fast-distances

Rust Similarity and Distance Metrics Library

This Rust package provides a wide range of functions for computing various distance and similarity metrics between vectors or points in a high-dimensional space. These metrics are widely used in fields such as machine learning, statistics, data science, and computational biology.

Modules

Each module in this package implements a specific distance or similarity measure, some with gradient computations for optimization tasks. Below is a list of available modules:

• approx_log_gamma: Approximation of the logarithm of the Gamma function.

• bray_curtis: Bray-Curtis dissimilarity, a measure for ecological distance.

• bray_curtis_grad: Gradient of the Bray-Curtis dissimilarity.

• canberra: Canberra distance, a city block-like metric with a normalization.

• canberra_grad: Gradient of the Canberra distance.

• chebyshev: Chebyshev distance (L∞ distance), the maximum distance along any coordinate axis.

• chebyshev_grad: Gradient of the Chebyshev distance.

• correlation: Pearson correlation coefficient, a measure of linear correlation between two vectors.

• cosine: Cosine similarity, measuring the cosine of the angle between two vectors.

• cosine_grad: Gradient of the cosine similarity.

• dice: Dice coefficient, a similarity measure often used in bioinformatics.

• euclidean: Euclidean distance, the straight-line distance between two points.

• euclidean_grad: Gradient of the Euclidean distance.

• hamming: Hamming distance, the number of differing positions between two strings of equal length.

• haversine: Haversine distance, used to calculate the great-circle distance between two points on a sphere.

• haversine_grad: Gradient of the Haversine distance.

• hellinger: Hellinger distance, a measure for comparing probability distributions.

• hellinger_grad: Gradient of the Hellinger distance.

• hyperboloid_grad: Gradient of the hyperboloid distance, a metric on hyperbolic spaces.

• jaccard: Jaccard similarity coefficient, a measure of the intersection between two sets divided by their union.

• kulsinski: Kulsinski similarity coefficient, a distance measure for binary vectors.

• ll_dirichlet: Log-Likelihood of the Dirichlet distribution, used for probabilistic comparison of Dirichlet-distributed data.

• log_beta: Log of the Beta distribution, used in statistical modeling.

• log_single_beta: Logarithmic computation of a single Beta distribution.

• mahalanobis: Mahalanobis distance, a distance metric that accounts for correlations between variables.

• mahalanobis_grad: Gradient of the Mahalanobis distance.

• manhattan: Manhattan distance (L1 distance), the sum of the absolute differences between coordinates.

• manhattan_grad: Gradient of the Manhattan distance.

• matching: Matching distance, a similarity measure based on matching elements in two sets.

• minkowski: Minkowski distance, a generalization of both Euclidean and Manhattan distances.

• minkowski_grad: Gradient of the Minkowski distance.

• poincare: Poincaré distance, used for hyperbolic spaces and geometries.

• rogers_tanimoto: Rogers-Tanimoto similarity, a distance measure for binary data.

• russellrao: Russell-Rao similarity, a measure for binary vectors.

• sokal_michener: Sokal-Michener similarity, a metric for categorical data.

• sokal_sneath: Sokal-Sneath similarity, another metric for categorical data.

• standardised_euclidean: Standardized Euclidean distance, which normalizes the Euclidean distance by the variance.

• standardised_euclidean_grad: Gradient of the standardized Euclidean distance.

• weighted_minkowski: Weighted Minkowski distance, a variant of Minkowski with weightings for each dimension.

• weighted_minkowski_grad: Gradient of the weighted Minkowski distance.

• yule: Yule's coefficient, used to measure association between two binary vectors.

Installation

Add this package to your Cargo.toml to use it in your project:

[dependencies] fast-distances = "0.1" Usage

To use one of the available distance or similarity metrics, import the respective module in your Rust code:

use distances::{cosine, euclidean, manhattan};

fn main() {
    let vector1 = vec![1.0, 2.0, 3.0];
    let vector2 = vec![4.0, 5.0, 6.0];

    // Compute cosine similarity
    let cosine_sim = cosine(&vector1, &vector2);
    println!("Cosine Similarity: {}", cosine_sim);

    // Compute Euclidean distance
    let euclidean_dist = euclidean(&vector1, &vector2);
    println!("Euclidean Distance: {}", euclidean_dist);

    // Compute Manhattan distance
    let manhattan_dist = manhattan(&vector1, &vector2);
    println!("Manhattan Distance: {}", manhattan_dist);
}

Contributing

Contributions are welcome! If you'd like to contribute a new metric or improve an existing one, feel free to open an issue or a pull request.

1. Fork the repository.
2. Clone your fork locally.
3. Make changes and run tests to ensure they pass.
4. Submit a pull request with a clear description of your changes.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgements

This package draws from many well-established distance and similarity metrics commonly used in data analysis, machine learning, and information retrieval.