pacmap

A Rust implementation of PaCMAP (Pairwise Controlled Manifold Approximation) for dimensionality reduction based on the original Python implementation.

Overview

Dimensionality reduction transforms high-dimensional data into a lower-dimensional representation while preserving important relationships between points. This is useful for visualization, analysis, and as preprocessing for other algorithms.

PaCMAP is a relatively recent dimensionality reduction technique that preserves both local and global structure through three types of point relationships:

• Nearest neighbor pairs preserve local structure
• Mid-near pairs preserve intermediate structure
• Far pairs prevent collapse and maintain separation

For details on the algorithm, see the original paper.

Features

• Fast approximate nearest neighbors for large datasets using USearch
• SIMD-optimized distance calculations
• Parallel processing with Rayon
• Optional PCA initialization using various BLAS backends
• Reproducible results with optional seeding

Usage

Basic usage with default parameters:

use anyhow::Result;
use ndarray::Array2;
use ndarray_rand::RandomExt;
use ndarray_rand::rand_distr::Uniform;
use pacmap::{Configuration, fit_transform};

fn main() -> Result<()> {
    // Your high-dimensional data as an n × d array
    let n_samples = 1000;
    let n_features = 1000;
    let mut data = Array2::random((n_samples, n_features), Uniform::new(-1.0, 1.0));

    let config = Configuration::default();
    let (embedding, _) = fit_transform(data.view(), config)?;

    // embedding is now an n × 2 array
    Ok(())
}

Customized embedding:

use anyhow::Result;
use pacmap::{Configuration, Initialization};

fn main() -> Result<()> {
    let config = Configuration::builder()
        .embedding_dimensions(3)
        .initialization(Initialization::Random(Some(42)))
        .learning_rate(0.8)
        .num_iters((50, 50, 100))
        .mid_near_ratio(0.3)
        .far_pair_ratio(2.0)
        .approx_threshold(8_000)  // Use approximate neighbors above this size
        .build();

    let (embedding, _) = fit_transform(data.view(), config)?;
    Ok(())
}

Capturing intermediate states:

use anyhow::Result;
use pacmap::Configuration;

fn main() -> Result<()> {
    let config = Configuration::builder()
        .snapshots(vec![100, 200, 300])
        .build();

    let (embedding, Some(states)) = fit_transform(data.view(), config)?;

    // states is now an s × n × d array where s is the number of snapshots
    Ok(())
}

For a standalone example, see the pacmap-rs-example repository.

Configuration

Core Parameters

• embedding_dimensions: Output dimensionality (default: 2)
• initialization: How to initialize coordinates:
  • Pca - Project data using PCA (default)
  • Value(array) - Use provided coordinates
  • Random(seed) - Random initialization with optional seed
• learning_rate: Learning rate for Adam optimizer (default: 1.0)
• num_iters: Iteration counts for three optimization phases (default: (100, 100, 250)):
  1. Mid-near weight reduction phase
  2. Balanced weight phase
  3. Local structure focus phase
• snapshots: Optional vector of iterations at which to save embedding states
• approx_threshold: Number of samples above which to use approximate nearest neighbors (default: 8,000)

Pair Sampling Parameters

• mid_near_ratio: Ratio of mid-near to nearest neighbor pairs (default: 0.5)
• far_pair_ratio: Ratio of far to nearest neighbor pairs (default: 2.0)
• override_neighbors: Optional fixed neighbor count override (default: None, auto-scaled with dataset size)
• seed: Optional random seed for reproducible sampling and initialization

Pair Configuration

• PairConfiguration::Generate - Generate all pairs from scratch (default)
• PairConfiguration::NeighborsProvided { pair_neighbors } - Use provided nearest neighbors, generate remaining pairs
• PairConfiguration::AllProvided { pair_neighbors, pair_mn, pair_fp } - Use all provided pairs

Feature Flags

BLAS/LAPACK Backends

Only one BLAS/LAPACK backend feature should be enabled at a time. These are required for PCA operations except on macOS which uses Accelerate by default.

• intel-mkl-static - Static linking with Intel MKL
• intel-mkl-system - Dynamic linking with system Intel MKL
• openblas-static - Static linking with OpenBLAS
• openblas-system - Dynamic linking with system OpenBLAS
• netlib-static - Static linking with Netlib
• netlib-system - Dynamic linking with system Netlib

For example:

[dependencies]
pacmap = { version = "0.2", features = ["openblas-static"] }

See ndarray-linalg's documentation for detailed information about BLAS/LAPACK configuration and performance considerations.

Performance Features

• simsimd - Enable SIMD optimizations in USearch for faster approximate nearest neighbor search. Requires GCC 13+ for compilation and a recent glibc at runtime.

Limitations

This implementation currently:

• Only supports Euclidean distances
• Does not support incremental transform

References

Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMap, and PaCMAP for Data Visualization. Wang, Y., Huang, H., Rudin, C., & Shaposhnik, Y. (2021). Journal of Machine Learning Research, 22(201), 1-73.

License

Apache License, Version 2.0