ml-distance
ml-distance
Maintained by Zakodium
Distance functions to compare vectors.
Installation
$ npm i ml-distance
This package is ESM-only. CommonJS consumers need Node.js >= 20.19, >= 22.12, or
any 24.x or later to require() it, or should migrate to import.
Usage
import { distance, similarity } from 'ml-distance';
const p = [0, 1, 2, 3, 4];
const q = [4, 3, 2, 1, 0];
distance.euclidean(p, q); // 6.324555320336759
distance.manhattan(p, q); // 12
similarity.cosine(p, q); // 0.3333333333333333
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
$d(p,q)=\frac{\sum\limits_{i=1}^{n}{\left|p_i-q_i\right|}}{\sum\limits_{i=1}^{n}{max(p_i,q_i)}}$
kulczynski(p, q)
Returns the Kulczynski distance between vectors p and q
$d(p,q)=\frac{\sum\limits_{i=1}^{n}{\left|p_i-q_i\right|}}{\sum\limits_{i=1}^{n}{min(p_i,q_i)}}$
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. The matching distance is soergel.
$s(p,q)=\frac{\sum\limits_{i=1}^{n}{min(p_i,q_i)}}{\sum\limits_{i=1}^{n}{max(p_i,q_i)}}$
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
$d(p,q)=2\sum\limits_{i=1}^{n}\frac{p_i\cdot{q_i}}{p_i+q_i}$
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
$d(p,q)=\frac{\sum\limits_{i=1}^{n}{(p_i-q_i)^2}}{\sum\limits_{i=1}^{n}{p_i^2}+\sum\limits_{i=1}^{n}{q_i^2}}$
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
cosine(p, q)
Returns the Cosine similarity between vectors p and q
$s(p,q)=\frac{\sum\limits_{i=1}^{n}{p_i\cdot{q_i}}}{\sqrt{\sum\limits_{i=1}^{n}{p_i^2}}\sqrt{\sum\limits_{i=1}^{n}{q_i^2}}}$
kumarHassebrook(p, q)
Returns the Kumar-Hassebrook similarity between vectors p and q
$s(p,q)=\frac{\sum\limits_{i=1}^{n}{p_i\cdot{q_i}}}{\sum\limits_{i=1}^{n}{p_i^2}+\sum\limits_{i=1}^{n}{q_i^2}-\sum\limits_{i=1}^{n}{p_i\cdot{q_i}}}$
pearson(p, q)
Returns the Pearson correlation between vectors p and q, i.e. the cosine similarity of the mean-centred vectors
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/distances (or src/similarities) directory. There should be a corresponding test file in the neighbouring __tests__ directory.
The metric should be then added in the exports of src/distances.ts (or src/similarities.ts) 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.