compute-minkowski-distance

Minkowski Distance
===
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> Computes the Minkowski distance between two arrays.

The Minkowski distance defines a distance between two points in a normed vector space.

Special cases:

* When p=1, the distance is known as the Manhattan distance.
* When p=2, the distance is known as the Euclidean distance.
* In the limit that p --> +infinity, the distance is known as the Chebyshev distance.

Installation

`` bash
$ npm install compute-minkowski-distance
`

For use in the browser, use browserify.

Usage

` javascript
var minkowski = require( 'compute-minkowski-distance' );
`

#### minkowski( x, y, [opts] )

Computes the Minkowski distance between two arrays.

` javascript
var x = [ 2, 4, 5, 3, 8, 2 ],
y = [ 3, 1, 5, -3, 7, 2 ];

var d = minkowski( x, y );
// returns ~6.86
`

The function accepts the following options:

* __p__: norm order (p > 0).
* __accessor__: accessor function for accessing array values.

By default, the norm order is 2 (Euclidean distance). To specify a different order, set the p option.

` javascript
var x = [ 2, 4, 5, 3, 8, 2 ],
y = [ 3, 1, 5, 3, 7, 2 ];

var d = minkowski( x, y, {
'p': 1
});
// returns 5
`

For object arrays, provide an accessor function for accessing numeric values.

` javascript
var x = [
{'x':2},
{'x':4},
{'x':5}
];

var y = [
[1,1],
[2,2],
[3,7]
];

function getValue( d, i, j ) {
if ( j === 0 ) {
return d.x;
}
return d[ 1 ];
}

var dist = minkowski( x, y, {
'accessor': getValue
});
// returns 3
`

The accessor function is provided three arguments:

- __d__: current datum.
- __i__: current datum index.
- __j__: array index; e.g., array x has index 0, and array y has index 1.

If provided empty arrays, the function returns null.

Notes

__Warning__: only specific p values allow for proper consideration of overflow and underflow; i.e., Euclidean, Manhattan, and Chebyshev distances. In the general case, you may overflow for large p values.

Examples

` javascript
var minkowski = require( 'compute-minkowski-distance' );

var x = new Array( 100 ),
y = new Array( 100 );

for ( var i = 0; i < x.length; i++ ) {
x[ i ] = Math.round( Math.random()*100 );
y[ i ] = Math.round( Math.random()*100 );
}

// Euclidean distance (default):
console.log( minkowski( x, y ) );

// Manhattan (city block) distance:
console.log( minkowski( x, y, {
'p': 1
}));

// Chebyshev distance:
console.log( minkowski( x, y, {
'p': Number.POSITIVE_INFINITY
}));

// Some other distance:
console.log( minkowski( x, y, {
'p': 3
}));
`

To run the example code from the top-level application directory,

` bash
$ node ./examples/index.js
`

Tests

$3

Unit tests use the Mocha test framework with Chai assertions. To run the tests, execute the following command in the top-level application directory:

` bash
$ make test
`

All new feature development should have corresponding unit tests to validate correct functionality.

$3

This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:

` bash
$ make test-cov
`

Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,

` bash
$ make view-cov
``

---

License

MIT license.

Copyright

Copyright © 2015. Philipp Burckhardt.

[npm-image]: http://img.shields.io/npm/v/compute-minkowski-distance.svg
[npm-url]: https://npmjs.org/package/compute-minkowski-distance

[travis-image]: http://img.shields.io/travis/compute-io/minkowski-distance/master.svg
[travis-url]: https://travis-ci.org/compute-io/minkowski-distance

[coveralls-image]: https://img.shields.io/coveralls/compute-io/minkowski-distance/master.svg
[coveralls-url]: https://coveralls.io/r/compute-io/minkowski-distance?branch=master

[dependencies-image]: http://img.shields.io/david/compute-io/minkowski-distance.svg
[dependencies-url]: https://david-dm.org/compute-io/minkowski-distance

[dev-dependencies-image]: http://img.shields.io/david/dev/compute-io/minkowski-distance.svg
[dev-dependencies-url]: https://david-dm.org/dev/compute-io/minkowski-distance

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[github-issues-url]: https://github.com/compute-io/minkowski-distance/issues