ml-distance

What is ml-distance?

The ml-distance npm package provides a collection of functions to calculate various types of distances between vectors. It is useful for tasks in machine learning, data analysis, and other fields where measuring similarity or dissimilarity between data points is important.

What are ml-distance's main functionalities?

Euclidean Distance

Calculates the Euclidean distance between two vectors. This is the straight-line distance in Euclidean space.

const distance = require('ml-distance');
const euclidean = distance.euclidean([1, 2], [4, 6]);
console.log(euclidean); // Output: 5

Manhattan Distance

Calculates the Manhattan distance between two vectors. This is the sum of the absolute differences of their Cartesian coordinates.

const distance = require('ml-distance');
const manhattan = distance.manhattan([1, 2], [4, 6]);
console.log(manhattan); // Output: 7

Cosine Similarity

Calculates the cosine similarity between two vectors. This measures the cosine of the angle between them, which is useful for determining how similar two vectors are.

const distance = require('ml-distance');
const cosine = distance.cosine([1, 2], [4, 6]);
console.log(cosine); // Output: 0.9838699100999074

Jaccard Index

Calculates the Jaccard index between two sets. This is the size of the intersection divided by the size of the union of the sets.

const distance = require('ml-distance');
const jaccard = distance.jaccard([1, 2, 3], [2, 3, 4]);
console.log(jaccard); // Output: 0.5

Other packages similar to ml-distance

compute-distance

The compute-distance package provides a variety of distance metrics similar to ml-distance, including Euclidean, Manhattan, and Chebyshev distances. It is a good alternative for users looking for a different implementation or additional distance metrics.

ml-matrix

The ml-matrix package offers a comprehensive set of matrix operations, including distance calculations. It is more feature-rich compared to ml-distance, providing additional functionalities for matrix manipulation and linear algebra.

distance

The distance package focuses on string distance metrics like Levenshtein, Jaro-Winkler, and Hamming distances. While it overlaps with ml-distance in some areas, it is more specialized in string comparison.

README

ml-distance

Distance functions to compare vectors.

Installation

$ npm i ml-distance

Methods

Distances

• euclidean(p, q)

Returns the euclidean distance between vectors p and q

$d(p,q)=\sqrt{\sum\limits_{i=1}^{n}(p_i-q_i)^2}$

• manhattan(p, q)

Returns the city block distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\left|p_i-q_i\right|}$

• minkowski(p, q, d)

Returns the Minkowski distance between vectors p and q for order d

• chebyshev(p, q)

Returns the Chebyshev distance between vectors p and q

$d(p,q)=\max\limits_i(|p_i-q_i|)$

• sorensen(p, q)

Returns the Sørensen distance between vectors p and q

$d(p,q)=\frac{\sum\limits_{i=1}^{n}{\left|p_i-q_i\right|}}{\sum\limits_{i=1}^{n}{p_i+q_i}}$

• gower(p, q)

Returns the Gower distance between vectors p and q

$d(p,q)=\frac{\sum\limits_{i=1}^{n}{\left|p_i-q_i\right|}}{n}$

• soergel(p, q)

Returns the Soergel distance between vectors p and q

$d(p,q)=\frac{\sum\limits_{i=1}^{n}{\left|p_i-q_i\right|}}{max(p_i,q_i)}$

• kulczynski(p, q)

Returns the Kulczynski distance between vectors p and q

$d(p,q)=\frac{\sum\limits_{i=1}^{n}{\left|p_i-q_i\right|}}{min(p_i,q_i)}$

• canberra(p, q)

Returns the Canberra distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}\frac{\left|{p_i-q_i}\right|}{p_i+q_i}$

• lorentzian(p, q)

Returns the Lorentzian distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}\ln(\left|{p_i-q_i}\right|+1)$

• intersection(p, q)

Returns the Intersection distance between vectors p and q

$d(p,q)=1-\sum\limits_{i=1}^{n}min(p_i,q_i)$

• waveHedges(p, q)

Returns the Wave Hedges distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}\left(1-\frac{min(p_i,q_i)}{max(p_i,q_i)}\right)$

• czekanowski(p, q)

Returns the Czekanowski distance between vectors p and q

$d(p,q)=1-\frac{2\sum\limits_{i=1}^{n}{min(p_i,q_i)}}{\sum\limits_{i=1}^{n}{p_i+q_i}}$

• motyka(p, q)

Returns the Motyka distance between vectors p and q

$d(p,q)=1-\frac{\sum\limits_{i=1}^{n}{min(p_i,q_i)}}{\sum\limits_{i=1}^{n}{p_i+q_i}}$

Note: distance between 2 identical vectors is 0.5 !

• ruzicka(p, q)

Returns the Ruzicka similarity between vectors p and q

$d(p,q)=\frac{\sum\limits_{i=1}^{n}{max(p_i,q_i)}}{\sum\limits_{i=1}^{n}{min(p_i,q_i)}}$

• tanimoto(p, q, [bitVector])

Returns the Tanimoto distance between vectors p and q, and accepts the bitVector use, see the test case for an example

• innerProduct(p, q)

Returns the Inner Product similarity between vectors p and q

$s(p,q)=\sum\limits_{i=1}^{n}{p_i\cdot{q_i}}$

• harmonicMean(p, q)

Returns the Harmonic mean similarity between vectors p and q

$d(p,q)=2\sum\limits_{i=1}^{n}\frac{p_i\cdot{q_i}}{p_i+q_i}$

• cosine(p, q)

Returns the Cosine similarity between vectors p and q

$d(p,q)=\frac{\sum\limits_{i=1}^{n}{p_i\cdot{q_i}}}{\sum\limits_{i=1}^{n}{p_i^2}\sum\limits_{i=1}^{n}{q_i^2}}$

• kumarHassebrook(p, q)

Returns the Kumar-Hassebrook similarity between vectors p and q

$d(p,q)=\frac{\sum\limits_{i=1}^{n}{p_i\cdot{q_i}}}{\sum\limits_{i=1}^{n}{p_i^2}+\sum\limits_{i=1}^{n}{q_i^2}-\sum\limits_{i=1}^{n}{p_i\cdot{q_i}}}$

• jaccard(p, q)

Returns the Jaccard distance between vectors p and q

$d(p,q)=1-\frac{\sum\limits_{i=1}^{n}{p_i\cdot{q_i}}}{\sum\limits_{i=1}^{n}{p_i^2}+\sum\limits_{i=1}^{n}{q_i^2}-\sum\limits_{i=1}^{n}{p_i\cdot{q_i}}}$

• dice(p,q)

Returns the Dice distance between vectors p and q

$d(p,q)=1-\frac{\sum\limits_{i=1}^{n}{(p_i-q_i)^2}}{\sum\limits_{i=1}^{n}{p_i^2}+\sum\limits_{i=1}^{n}{q_i^2}}$

• fidelity(p, q)

Returns the Fidelity similarity between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\sqrt{p_i\cdot{q_i}}}$

• bhattacharyya(p, q)

Returns the Bhattacharyya distance between vectors p and q

$d(p,q)=-\ln\left(\sum\limits_{i=1}^{n}{\sqrt{p_i\cdot{q_i}}}\right)$

• hellinger(p, q)

Returns the Hellinger distance between vectors p and q

$d(p,q)=2\cdot\sqrt{1-\sum\limits_{i=1}^{n}{\sqrt{p_i\cdot{q_i}}}}$

• matusita(p, q)

Returns the Matusita distance between vectors p and q

$d(p,q)=\sqrt{2-2\cdot\sum\limits_{i=1}^{n}{\sqrt{p_i\cdot{q_i}}}}$

• squaredChord(p, q)

Returns the Squared-chord distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{(\sqrt{p_i}-\sqrt{q_i})^2}$

• squaredEuclidean(p, q)

Returns the squared euclidean distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{(p_i-q_i)^2}$

• pearson(p, q)

Returns the Pearson distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\frac{(p_i-q_i)^2}{q_i}}$

• neyman(p, q)

Returns the Neyman distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\frac{(p_i-q_i)^2}{p_i}}$

• squared(p, q)

Returns the Squared distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\frac{(p_i-q_i)^2}{p_i+q_i}}$

• probabilisticSymmetric(p, q)

Returns the Probabilistic Symmetric distance between vectors p and q

$d(p,q)=2\cdot\sum\limits_{i=1}^{n}{\frac{(p_i-q_i)^2}{p_i+q_i}}$

• divergence(p, q)

Returns the Divergence distance between vectors p and q

$d(p,q)=2\cdot\sum\limits_{i=1}^{n}{\frac{(p_i-q_i)^2}{(p_i+q_i)^2}}$

• clark(p, q)

Returns the Clark distance between vectors p and q

$d(p,q)=\sqrt{\sum\limits_{i=1}^{n}{\left(\frac{\left|p_i-q_i\right|}{(p_i+q_i)}\right)^2}}$

• additiveSymmetric(p, q)

Returns the Additive Symmetric distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\frac{(p_i-q_i)^2\cdot(p_i+q_i)}{p_i\cdot{q_i}}}$

• kullbackLeibler(p, q)

Returns the Kullback-Leibler distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{p_i\cdot\ln\frac{p_i}{q_i}}$

• jeffreys(p, q)

Returns the Jeffreys distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\left((p_i-q_i)\ln\frac{p_i}{q_i}\right)}$

• kdivergence(p, q)

Returns the K divergence distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\left(p_i\cdot\ln\frac{2p_i}{p_i+q_i}\right)}$

• topsoe(p, q)

Returns the Topsøe distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\left(p_i\cdot\ln\frac{2p_i}{p_i+q_i}+q_i\cdot\ln\frac{2q_i}{p_i+q_i}\right)}$

• jensenShannon(p, q)

Returns the Jensen-Shannon distance between vectors p and q

$d(p,q)=\frac{1}{2}\left[\sum\limits_{i=1}^{n}{p_i\cdot\ln\frac{2p_i}{p_i+q_i}}+\sum\limits_{i=1}^{n}{q_i\cdot\ln\frac{2q_i}{p_i+q_i}}\right]$

• jensenDifference(p, q)

Returns the Jensen difference distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\left[\frac{p_i\ln{p_i}+q_i\ln{q_i}}{2}-\left(\frac{p_i+q_i}{2}\right)\ln\left(\frac{p_i+q_i}{2}\right)\right]}$

• taneja(p, q)

Returns the Taneja distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\left[\frac{p_i+q_i}{2}\ln\left(\frac{p_i+q_i}{2\sqrt{p_i\cdot{q_i}}}\right)\right]}$

• kumarJohnson(p, q)

Returns the Kumar-Johnson distance between vectors p and q

$d(p,q)=\sum\limits_{i=1}^{n}{\frac{\left(p_i^2-q_i^2\right)^2}{2(p_i\cdot{q_i})^{3/2}}}$

• avg(p, q)

Returns the average of city block and Chebyshev distances between vectors p and q

$d(p,q)=\frac{\sum\limits_{i=1}^{n}{\left|p_i-q_i\right|}+\max\limits_i(|p_i-q_i|)}{2}$

Similarities

• intersection(p, q)

Returns the Intersection similarity between vectors p and q

• czekanowski(p, q)

Returns the Czekanowski similarity between vectors p and q

• motyka(p, q)

Returns the Motyka similarity between vectors p and q

• kulczynski(p, q)

Returns the Kulczynski similarity between vectors p and q

• squaredChord(p, q)

Returns the Squared-chord similarity between vectors p and q

• jaccard(p, q)

Returns the Jaccard similarity between vectors p and q

• dice(p, q)

Returns the Dice similarity between vectors p and q

• tanimoto(p, q, [bitVector])

Returns the Tanimoto similarity between vectors p and q, and accepts the bitVector use, see the test case for an example

• tree(a,b, from, to, [options])

Refer to ml-tree-similarity

Contributing

A new metric should normally be in its own file in the src/dist directory. There should be a corresponding test file in test/dist.
The metric should be then added in the exports of src/index.js with a relatively small but understandable name (use camelCase).
It should also be added to this README with either a link to the formula or an inline description.

Authors

• Michaël Zasso
• Miguel Angel Asencio Hurtado

License

MIT

Changelog

4.0.1 (2023-06-01)

Bug Fixes

• correct exported types in similarities (#15) (ad95f92)