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ml-distance\n\n[![NPM version][npm-image]][npm-url]\n[![build status][travis-image]][travis-url]\n[![npm download][download-image]][download-url]\n\nDistance functions to compare vectors.\n\n## Installation\n\n`$ npm i ml-distance`\n\n## Methods\n\n### Distances\n\n- `euclidean(p, q)`\n\nReturns the [euclidean distance](http://en.wikipedia.org/wiki/Euclidean_distance#n_dimensions) between vectors p and q\n\n$d(p,q)=\\sqrt{\\sum\\limits_{i=1}^{n}(p_i-q_i)^2}$\n\n- `manhattan(p, q)`\n\nReturns the [city block distance](http://en.wikipedia.org/wiki/Taxicab_geometry) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\left|p_i-q_i\\right|}$\n\n- `minkowski(p, q, d)`\n\nReturns the [Minkowski distance](http://en.wikipedia.org/wiki/Minkowski_distance) between vectors p and q for order d\n\n- `chebyshev(p, q)`\n\nReturns the [Chebyshev distance](http://en.wikipedia.org/wiki/Chebyshev_distance) between vectors p and q\n\n$d(p,q)=\\max\\limits_i(|p_i-q_i|)$\n\n- `sorensen(p, q)`\n\nReturns the [Sørensen distance](http://en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient) between vectors p and q\n\n$d(p,q)=\\frac{\\sum\\limits_{i=1}^{n}{\\left|p_i-q_i\\right|}}{\\sum\\limits_{i=1}^{n}{p_i+q_i}}$\n\n- `gower(p, q)`\n\nReturns the [Gower distance](https://stat.ethz.ch/education/semesters/ss2012/ams/slides/v4.2.pdf) between vectors p and q\n\n$d(p,q)=\\frac{\\sum\\limits_{i=1}^{n}{\\left|p_i-q_i\\right|}}{n}$\n\n- `soergel(p, q)`\n\nReturns the [Soergel distance](http://www.orgchm.bas.bg/~vmonev/SimSearch.pdf) between vectors p and q\n\n$d(p,q)=\\frac{\\sum\\limits_{i=1}^{n}{\\left|p_i-q_i\\right|}}{max(p_i,q_i)}$\n\n- `kulczynski(p, q)`\n\nReturns the [Kulczynski distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\frac{\\sum\\limits_{i=1}^{n}{\\left|p_i-q_i\\right|}}{min(p_i,q_i)}$\n\n- `canberra(p, q)`\n\nReturns the [Canberra distance](http://en.wikipedia.org/wiki/Canberra_distance) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}\\frac{\\left|{p_i-q_i}\\right|}{p_i+q_i}$\n\n- `lorentzian(p, q)`\n\nReturns the [Lorentzian distance](https://stat.ethz.ch/education/semesters/ss2012/ams/slides/v4.2.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}\\ln(\\left|{p_i-q_i}\\right|+1)$\n\n- `intersection(p, q)`\n\nReturns the [Intersection distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=1-\\sum\\limits_{i=1}^{n}min(p_i,q_i)$\n\n- `waveHedges(p, q)`\n\nReturns the [Wave Hedges distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}\\left(1-\\frac{min(p_i,q_i)}{max(p_i,q_i)}\\right)$\n\n- `czekanowski(p, q)`\n\nReturns the [Czekanowski distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=1-\\frac{2\\sum\\limits_{i=1}^{n}{min(p_i,q_i)}}{\\sum\\limits_{i=1}^{n}{p_i+q_i}}$\n\n- `motyka(p, q)`\n\nReturns the [Motyka distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=1-\\frac{\\sum\\limits_{i=1}^{n}{min(p_i,q_i)}}{\\sum\\limits_{i=1}^{n}{p_i+q_i}}$\n\nNote: distance between 2 identical vectors is 0.5 !\n\n- `ruzicka(p, q)`\n\nReturns the [Ruzicka similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\frac{\\sum\\limits_{i=1}^{n}{max(p_i,q_i)}}{\\sum\\limits_{i=1}^{n}{min(p_i,q_i)}}$\n\n- `tanimoto(p, q, [bitVector])`\n\nReturns the [Tanimoto distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q, and accepts the bitVector use, see the test case for an example\n\n- `innerProduct(p, q)`\n\nReturns the [Inner Product similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$s(p,q)=\\sum\\limits_{i=1}^{n}{p_i\\cdot{q_i}}$\n\n- `harmonicMean(p, q)`\n\nReturns the [Harmonic mean similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=2\\sum\\limits_{i=1}^{n}\\frac{p_i\\cdot{q_i}}{p_i+q_i}$\n\n- `cosine(p, q)`\n\nReturns the [Cosine similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\frac{\\sum\\limits_{i=1}^{n}{p_i\\cdot{q_i}}}{\\sum\\limits_{i=1}^{n}{p_i^2}\\sum\\limits_{i=1}^{n}{q_i^2}}$\n\n- `kumarHassebrook(p, q)`\n\nReturns the [Kumar-Hassebrook similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\frac{\\sum\\limits_{i=1}^{n}{p_i\\cdot{q_i}}}{\\sum\\limits_{i=1}^{n}{p_i^2}+\\sum\\limits_{i=1}^{n}{q_i^2}-\\sum\\limits_{i=1}^{n}{p_i\\cdot{q_i}}}$\n\n- `jaccard(p, q)`\n\nReturns the [Jaccard distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=1-\\frac{\\sum\\limits_{i=1}^{n}{p_i\\cdot{q_i}}}{\\sum\\limits_{i=1}^{n}{p_i^2}+\\sum\\limits_{i=1}^{n}{q_i^2}-\\sum\\limits_{i=1}^{n}{p_i\\cdot{q_i}}}$\n\n- `dice(p,q)`\n\nReturns the [Dice distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=1-\\frac{\\sum\\limits_{i=1}^{n}{(p_i-q_i)^2}}{\\sum\\limits_{i=1}^{n}{p_i^2}+\\sum\\limits_{i=1}^{n}{q_i^2}}$\n\n- `fidelity(p, q)`\n\nReturns the [Fidelity similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\sqrt{p_i\\cdot{q_i}}}$\n\n- `bhattacharyya(p, q)`\n\nReturns the [Bhattacharyya distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=-\\ln\\left(\\sum\\limits_{i=1}^{n}{\\sqrt{p_i\\cdot{q_i}}}\\right)$\n\n- `hellinger(p, q)`\n\nReturns the [Hellinger distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=2\\cdot\\sqrt{1-\\sum\\limits_{i=1}^{n}{\\sqrt{p_i\\cdot{q_i}}}}$\n\n- `matusita(p, q)`\n\nReturns the [Matusita distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sqrt{2-2\\cdot\\sum\\limits_{i=1}^{n}{\\sqrt{p_i\\cdot{q_i}}}}$\n\n- `squaredChord(p, q)`\n\nReturns the [Squared-chord distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{(\\sqrt{p_i}-\\sqrt{q_i})^2}$\n\n- `squaredEuclidean(p, q)`\n\nReturns the [squared euclidean distance](http://en.wikipedia.org/wiki/Euclidean_distance#Squared_Euclidean_distance) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{(p_i-q_i)^2}$\n\n- `pearson(p, q)`\n\nReturns the [Pearson distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\frac{(p_i-q_i)^2}{q_i}}$\n\n- `neyman(p, q)`\n\nReturns the [Neyman distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\frac{(p_i-q_i)^2}{p_i}}$\n\n- `squared(p, q)`\n\nReturns the [Squared distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\frac{(p_i-q_i)^2}{p_i+q_i}}$\n\n- `probabilisticSymmetric(p, q)`\n\nReturns the [Probabilistic Symmetric distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=2\\cdot\\sum\\limits_{i=1}^{n}{\\frac{(p_i-q_i)^2}{p_i+q_i}}$\n\n- `divergence(p, q)`\n\nReturns the [Divergence distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=2\\cdot\\sum\\limits_{i=1}^{n}{\\frac{(p_i-q_i)^2}{(p_i+q_i)^2}}$\n\n- `clark(p, q)`\n\nReturns the [Clark distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sqrt{\\sum\\limits_{i=1}^{n}{\\left(\\frac{\\left|p_i-q_i\\right|}{(p_i+q_i)}\\right)^2}}$\n\n- `additiveSymmetric(p, q)`\n\nReturns the [Additive Symmetric distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\frac{(p_i-q_i)^2\\cdot(p_i+q_i)}{p_i\\cdot{q_i}}}$\n\n- `kullbackLeibler(p, q)`\n\nReturns the [Kullback-Leibler distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{p_i\\cdot\\ln\\frac{p_i}{q_i}}$\n\n- `jeffreys(p, q)`\n\nReturns the [Jeffreys distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\left((p_i-q_i)\\ln\\frac{p_i}{q_i}\\right)}$\n\n- `kdivergence(p, q)`\n\nReturns the [K divergence distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\left(p_i\\cdot\\ln\\frac{2p_i}{p_i+q_i}\\right)}$\n\n- `topsoe(p, q)`\n\nReturns the [Topsøe distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\left(p_i\\cdot\\ln\\frac{2p_i}{p_i+q_i}+q_i\\cdot\\ln\\frac{2q_i}{p_i+q_i}\\right)}$\n\n- `jensenShannon(p, q)`\n\nReturns the [Jensen-Shannon distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\frac{1}{2}\\left[\\sum\\limits_{i=1}^{n}{p_i\\cdot\\ln\\frac{2p_i}{p_i+q_i}}+\\sum\\limits_{i=1}^{n}{q_i\\cdot\\ln\\frac{2q_i}{p_i+q_i}}\\right]$\n\n- `jensenDifference(p, q)`\n\nReturns the [Jensen difference distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\left[\\frac{p_i\\ln{p_i}+q_i\\ln{q_i}}{2}-\\left(\\frac{p_i+q_i}{2}\\right)\\ln\\left(\\frac{p_i+q_i}{2}\\right)\\right]}$\n\n- `taneja(p, q)`\n\nReturns the [Taneja distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\left[\\frac{p_i+q_i}{2}\\ln\\left(\\frac{p_i+q_i}{2\\sqrt{p_i\\cdot{q_i}}}\\right)\\right]}$\n\n- `kumarJohnson(p, q)`\n\nReturns the [Kumar-Johnson distance](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n$d(p,q)=\\sum\\limits_{i=1}^{n}{\\frac{\\left(p_i^2-q_i^2\\right)^2}{2(p_i\\cdot{q_i})^{3/2}}}$\n\n- `avg(p, q)`\n\nReturns the average of city block and Chebyshev distances between vectors p and q\n\n$d(p,q)=\\frac{\\sum\\limits_{i=1}^{n}{\\left|p_i-q_i\\right|}+\\max\\limits_i(|p_i-q_i|)}{2}$\n\n### Similarities\n\n- `intersection(p, q)`\n\nReturns the [Intersection similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n- `czekanowski(p, q)`\n\nReturns the [Czekanowski similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n- `motyka(p, q)`\n\nReturns the [Motyka similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n- `kulczynski(p, q)`\n\nReturns the [Kulczynski similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n- `squaredChord(p, q)`\n\nReturns the [Squared-chord similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n- `jaccard(p, q)`\n\nReturns the [Jaccard similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n- `dice(p, q)`\n\nReturns the [Dice similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q\n\n- `tanimoto(p, q, [bitVector])`\n\nReturns the [Tanimoto similarity](http://www.naun.org/main/NAUN/ijmmas/mmmas-49.pdf) between vectors p and q, and accepts the bitVector use, see the test case for an example\n\n- `tree(a,b, from, to, [options])`\n\nRefer to [ml-tree-similarity](https://github.com/mljs/tree-similarity)\n\n## Contributing\n\nA new metric should normally be in its own file in the src/dist directory. There should be a corresponding test file in test/dist.  \nThe metric should be then added in the exports of src/index.js with a relatively small but understandable name (use camelCase).  \nIt should also be added to this README with either a link to the formula or an inline description.\n\n## Authors\n\n- [Michaël Zasso](https://github.com/targos)\n- [Miguel Angel Asencio Hurtado](https://github.com/maasencioh)\n\n## License\n\n[MIT](./LICENSE)\n\n[npm-image]: https://img.shields.io/npm/v/ml-distance.svg?style=flat-square\n[npm-url]: https://npmjs.org/package/ml-distance\n[travis-image]: https://img.shields.io/travis/mljs/distance/master.svg?style=flat-square\n[travis-url]: https://travis-ci.org/mljs/distance\n[download-image]: https://img.shields.io/npm/dm/ml-distance.svg?style=flat-square\n[download-url]: https://npmjs.org/package/ml-distance\n","maintainers":[{"name":"stropitek","email":"kostro.d@gmail.com"},{"name":"targos","email":"targos+npm@protonmail.com"},{"name":"lpatiny","email":"luc@patiny.com"},{"name":"mljs-bot","email":"bot+npm-mljs@zakodium.com"},{"name":"cheminfo-bot","email":"bot+npm-cheminfo@zakodium.com"},{"name":"maasencioh","email":"maasencioh@gmail.com"},{"name":"jeffersonh44","email":"jeffersonh44@gmail.com"},{"name":"andcastillo","email":"andcastillo@gmail.com"}],"time":{"modified":"2023-06-01T09:56:54.123Z","created":"2014-11-18T06:40:55.442Z","1.0.0":"2014-11-18T06:40:55.442Z","1.0.1":"2015-06-23T08:33:45.820Z","1.0.2":"2015-06-23T11:52:34.300Z","1.1.0":"2015-07-15T09:33:35.687Z","2.0.0":"2015-07-15T09:38:15.399Z","2.0.1":"2015-07-15T12:16:29.562Z","2.1.0":"2015-08-20T12:07:49.441Z","2.1.1":"2016-08-03T06:36:51.567Z","3.0.0":"2019-06-29T22:27:23.047Z","4.0.0":"2023-01-06T17:08:59.212Z","4.0.1":"2023-06-01T09:56:54.011Z"},"homepage":"https://github.com/mljs/distance","keywords":["distance","similarity","metric","vector","data","mining","datamining","machine","learning"],"repository":{"type":"git","url":"git+https://github.com/mljs/distance.git"},"bugs":{"url":"https://github.com/mljs/distance/issues"},"license":"MIT","readmeFilename":"README.md","contributors":[{"name":"Miguel Asencio"}],"author":{"name":"Michaël Zasso"},"users":{"dhrubins":true,"maasencioh":true,"eterna2":true}}