardware: AMD Ryzen Threadripper 7960X CPU and NVIDIA RTX 4090 GPU.

The performance scaling demonstrates that CCC-GPU is particularly effective for large-scale datasets commonly encountered in genomics research.

Why CCC?

Traditional correlation measures like Pearson and Spearman correlation have limitations:

  • Pearson correlation: Only detects linear relationships

  • Spearman correlation: Limited to monotonic relationships

  • Mutual information: Requires careful binning and parameter tuning

CCC addresses these limitations by:

  1. Adaptive Clustering: Uses quantile-based clustering that adapts to data distribution

  2. Multiple Scales: Tests different numbers of clusters to capture relationships at various scales

  3. Robust Statistics: Based on the Adjusted Rand Index, which is corrected for chance

  4. Parameter-free: Requires minimal parameter tuning for most applications

Technical Innovation

The GPU implementation leverages several technical innovations:

  • CUDA Kernel Optimization: Custom kernels for ARI computation and maximum finding

  • Memory Hierarchy Utilization: Strategic use of GPU memory hierarchy for performance

  • Parallel Algorithm Design: Efficient parallelization of inherently sequential algorithms

  • Memory Management: Advanced memory management using Thrust and CUB libraries

Project Structure

This repository contains:

  • CCC-GPU Library (libs/ccc/): Main Python package with GPU and CPU implementations

  • CUDA Extension (libs/ccc_cuda_ext/): Low-level CUDA implementation with pybind11 bindings

  • Comprehensive Testing: Extensive test suites for validation and benchmarking

  • Analysis Notebooks: Real-world examples and research applications

  • Documentation: Complete usage guides and algorithm explanations

Getting Started

To get started with CCC-GPU, follow the Installation guide and then explore the Usage examples. The Algorithms section provides detailed information about the underlying mathematical foundations and implementation details.

Citation

If you use CCC-GPU in your research, please cite:

@article{zhang2025cccgpu,
  title={CCC-GPU: A graphics processing unit (GPU)-optimized nonlinear correlation coefficient for large transcriptomic analyses},
  author={Zhang, Hang and Fotso, Kenneth and Pividori, Milton},
  journal={bioRxiv},
  year={2025},
  publisher={Cold Spring Harbor Laboratory},
  doi={10.1101/2025.06.03.657735},
  pmid={40502087},
  pmcid={PMC12157546}
}

The original CCC implementation and methodology can be found at: https://github.com/greenelab/ccc